chapter 2 heading sensors

chapter 2 heading sensors
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
PART I SENSORS FOR MOBILE ROBOT POSITIONING
Chapter 1 Sensors for Dead Reckoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1 Optical Encoders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1.1 Incremental Optical Encoders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1.2 Absolute Optical Encoders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Doppler Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2.1 Micro-Trak Trak-Star Ultrasonic Speed Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2.2 Other Doppler-Effect Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3 Typical Mobility Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3.1 Differential Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3.2 Tricycle Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.3 Ackerman Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3.4 Synchro Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.5 Omnidirectional Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3.6 Multi-Degree-of-Freedom Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.3.7 MDOF Vehicle with Compliant Linkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3.8 Tracked Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Chapter 2 Heading Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1 Mechanical Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.1 Space-Stable Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.2 Gyrocompasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.1.3 Commercially Available Mechanical Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.1.3.1 Futaba Model Helicopter Gyro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.3.2 Gyration, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Piezoelectric Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Optical Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.1 Active Ring Laser Gyros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.2 Passive Ring Resonator Gyros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.3 Open-Loop Interferometric Fiber Optic Gyros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.4 Closed-Loop Interferometric Fiber Optic Gyros . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.5 Resonant Fiber Optic Gyros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.6 Commercially Available Optical Gyroscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.6.1 The Andrew “Autogyro" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.6.2 Hitachi Cable Ltd. OFG-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 Geomagnetic Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4.1 Mechanical Magnetic Compasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4.2 Fluxgate Compasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2.1 Zemco Fluxgate Compasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5
2.4.2.2 Watson Gyrocompass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.4.2.3 KVH Fluxgate Compasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.4.3 Hall-Effect Compasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4.4 Magnetoresistive Compasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.4.1 Philips AMR Compass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.5 Magnetoelastic Compasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Chapter 3 Ground-Based RF-Beacons and GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1 Ground-Based RF Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.1 Loran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.2 Kaman Sciences Radio Frequency Navigation Grid . . . . . . . . . . . . . . . . . . . . . . . 66
3.1.3 Precision Location Tracking and Telemetry System . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.1.4 Motorola Mini-Ranger Falcon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1.5 Harris Infogeometric System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Overview of Global Positioning Systems (GPSs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 Evaluation of Five GPS Receivers by Byrne [1993] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.1 Project Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.2 Test Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.2.1 Parameters tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.2.2 Test hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.3.2.3 Data post processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.3 Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.3.3.1 Static test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.3.3.2 Dynamic test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.3.3 Summary of test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.4 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.4.1 Summary of problems encountered with the tested GPS receivers . . . . . . . . . . 92
3.3.4.2 Summary of critical integration issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 4 Sensors for Map-Based Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.1 Time-of-Flight Range Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.1.1 Ultrasonic TOF Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1.1.1 Massa Products Ultrasonic Ranging Module Subsystems . . . . . . . . . . . . . . . . . 97
4.1.1.2 Polaroid Ultrasonic Ranging Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.1.2 Laser-Based TOF Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.1.2.1 Schwartz Electro-Optics Laser Rangefinders . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.1.2.2 RIEGL Laser Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.2.3 RVSI Long Optical Ranging and Detection System . . . . . . . . . . . . . . . . . . . . 109
4.2 Phase-Shift Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.2.1 Odetics Scanning Laser Imaging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.2.2 ESP Optical Ranging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.2.3 Acuity Research AccuRange 3000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2.4 TRC Light Direction and Ranging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2.5 Swiss Federal Institute of Technology's “3-D Imaging Scanner” . . . . . . . . . . . . . . 120
4.2.6 Improving Lidar Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3 Frequency Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
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4.3.1 Eaton VORAD Vehicle Detection and Driver Alert System . . . . . . . . . . . . . . . . . 125
4.3.2 Safety First Systems Vehicular Obstacle Detection and Warning System . . . . . . . 127
PART II SYSTEMS AND METHODS FOR MOBILE ROBOT POSITIONING
Chapter 5 Odometry and Other Dead-Reckoning Methods . . . . . . . . . . . . . . . . . . . . . . . 130
5.1 Systematic and Non-Systematic Odometry Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.2 Measurement of Odometry Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.2.1 Measurement of Systematic Odometry Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.2.1.1 The Unidirectional Square-Path Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.2.1.2 The Bidirectional Square-Path Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.2.2 Measurement of Non-Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.3 Reduction of Odometry Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.3.1 Reduction of Systematic Odometry Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.3.1.1 Auxiliary Wheels and Basic Encoder Trailer . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.3.1.2 The Basic Encoder Trailer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.3.1.3 Systematic Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.3.2 Reducing Non-Systematic Odometry Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.3.2.1 Mutual Referencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.3.2.2 Internal Position Error Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.4 Inertial Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.4.1 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.4.2 Gyros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.4.2.1 Barshan and Durrant-Whyte [1993; 1994; 1995] . . . . . . . . . . . . . . . . . . . . . . 147
5.4.2.2 Komoriya and Oyama [1994] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Chapter 6 Active Beacon Navigation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.1 Discussion on Triangulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.1.1 Three-Point Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.1.2 Triangulation with More Than Three Landmarks . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.2 Ultrasonic Transponder Trilateration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.2.1 IS Robotics 2-D Location System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.2.2 Tulane University 3-D Location System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.3 Optical Positioning Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.3.1 Cybermotion Docking Beacon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.3.2 Hilare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.3.3 NAMCO LASERNET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.3.3.1 U.S. Bureau of Mines' application of the LaserNet sensor . . . . . . . . . . . . . . . 161
6.3.4 Denning Branch International Robotics LaserNav Position Sensor . . . . . . . . . . . 163
6.3.5 TRC Beacon Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.3.6 Siman Sensors and Intelligent Machines Ltd., ROBOSENSE . . . . . . . . . . . . . . . . . 164
6.3.7 Imperial College Beacon Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.3.8 MTI Research CONACTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.3.9 Spatial Positioning Systems, inc.: Odyssey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
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6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Chapter 7 Landmark Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.1 Natural Landmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.2 Artificial Landmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.2.1 Global Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.3 Artificial Landmark Navigation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.3.1 MDARS Lateral-Post Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
7.3.2 Caterpillar Self Guided Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.3.3 Komatsu Ltd, Z-shaped landmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
7.4 Line Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.4.1 Thermal Navigational Marker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.4.2 Volatile Chemicals Navigational Marker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Chapter 8 Map-based Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
8.1 Map Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.1.1 Map-Building and Sensor Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8.1.2 Phenomenological vs. Geometric Representation, Engelson & McDermott [1992] 186
8.2 Map Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.2.1 Schiele and Crowley [1994] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8.2.2 Hinkel and Knieriemen [1988] — The Angle Histogram . . . . . . . . . . . . . . . . . . . . 189
8.2.3 Weiß, Wetzler, and Puttkamer — More on the Angle Histogram . . . . . . . . . . . . . 191
8.2.4 Siemens' Roamer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.2.5 Bauer and Rencken: Path Planning for Feature-based Navigation . . . . . . . . . . . . . 194
8.3 Geometric and Topological Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.3.1 Geometric Maps for Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.3.1.1 Cox [1991] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.3.1.2 Crowley [1989] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.3.1.3 Adams and von Flüe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
8.3.2 Topological Maps for Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.3.2.1 Taylor [1991] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.3.2.2 Courtney and Jain [1994] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.3.2.3 Kortenkamp and Weymouth [1993] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
8
Chapter 9 Vision-Based Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1 Camera Model and Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Landmark-Based Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1 Two-Dimensional Positioning Using a Single Camera . . . . . . . . . . . . . . . . . . . . .
9.2.2 Two-Dimensional Positioning Using Stereo Cameras . . . . . . . . . . . . . . . . . . . . . .
9.3 Camera-Calibration Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4 Model-Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4.1 Three-Dimensional Geometric Model-Based Positioning . . . . . . . . . . . . . . . . . . .
9.4.2 Digital Elevation Map-Based Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5 Feature-Based Visual Map Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.6 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
207
207
209
209
211
211
213
214
215
215
216
Appendix A A Wor d on Kalman Filter s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Appendix B Unit Conver sions and Abbr eviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Appendix C Systems-at-a-Glance Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Refer ences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Company Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Bookmar k Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Video Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Full-length Paper s Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
9
INTRODUCTION
Leonard and Durrant-Whyte [1991] summarized the general problem of mobile robot navigation by
three questions: “Where am I?,” “Where am I going?,” and “How should I get there?.” This report
surveys the state-of-the-art in sensors, systems, methods, and technologies that aim at answering the
first question, that is: robot positioning in its environment.
Perhaps the most important result from surveying the vast body of literature on mobile robot
positioning is that to date there is no truly elegant solution for the problem. The many partial
solutions can roughly be categorized into two groups: relative and absolute position measurements.
Because of the lack of a single, generally good method, developers of automated guided vehicles
(AGVs) and mobile robots usually combine two methods, one from each category. The two
categories can be further divided into the following subgroups.
Relative Position Measurements
a. Odometry This method uses encoders to measure wheel rotation and/or steering orientation.
Odometry has the advantage that it is totally self-contained, and it is always capable of providing
the vehicle with an estimate of its position. The disadvantage of odometry is that the position
error grows without bound unless an independent reference is used periodically to reduce the
error [Cox, 1991].
b. Inertial Navigation This method uses gyroscopes and sometimes accelerometers to measure rate
of rotation and acceleration. Measurements are integrated once (or twice) to yield position.
Inertial navigation systems also have the advantage that they are self-contained. On the downside,
inertial sensor data drifts with time because of the need to integrate rate data to yield position;
any small constant error increases without bound after integration. Inertial sensors are thus
unsuitable for accurate positioning over an extended period of time. Another problem with inertial
navigation is the high equipment cost. For example, highly accurate gyros, used in airplanes, are
inhibitively expensive. Very recently fiber-optic gyros (also called laser gyros), which are said to
be very accurate, have fallen dramatically in price and have become a very attractive solution for
mobile robot navigation.
Absolute Position Measurements
c. Active Beacons This method computes the absolute position of the robot from measuring the
direction of incidence of three or more actively transmitted beacons. The transmitters, usually
using light or radio frequencies, must be located at known sites in the environment.
d. Artificial Landmark Recognition In this method distinctive artificial landmarks are placed at
known locations in the environment. The advantage of artificial landmarks is that they can be
designed for optimal detectability even under adverse environmental conditions. As with active
beacons, three or more landmarks must be “in view” to allow position estimation. Landmark
positioning has the advantage that the position errors are bounded, but detection of external
10
landmarks and real-time position fixing may not always be possible. Unlike the usually pointshaped beacons, artificial landmarks may be defined as a set of features, e.g., a shape or an area.
Additional information, for example distance, can be derived from measuring the geometric
properties of the landmark, but this approach is computationally intensive and not very accurate.
e. Natural Landmark Recognition Here the landmarks are distinctive features in the environment.
There is no need for preparation of the environment, but the environment must be known in
advance. The reliability of this method is not as high as with artificial landmarks.
f. Model Matching In this method information acquired from the robot's onboard sensors is
compared to a map or world model of the environment. If features from the sensor-based map
and the world model map match, then the vehicle's absolute location can be estimated. Mapbased positioning often includes improving global maps based on the new sensory observations
in a dynamic environment and integrating local maps into the global map to cover previously
unexplored areas. The maps used in navigation include two major types: geometric maps and
topological maps. Geometric maps represent the world in a global coordinate system, while
topological maps represent the world as a network of nodes and arcs.
This book presents and discusses the state-of-the-art in each of the above six categories. The
material is organized in two parts: Part I deals with the sensors used in mobile robot positioning, and
Part II discusses the methods and techniques that make use of these sensors.
Mobile robot navigation is a very diverse area, and a useful comparison of different approaches
is difficult because of the lack of commonly accepted test standards and procedures. The research
platforms used differ greatly and so do the key assumptions used in different approaches. Further
difficulty arises from the fact that different systems are at different stages in their development. For
example, one system may be commercially available, while another system, perhaps with better
performance, has been tested only under a limited set of laboratory conditions. For these reasons we
generally refrain from comparing or even judging the performance of different systems or
techniques. Furthermore, we have not tested most of the systems and techniques, so the results and
specifications given in this book are merely quoted from the respective research papers or product
spec-sheets.
Because of the above challenges we have defined the purpose of this book to be a survey of the
expanding field of mobile robot positioning. It took well over 1.5 man-years to gather and compile
the material for this book; we hope this work will help the reader to gain greater understanding in
much less time.
11
Part I
Sensors for
Mobile Robot Positioning
CARMEL, the University of Michigan's first mobile robot, has been in service since 1987. Since then, CARMEL
has served as a reliable testbed for countless sensor systems. In the extra “shelf” underneath the robot is an
8086 XT compatible single-board computer that runs U of M's ultrasonic sensor firing algorithm. Since this code
was written in 1987, the computer has been booting up and running from floppy disk. The program was written
in FORTH and was never altered; should anything ever go wrong with the floppy, it will take a computer historian
to recover the code...
12
CHAPTER 1
SENSORS FOR DEAD RECKONING
Dead reckoning (derived from “deduced reckoning” of sailing days) is a simple mathematical
procedure for determining the present location of a vessel by advancing some previous position
through known course and velocity information over a given length of time [Dunlap and Shufeldt,
1972]. The vast majority of land-based mobile robotic systems in use today rely on dead reckoning
to form the very backbone of their navigation strategy, and like their nautical counterparts,
periodically null out accumulated errors with recurring “fixes” from assorted navigation aids.
The most simplistic implementation of dead reckoning is sometimes termed odometry; the term
implies vehicle displacement along the path of travel is directly derived from some onboard
“odometer.” A common means of odometry instrumentation involves optical encoders directly
coupled to the motor armatures or wheel axles.
Since most mobile robots rely on some variation of wheeled locomotion, a basic understanding
of sensors that accurately quantify angular position and velocity is an important prerequisite to
further discussions of odometry. There are a number of different types of rotational displacement
and velocity sensors in use today:
Brush encoders.
Potentiometers.
Synchros.
Resolvers.
Optical encoders.
Magnetic encoders.
Inductive encoders.
Capacitive encoders.
A multitude of issues must be considered in choosing the appropriate device for a particular
application. Avolio [1993] points out that over 17 million variations on rotary encoders are offered
by one company alone. For mobile robot applications incremental and absolute optical encoders are
the most popular type. We will discuss those in the following sections.
1.1 Optical Encoders
The first optical encoders were developed in the mid-1940s by the Baldwin Piano Company for use
as “tone wheels” that allowed electric organs to mimic other musical instruments [Agent, 1991].
Today’s corresponding devices basically embody a miniaturized version of the break-beam
proximity sensor. A focused beam of light aimed at a matched photodetector is periodically
interrupted by a coded opaque/transparent pattern on a rotating intermediate disk attached to the
shaft of interest. The rotating disk may take the form of chrome on glass, etched metal, or photoplast
such as Mylar [Henkel, 1987]. Relative to the more complex alternating-current resolvers, the
straightforward encoding scheme and inherently digital output of the optical encoder results in a lowcost reliable package with good noise immunity.
14
Part I Sensors for Mobile Robot Positioning
There are two basic types of optical encoders: incremental and absolute. The incremental version
measures rotational velocity and can infer relative position, while absolute models directly measure
angular position and infer velocity. If non volatile position information is not a consideration,
incremental encoders generally are easier to interface and provide equivalent resolution at a much
lower cost than absolute optical encoders.
1.1.1 Incremental Optical Encoders
The simplest type of incremental encoder is a single-channel tachometer encoder, basically an
instrumented mechanical light chopper that produces a certain number of sine- or square-wave
pulses for each shaft revolution. Adding pulses increases the resolution (and subsequently the cost)
of the unit. These relatively inexpensive devices are well suited as velocity feedback sensors in
medium- to high-speed control systems, but run into noise and stability problems at extremely slow
velocities due to quantization errors [Nickson, 1985]. The tradeoff here is resolution versus update
rate: improved transient response requires a faster update rate, which for a given line count reduces
the number of possible encoder pulses per sampling interval. A very simple, do-it-yourself encoder
is described in [Jones and Flynn, 1993]. More sophisticated single-channel encoders are typically
limited to 2540 lines for a 5-centimeter (2 in) diameter incremental encoder disk [Henkel, 1987].
In addition to low-speed instabilities, single-channel tachometer encoders are also incapable of
detecting the direction of rotation and thus cannot be used as position sensors. Phase-quadrature
incremental encoders overcome these problems by adding a second channel, displaced from the
first, so the resulting pulse trains are 90 degrees out of phase as shown in Figure 1.1. This technique
allows the decoding electronics to determine which channel is leading the other and hence ascertain
the direction of rotation, with the added benefit of increased resolution. Holle [1990] provides an
in-depth discussion of output options (single-ended TTL or differential drivers) and various design
issues (i.e., resolution, bandwidth, phasing, filtering) for consideration when interfacing phasequadrature incremental encoders to digital control systems.
The incremental nature of the phase-quadrature output signals dictates that any resolution of
angular position can only be relative to some specific reference, as opposed to absolute. Establishing
such a reference can be accomplished in a number of ways. For applications involving continuous
360-degree rotation, most encoders incorporate as a third channel a special index output that goes
high once for each complete revolution of the shaft (see Figure 1.1 above). Intermediate shaft
State
Ch A
Ch B
S1
High
Low
S2
High
High
S3
Low
High
S4
Low
Low
I
A
B
1 2 3 4
Figure 1.1: The observed phase relationship between Channel A and B pulse trains can be used to determine
the direction of rotation with a phase-quadrature encoder, while unique output states S1 - S4 allow for up to a
four-fold increase in resolution. The single slot in the outer track generates one index pulse per disk rotation
[Everett, 1995].
Chapter 1: Sensors for Dead Reckoning
15
positions are then specified by the number of encoder up counts or down counts from this known
index position. One disadvantage of this approach is that all relative position information is lost in
the event of a power interruption.
In the case of limited rotation, such as the back-and-forth motion of a pan or tilt axis, electrical
limit switches and/or mechanical stops can be used to establish a home reference position. To
improve repeatability this homing action is sometimes broken into two steps. The axis is rotated at
reduced speed in the appropriate direction until the stop mechanism is encountered, whereupon
rotation is reversed for a short predefined interval. The shaft is then rotated slowly back into the stop
at a specified low velocity from this designated start point, thus eliminating any variations in inertial
loading that could influence the final homing position. This two-step approach can usually be
observed in the power-on initialization of stepper-motor positioners for dot-matrix printer heads.
Alternatively, the absolute indexing function can be based on some external referencing action
that is decoupled from the immediate servo-control loop. A good illustration of this situation involves
an incremental encoder used to keep track of platform steering angle. For example, when the K2A
Navmaster [CYBERMOTION] robot is first powered up, the absolute steering angle is unknown,
and must be initialized through a “referencing” action with the docking beacon, a nearby wall, or
some other identifiable set of landmarks of known orientation. The up/down count output from the
decoder electronics is then used to modify the vehicle heading register in a relative fashion.
A growing number of very inexpensive off-the-shelf components have contributed to making the
phase-quadrature incremental encoder the rotational sensor of choice within the robotics research
and development community. Several manufacturers now offer small DC gear-motors with
incremental encoders already attached to the armature shafts. Within the U.S. automated guided
vehicle (AGV) industry, however, resolvers are still generally preferred over optical encoders for
their perceived superiority under harsh operating conditions, but the European AGV community
seems to clearly favor the encoder [Manolis, 1993].
Interfacing an incremental encoder to a computer is not a trivial task. A simple state-based
interface as implied in Figure 1.1 is inaccurate if the encoder changes direction at certain positions,
and false pulses can result from the interpretation of the sequence of state changes [Pessen, 1989].
Pessen describes an accurate circuit that correctly interprets directional state changes. This circuit
was originally developed and tested by Borenstein [1987].
A more versatile encoder interface is the HCTL 1100 motion controller chip made by Hewlett
Packard [HP]. The HCTL chip performs not only accurate quadrature decoding of the incremental
wheel encoder output, but it provides many important additional functions, including among others:
closed-loop position control,
closed-loop velocity control in P or PI fashion,
24-bit position monitoring.
At the University of Michigan's Mobile Robotics Lab, the HCTL 1100 has been tested and used
in many different mobile robot control interfaces. The chip has proven to work reliably and
accurately, and it is used on commercially available mobile robots, such as the TRC LabMate and
HelpMate. The HCTL 1100 costs only $40 and it comes highly recommended.
16
Part I Sensors for Mobile Robot Positioning
1.1.2 Absolute Optical Encoders
Absolute encoders are typically used for slower rotational applications that require positional
information when potential loss of reference from power interruption cannot be tolerated. Discrete
detector elements in a photovoltaic array are individually aligned in break-beam fashion with
concentric encoder tracks as shown in Figure 1.2, creating in effect a non-contact implementation
of a commutating brush encoder. The assignment of a dedicated track for each bit of resolution
results in larger size disks (relative to incremental designs), with a corresponding decrease in shock
and vibration tolerance. A general rule of thumb is that each additional encoder track doubles the
resolution but quadruples the cost [Agent, 1991].
Detector
array
LED
source
Beam
expander
Collimating
lens
Cylindrical
lens
Multi-track
encoder
disk
Figure 1.2: A line source of light passing through a coded pattern of opaque and
transparent segments on the rotating encoder disk results in a parallel output that
uniquely specifies the absolute angular position of the shaft. (Adapted from [Agent,
1991].)
Instead of the serial bit streams of incremental designs, absolute optical encoders provide a
parallel word output with a unique code pattern for each quantized shaft position. The most common
coding schemes are Gray code, natural binary, and binary-coded decimal [Avolio, 1993]. The Gray
code (for inventor Frank Gray of Bell Labs) is characterized by the fact that only one bit changes
at a time, a decided advantage in eliminating asynchronous ambiguities caused by electronic and
mechanical component tolerances (see Figure 1.3a). Binary code, on the other hand, routinely
involves multiple bit changes when incrementing or decrementing the count by one. For example,
when going from position 255 to position 0 in Figure 1.3b, eight bits toggle from 1s to 0s. Since there
is no guarantee all threshold detectors monitoring the detector elements tracking each bit will toggle
at the same precise instant, considerable ambiguity can exist during state transition with a coding
scheme of this form. Some type of handshake line signaling valid data available would be required
if more than one bit were allowed to change between consecutive encoder positions.
Absolute encoders are best suited for slow and/or infrequent rotations such as steering angle
encoding, as opposed to measuring high-speed continuous (i.e., drive wheel) rotations as would be
required for calculating displacement along the path of travel. Although not quite as robust as
resolvers for high-temperature, high-shock applications, absolute encoders can operate at
temperatures over 125C, and medium-resolution (1000 counts per revolution) metal or Mylar disk
designs can compete favorably with resolvers in terms of shock resistance [Manolis, 1993].
A potential disadvantage of absolute encoders is their parallel data output, which requires a more
complex interface due to the large number of electrical leads. A 13-bit absolute encoder using
Chapter 1: Sensors for Dead Reckoning
17
complimentary output signals for noise immunity would require a 28-conductor cable (13 signal pairs
plus power and ground), versus only six for a resolver or incremental encoder [Avolio, 1993].
a.
b.
Figure 1.3: Rotating an 8-bit absolute Gray code disk.
a. Counterclockwise rotation by one position increment will cause
only one bit to change.
b. The same rotation of a binary-coded disk will cause all bits to
change in the particular case (255 to 0) illustrated by the
reference line at 12 o’clock.
[Everett, 1995].
1.2 Doppler Sensors
The rotational displacement sensors discussed above derive navigation parameters directly from
wheel rotation, and are thus subject to problems arising from slippage, tread wear, and/or improper
tire inflation. In certain applications, Doppler and inertial navigation techniques are sometimes
employed to reduce the effects of such error sources.
Doppler navigation systems are routinely employed in maritime and aeronautical applications to
yield velocity measurements with respect to the earth itself, thus eliminating dead-reckoning errors
introduced by unknown ocean or air currents. The principle of operation is based on the Doppler
shift in frequency observed when radiated energy reflects off a surface that is moving with respect
to the emitter. Maritime systems employ acoustical energy reflected from the ocean floor, while
airborne systems sense microwave RF energy bounced off the surface of the earth. Both
configurations typically involve an array of four transducers spaced 90 degrees apart in azimuth and
inclined downward at a common angle with respect to the horizontal plane [Dunlap and Shufeldt,
1972].
Due to cost constraints and the reduced likelihood of transverse drift, most robotic implementations employ but a single forward-looking transducer to measure ground speed in the direction of
travel. Similar configurations are sometimes used in the agricultural industry, where tire slippage in
soft freshly plowed dirt can seriously interfere with the need to release seed or fertilizer at a rate
commensurate with vehicle advance. The M113-based Ground Surveillance Vehicle [Harmon, 1986]
employed an off-the-shelf unit of this type manufactured by John Deere to compensate for track
slippage.
The microwave radar sensor is aimed downward at a prescribed angle (typically 45) to sense
ground movement as shown in Figure 1.4. Actual ground speed VA is derived from the measured
velocity VD according to the following equation [Schultz, 1993]:
18
VA Part I Sensors for Mobile Robot Positioning
VD
cos
where
VA =
VD =
=
c
=
FD =
F0
=
cF D
2F0cos
(1.1)
actual ground velocity along path
measured Doppler velocity
angle of declination
speed of light
observed Doppler shift frequency
transmitted frequency.
VD
VA
α
Figure 1.4: A Doppler ground-speed sensor inclined at an
angle as shown measures the velocity component VD of
true ground speed VA . (Adapted from [Schultz, 1993].)
Errors in detecting true ground speed
arise due to side-lobe interference, vertical
velocity components introduced by vehicle reaction to road surface anomalies, and uncertainties in
the actual angle of incidence due to the finite width of the beam. Byrne et al. [1992] point out
another interesting scenario for potentially erroneous operation, involving a stationary vehicle parked
over a stream of water. The Doppler ground-speed sensor in this case would misinterpret the relative
motion between the stopped vehicle and the running water as vehicle travel.
1.2.1 Micro-Trak Trak-Star Ultrasonic Speed Sensor
One commercially available speed sensor that is based on Doppler speed measurements is the TrakStar Ultrasonic Speed Sensor [MICRO-TRAK]. This device, originally designed for agricultural
applications, costs $420. The manufacturer claims that this is the most accurate Doppler speed
sensor available. The technical specifications are listed in Table 1.1.
Figure 1.5: The Trak-Star Ultrasonic Speed Sensor is based on the
Doppler effect. This device is primarily targeted at the agricultural
market. (Courtesy of Micro-Trak.)
Chapter 1: Sensors for Dead Reckoning
19
1.2.2 Other Doppler-Effect Systems
A non-radar Doppler-effect device is the Table 1.1: Specifications for the Trak-Star Ultrasonic
Monitor 1000, a distance and speed monitor Speed Sensor.
for runners. This device was temporarily
Parameter
Value Units
marketed by the sporting goods manufacSpeed
range
17.7 m/s
turer [NIKE]. The Monitor 1000 was worn
0-40 mph
by the runner like a front-mounted fanny
Speed resolution
1.8 cm/s
pack. The small and lightweight device used
0.7 in/s
ultrasound as the carrier, and was said to
Accuracy
±1.5%+0.04 mph
have an accuracy of two to five percent,
Transmit frequency
62.5 kHz
depending on the ground characteristics. The
Temperature range
-29 to +50 C
manufacturer of the Monitor 1000 is Ap-20 to +120 F
plied Design Laboratories [ADL]. A microWeight
1.3 kg
wave radar Doppler effect distance sensor
3 lb
Power requirements
12 VDC
has also been developed by ADL. This radar
0.03 A
sensor is a prototype and is not commercially
available. However, it differs from the Monitor 1000 only in its use of a radar sensor
head as opposed to the ultrasonic sensor head used by the Monitor 1000. The prototype radar sensor
measures 15×10×5 centimeters (6×4×2 in), weighs 250 grams (8.8 oz), and consumes 0.9 W.
1.3 Typical Mobility Configurations
The accuracy of odometry measurements for dead reckoning is to a great extent a direct function
of the kinematic design of a vehicle. Because of this close relation between kinematic design and
positioning accuracy, one must consider the kinematic design closely before attempting to improve
dead-reckoning accuracy. For this reason, we will briefly discuss some of the more popular vehicle
designs in the following sections. In Part II of this report, we will discuss some recently developed
methods for reducing odometry errors (or the feasibility of doing so) for some of these vehicle
designs.
1.3.1 Differential Drive
Figure 1.6 shows a typical differential drive
mobile robot, the LabMate platform, manufactured by [TRC]. In this design incremental
encoders are mounted onto the two drive
motors to count the wheel revolutions. The
robot can perform dead reckoning by using
simple geometric equations to compute the
momentary position of the vehicle relative to
a known starting position.
deadre05.ds4, .wmf, 10/19/94
Figure 1.6: A typical differential-drive mobile robot
(bottom view).
20
Part I Sensors for Mobile Robot Positioning
For completeness, we rewrite the well-known equations for odometry below (also, see [Klarer,
1988; Crowley and Reignier, 1992]). Suppose that at sampling interval I the left and right wheel
encoders show a pulse increment of NL and NR, respectively. Suppose further that
cm = %Dn/nCe
where
cm
=
Dn =
Ce =
n
=
(1.2)
conversion factor that translates encoder pulses into linear wheel displacement
nominal wheel diameter (in mm)
encoder resolution (in pulses per revolution)
gear ratio of the reduction gear between the motor (where the encoder is attached) and the
drive wheel.
We can compute the incremental travel distance for the left and right wheel, UL,i and UR,i,
according to
UL/R, i = cm NL/R, i
(1.3)
and the incremental linear displacement of the robot's centerpoint C, denoted Ui , according to
Ui = (UR + UL)/2.
(1.4)
Next, we compute the robot's incremental change of orientation
i = (UR - UL)/b
(1.5)
where b is the wheelbase of the vehicle, ideally measured as the distance between the two contact
points between the wheels and the floor.
The robot's new relative orientation i can be computed from
i
= i-1 + i
(1.6)
and the relative position of the centerpoint is
xi = xi-1 + Ui cosi
yi = yi-1 + Ui sini
where
xi, yi = relative position of the robot's centerpoint c at instant i.
(1.7a)
(1.7b)
Chapter 1: Sensors for Dead Reckoning
21
1.3.2 Tricycle Drive
Tricycle-drive configurations (see Figure 1.7) employing a single driven front wheel and two passive
rear wheels (or vice versa) are fairly common in AGV applications because of their inherent
simplicity. For odometry instrumentation in the form of a steering-angle encoder, the dead-reckoning
solution is equivalent to that of an Ackerman-steered vehicle, where the steerable wheel replaces
the imaginary center wheel discussed in Section 1.3.3. Alternatively, if rear-axle differential
odometry is used to determine heading, the solution is identical to the differential-drive configuration
discussed in Section 1.3.1.
One problem associated with the tricycle-drive configuration is that the vehicle’s center of gravity
tends to move away from the front wheel when traversing up an incline, causing a loss of traction.
As in the case of Ackerman-steered designs, some surface damage and induced heading errors are
possible when actuating the steering while the platform is not moving.
Steerable driven wheel
l
d
Y
X
Passive wheels
Figure 1.7: Tricycle-drive configurations employing a steerable driven wheel and
two passive trailing wheels can derive heading information directly from a steering
angle encoder or indirectly from differential odometry [Everett, 1995].
1.3.3 Ackerman Steering
Used almost exclusively in the automotive industry, Ackerman steering is designed to ensure that
the inside front wheel is rotated to a slightly sharper angle than the outside wheel when turning,
thereby eliminating geometrically induced tire slippage. As seen in Figure 1.8, the extended axes for
the two front wheels intersect in a common point that lies on the extended axis of the rear axle. The
locus of points traced along the ground by the center of each tire is thus a set of concentric arcs
about this centerpoint of rotation P 1, and (ignoring for the moment any centrifugal accelerations) all
instantaneous velocity vectors will subsequently be tangential to these arcs. Such a steering geometry
is said to satisfy the Ackerman equation [Byrne et al., 1992]:
22
cot
Part I Sensors for Mobile Robot Positioning
cot
i
d
l
o
(1.8)
where
i = relative steering angle of the inner wheel
o = relative steering angle of the outer wheel
l = longitudinal wheel separation
d = lateral wheel separation.
For the sake of convenience, the vehicle steering angle SA can be thought of as the angle (relative
to vehicle heading) associated with an imaginary center wheel located at a reference point P 2 as
shown in the figure above. SA can be expressed in terms of either the inside or outside steering
angles ( i or o) as follows [Byrne et al., 1992]:
cot
SA
d
cot
2l
(1.9)
i
or, alternatively,
cot
SA
cot
o
d
.
2l
(1.10)
Ackerman steering provides a fairly accurate odometry solution while supporting the traction and
ground clearance needs of all-terrain operation. Ackerman steering is thus the method of choice for
outdoor autonomous vehicles. Associated drive implementations typically employ a gasoline or diesel
engine coupled to a manual or automatic transmission, with power applied to four wheels through
o
SA
i
P2
l
d
Y
P1
Figure 1.8: In an Ackerman-steered vehicle, the extended axes for all wheels
intersect in a common point. (Adapted from [Byrne et al., 1992].)
X
Chapter 1: Sensors for Dead Reckoning
23
a transfer case, a differential, and a series of universal joints. A representative example is seen in the
HMMWV-based prototype of the USMC Tele-Operated Vehicle (TOV) Program [Aviles et al.,
1990]. From a military perspective, the use of existing-inventory equipment of this type simplifies
some of the logistics problems associated with vehicle maintenance. In addition, reliability of the drive
components is high due to the inherited stability of a proven power train. (Significant interface
problems can be encountered, however, in retrofitting off-the-shelf vehicles intended for human
drivers to accommodate remote or computer control.)
1.3.4 Synchr o Dr ive
An innovative configuration known as synchro drive features three or more wheels (Figure 1.9)
mechanically coupled in such a way that all rotate in the same direction at the same speed, and
similarly pivot in unison about their respective steering axes when executing a turn. This drive and
steering “synchronization” results in improved odometry accuracy through reduced slippage, since
all wheels generate equal and parallel force vectors at all times.
The required mechanical synchronization can be accomplished in a number of ways, the most
common being a chain, belt, or gear drive. Carnegie Mellon University has implemented an
electronically synchronized version on one of their Rover series robots, with dedicated drive motors
for each of the three wheels. Chain- and belt-drive configurations experience some degradation in
steering accuracy and alignment due to uneven distribution of slack, which varies as a function of
loading and direction of rotation. In addition, whenever chains (or timing belts) are tightened to
reduce such slack, the individual wheels must be realigned. These problems are eliminated with a
completely enclosed gear-drive approach. An enclosed gear train also significantly reduces noise as
well as particulate generation, the latter being very important in clean-room applications.
An example of a three-wheeled belt-drive implementation is seen in the Denning Sentry formerly
manufactured by Denning Mobile Robots, Woburn, MA [Kadonoff, 1986] and now by Denning
Branch Robotics International [DBIR]. Referring to Figure 1.9, drive torque is transferred down
through the three steering columns to polyurethane-filled rubber tires. The drive-motor output shaft
is mechanically coupled to each of the steering-column power shafts by a heavy-duty timing belt to
ensure synchronous operation. A second timing belt transfers the rotational output of the steering
motor to the three steering columns, allowing them to synchronously pivot throughout a full 360-
Wheel
Steering chain
(Foot)
Drive chain
Steering
motor shaft
a.
b.
Figure 1.9: A four-wheel synchro-drive configuration:
Upper torso
Rotation shaft
Steering
sprocket
Power
sprocket
Drive
motor shaft
a. Bottom view. b. Top view.
(Adapted from Holland [1983].)
24
Part I Sensors for Mobile Robot Positioning
degree range [Everett, 1985]. The Sentry’s upper head assembly is mechanically coupled to the
steering mechanism in a manner similar to that illustrated in Figure 1.9, and thus always points in the
direction of forward travel. The three-point configuration ensures good stability and traction, while
the actively driven large-diameter wheels provide more than adequate obstacle climbing capability for
indoor scenarios. The disadvantages of this particular implementation include odometry errors
introduced by compliance in the drive belts as well as by reactionary frictional forces exerted by the
floor surface when turning in place.
To overcome these problems, the Cybermotion K2A Navmaster robot employs an enclosed geardrive configuration with the wheels offset from the steering axis as shown in Figure 1.10 and Figure
1.11. When a foot pivots during a turn, the attached wheel rotates in the appropriate direction to
minimize floor and tire wear, power consumption, and slippage. Note that for correct compensation,
the miter gear on the wheel axis must be on the opposite side of the power shaft gear from the wheel
as illustrated. The governing equation for minimal slippage is [Holland, 1983]
A
B
r
r
(1.11)
where
A = number of teeth on the power shaft gear
B = number of teeth on the wheel axle
gear
r’ = wheel offset from steering pivot axis
r = wheel radius.
One drawback of this approach is seen
in the decreased lateral stability that results when one wheel is turned in under
the vehicle. Cybermotion’s improved K3A
design solves this problem (with an even
smaller wheelbase) by incorporating a
dual-wheel arrangement on each foot
[Fisher et al., 1994]. The two wheels turn
in opposite directions in differential fashion as the foot pivots during a turn, but
good stability is maintained in the foregoing example by the outward swing of the
additional wheel.
The odometry calculations for the
synchro drive are almost trivial; vehicle
heading is simply derived from the
steering-angle encoder, while displacement in the direction of travel is given as
follows:
Power shaft
A
90 Miter gear
B
r
r'
Figure 1.10: Slip compensation during a turn is
accomplished through use of an offset foot assembly on
the three-wheeled K2A Navmaster robot. (Adapted from
[Holland, 1983].)
Chapter 1: Sensors for Dead Reckoning
25
Figure 1.11: The Denning Sentry (foreground) incorporates a three-point synchro-drive
configuration with each wheel located directly below the pivot axis of the associated steering
column. In contrast, the Cybermotion K2A (background) has wheels that swivel around the
steering column. Both robots were extensively tested at the University of Michigan's Mobile
Robotics Lab. (Courtesy of The University of Michigan.)
D 2N
R
Ce e
(1.12)
where
D = vehicle displacement along path
N = measured counts of drive motor shaft encoder
Ce = encoder counts per complete wheel revolution
Re = effective wheel radius.
1.3.5 Omnidirectional Drive
The odometry solution for most multi-degree-of-freedom (MDOF) configurations is done in similar
fashion to that for differential drive, with position and velocity data derived from the motor (or
wheel) shaft encoders. For the three-wheel example illustrated in Figure 1.12, the equations of
motion relating individual motor speeds to velocity components V x and V y in the reference frame of
the vehicle are given by [Holland, 1983]:
26
Part I Sensors for Mobile Robot Positioning
Forward
Motor 1
Motor 3
Top view
of base
Motor 2
R
a.
b.
Figure 1.12: a. Schematic of the wheel assembly used by the Veterans
Administration [La et al., 1981] on an omnidirectional wheelchair.
b. Top view of base showing relative orientation of components in
the three-wheel configuration. (Adapted from [Holland, 1983].)
V1 =
V2 =
V3 =
r = Vx + p R
2r = -0.5Vx + 0.867Vy +
3r = -0.5Vx - 0.867Vy +
1
p
R
p R
(1.13)
where
Vi = tangential velocity of wheel number i
i = rotational speed of motor number i
p = rate of base rotation about pivot axis
r = effective wheel radius
R = effective wheel offset from pivot axis.
1.3.6 Multi-Degr ee-of-Fr eedom Vehicles
Multi-degree-of-freedom (MDOF) vehicles have multiple
drive and steer motors. Different designs are possible. For
example, HERMIES-III, a sophisticated platform designed
and built at the Oak Ridge National Laboratory [Pin et al.,
1989; Reister et al., 1991; Reister, 1991] has two powered
wheels that are also individually steered (see Figure 1.13).
With four independent motors, HERMIES-III is a 4-degreeof-freedom vehicle.
MDOF configurations display exceptional maneuverability
in tight quarters in comparison to conventional 2-DOF
mobility systems, but have been found to be difficult to
control due to their overconstrained nature [Reister et al.,
1991; Killough and Pin, 1992; Pin and Killough, 1994;
Borenstein, 1995]. Resulting problems include increased
wheel slippage and thus reduced odometry accuracy.
Recently, Reister and Unseren [1992; 1993] introduced a
new control algorithm based on Force Control. The researchers reported on a substantial reduction in wheel
mdof01.ds4, mdof01.wmf, 5/19/94
Figure 1.13: A 4-degree-of-freedom
vehicle platform can travel in all
directions, including sideways and
diagonally. The difficulty lies in
coordinating all four motors so as to
avoid slippage.
Chapter 1: Sensors for Dead Reckoning
27
slippage for their two-wheel drive/two-wheel steer platform, resulting in a reported 20-fold
improvement of accuracy. However, the experiments on which these results were based avoided
simultaneous steering and driving of the two steerable drive wheels. In this way, the critical problem
of coordinating the control of all four motors simultaneously and during transients was completely
avoided.
Unique Mobility, Inc. built an 8-DOF vehicle for the U.S. Navy under an SBIR grant (see
Figure 1.14). In personal correspondence, engineers from that company mentioned to us difficulties
in controlling and coordinating all eight motors.
Figure 1.14: An 8-DOF platform with four wheels individually driven and steered.
This platform was designed and built by Unique Mobility, Inc. (Courtesy of
[UNIQUE].)
1.3.7 MDOF Vehicle with Compliant Linkage
To overcome the problems of control and the resulting excessive wheel slippage described above,
researchers at the University of Michigan designed the unique Multi-Degree-of-Freedom (MDOF)
vehicle shown in Figures 1.15 and 1.16 [Borenstein, 1992; 1993; 1994c; 1995]. This vehicle
comprises two differential-drive LabMate robots from [TRC]. The two LabMates, here referred to
as “trucks,” are connected by a compliant linkage and two rotary joints, for a total of three internal
degrees of freedom.
The purpose of the compliant linkage is to accommodate momentary controller errors without
transferring any mutual force reactions between the trucks, thereby eliminating the excessive wheel
slippage reported for other MDOF vehicles. Because it eliminates excessive wheel slippage, the
MDOF vehicle with compliant linkage is one to two orders of magnitude more accurate than other
MDOF vehicles, and as accurate as conventional, 2-DOF vehicles.
28
Truck A
Castor
Part I Sensors for Mobile Robot Positioning
Castor
Drive
wheel
Drive
wheel
Drive
wheel
Truck B
Drive
wheel
\ book\clap30.ds4, clap30. wmf, 07/ 19/ 95
Figure 1.15: The compliant linkage is
instrumented with two absolute rotary
encoders and a linear encoder to
measure the relative orientations and
separation distance between the two
trucks.
Figure 1.16: The University of Michigan's MDOF vehicle is a dualdifferential-drive multi-degree-of-freedom platform comprising two
TRC LabMates. These two "trucks” are coupled together with a
compliant linkage, designed to accommodate momentary controller
errors that would cause excessive wheel slippage in other MDOF
vehicles. (Courtesy of The University of Michigan.)
1.3.8 Tracked Vehicles
Yet another drive configuration for
mobile robots uses tracks instead of
wheels. This very special impledmin
mentation of a differential drive is
Track
known as skid steering and is roufootprint
tinely implemented in track form
dmax
on bulldozers and armored vehicles. Such skid-steer configurations
intentionally rely on track or wheel
slippage for normal operation (Fig- Figure 1.17: The effective point of contact for a skid-steer vehicle is
ure 1.17), and as a consequence roughly constrained on either side by a rectangular zone of ambiguity
corresponding to the track footprint. As is implied by the concentric
provide rather poor dead-reckoning circles, considerable slippage must occur in order for the vehicle to
information. For this reason, skid turn [Everett, 1995].
steering is generally employed only
in tele-operated as opposed to autonomous robotic applications, where the ability to surmount significant floor discontinuities is more
desirable than accurate odometry information. An example is seen in the track drives popular with
remote-controlled robots intended for explosive ordnance disposal. Figure 1.18 shows the Remotec
Andros V platform being converted to fully autonomous operation (see Sec. 5.3.1.2).
Chapter 1: Sensors for Dead Reckoning
Figure 1.18: A Remotec Andros V tracked vehicle is outfitted with computer control
at the University of Michigan. Tracked mobile platforms are commonly used in teleoperated applications. However, because of the lack of odometry feedback they are
rarely (if at all) used in fully autonomous applications. (Courtesy of The University of
Michigan.)
29
CHAPTER 2
HEADING SENSORS
Heading sensors are of particular importance to mobile robot positioning because they can help
compensate for the foremost weakness of odometry: in an odometry-based positioning method, any
small momentary orientation error will cause a constantly growing lateral position error. For this
reason it would be of great benefit if orientation errors could be detected and corrected immediately.
In this chapter we discuss gyroscopes and compasses, the two most widely employed sensors for
determining the heading of a mobile robot (besides, of course, odometry). Gyroscopes can be
classified into two broad categories: (a) mechanical gyroscopes and (b) optical gyroscopes.
2.1 Mechanical Gyroscopes
The mechanical gyroscope, a well-known and reliable rotation sensor based on the inertial properties
of a rapidly spinning rotor, has been around since the early 1800s. The first known gyroscope was
built in 1810 by G.C. Bohnenberger of Germany. In 1852, the French physicist Leon Foucault
showed that a gyroscope could detect the rotation of the earth [Carter, 1966]. In the following
sections we discuss the principle of operation of various gyroscopes.
Anyone who has ever ridden a bicycle has experienced (perhaps unknowingly) an interesting
characteristic of the mechanical gyroscope known as gyroscopic precession. If the rider leans the
bike over to the left around its own horizontal axis, the front wheel responds by turning left around
the vertical axis. The effect is much more noticeable if the wheel is removed from the bike, and held
by both ends of its axle while rapidly spinning. If the person holding the wheel attempts to yaw it left
or right about the vertical axis, a surprisingly violent reaction will be felt as the axle instead twists
about the horizontal roll axis. This is due to the angular momentum associated with a spinning
flywheel, which displaces the applied force by 90 degrees in the direction of spin. The rate of
precession $ is proportional to the applied torque T [Fraden, 1993]:
Apparent Drift Calculation
(Reproduced with permission from [Sammarco, 1990].)
Apparent drift is a change in the output of the gyroscope as a result of the Earth's rotation. This change
in output is at a constant rate; however, this rate
depends on the location of the gyroscope on the Earth.
At the North Pole, a gyroscope encounters a rotation of
360 per 24-h period or 15/h. The apparent drift will
vary as a sine function of the latitude as a directional
gyroscope moves southward. The direction of the
apparent drift will change once in the southern
hemisphere. The equations for Northern and Southern
Hemisphere apparent drift follow. Counterclockwise
(ccw) drifts are considered positive and clockwise (cw)
drifts are considered negative.
Northern Hemisphere: 15/h [sin (latitude)] ccw.
Southern Hemisphere: 15/h [sin (latitude,)] cw.
The apparent drift for Pittsburgh, PA (40.443 latitude) is
calculated as follows: 15/h [sin (40.443)] = 9.73/h
CCW or apparent drift = 0.162/min. Therefore, a gyroscope reading of 52 at a time period of 1 minute would
be corrected for apparent drift where
corrected reading = 52 - (0.162/min)(1 min) = 51.838.
Small changes in latitude generally do not require
changes in the correction factor. For example, a 0.2
change in latitude (7 miles) gives an additional apparent
drift of only 0.00067/min.
Chapter 2: Heading Sensors
T=I%
31
(2.1)
where
T = applied input torque
I = rotational inertia of rotor
% = rotor spin rate
$ = rate of precession.
Gyroscopic precession is a key factor involved in the concept of operation for the north-seeking
gyrocompass, as will be discussed later.
Friction in the support bearings, external influences, and small imbalances inherent in the
construction of the rotor cause even the best mechanical gyros to drift with time. Typical systems
employed in inertial navigation packages by the commercial airline industry may drift about 0.1
during a 6-hour flight [Martin, 1986].
2.1.1 Space-Stable Gyroscopes
The earth’s rotational velocity at any given point on the globe can be broken into two components:
one that acts around an imaginary vertical axis normal to the surface, and another that acts around
an imaginary horizontal axis tangent to the surface. These two components are known as the vertical
earth rate and the horizontal earth rate, respectively. At the North Pole, for example, the
component acting around the local vertical axis (vertical earth rate) would be precisely equal to the
rotation rate of the earth, or 15/hr. The horizontal earth rate at the pole would be zero.
As the point of interest moves down a meridian toward the equator, the vertical earth rate at that
particular location decreases proportionally to a value of zero at the equator. Meanwhile, the
horizontal earth rate, (i.e., that component acting around a horizontal axis tangent to the earth’s
surface) increases from zero at the pole to a maximum value of 15/hr at the equator.
There are two basic classes of rotational sensing gyros: 1) rate gyros, which provide a voltage or
frequency output signal proportional to the turning rate, and 2) rate integrating gyros, which indicate
the actual turn angle [Udd, 1991]. Unlike the magnetic compass, however, rate integrating gyros can
only measure relative as opposed to absolute angular position, and must be initially referenced to a
known orientation by some external means.
A typical gyroscope configuration is shown in Figure 2.1. The electrically driven rotor is
suspended in a pair of precision low-friction bearings at either end of the rotor axle. The rotor
bearings are in turn supported by a circular ring, known as the inner gimbal ring; this inner gimbal
ring pivots on a second set of bearings that attach it to the outer gimbal ring. This pivoting action
of the inner gimbal defines the horizontal axis of the gyro, which is perpendicular to the spin axis of
the rotor as shown in Figure 2.1. The outer gimbal ring is attached to the instrument frame by a third
set of bearings that define the vertical axis of the gyro. The vertical axis is perpendicular to both the
horizontal axis and the spin axis.
Notice that if this configuration is oriented such that the spin axis points east-west, the horizontal
axis is aligned with the north-south meridian. Since the gyro is space-stable (i.e., fixed in the inertial
reference frame), the horizontal axis thus reads the horizontal earth rate component of the planet’s
rotation, while the vertical axis reads the vertical earth rate component. If the spin axis is rotated 90
degrees to a north-south alignment, the earth’s rotation does not affect the gyro’s horizontal axis,
since that axis is now orthogonal to the horizontal earth rate component.
32
Part I Sensors for Mobile Robot Positioning
Outer pivot
W heel
Outer gimbal
Inner pivot
W heel bearing
Inner gimbal
Figure 2.1: Typical two-axis mechanical gyroscope configuration [Everett, 1995].
2.1.2 Gyrocompasses
The gyrocompass is a special configuration of the rate integrating gyroscope, employing a gravity
reference to implement a north-seeking function that can be used as a true-north navigation
reference. This phenomenon, first demonstrated in the early 1800s by Leon Foucault, was patented
in Germany by Herman Anschutz-Kaempfe in 1903, and in the U.S. by Elmer Sperry in 1908 [Carter,
1966]. The U.S. and German navies had both introduced gyrocompasses into their fleets by 1911
[Martin, 1986].
The north-seeking capability of the gyrocompass is directly tied to the horizontal earth rate
component measured by the horizontal axis. As mentioned earlier, when the gyro spin axis is
oriented in a north-south direction, it is insensitive to the earth's rotation, and no tilting occurs. From
this it follows that if tilting is observed, the spin axis is no longer aligned with the meridian. The
direction and magnitude of the measured tilt are directly related to the direction and magnitude of
the misalignment between the spin axis and true north.
2.1.3 Commercially Available Mechanical Gyroscopes
Numerous mechanical gyroscopes are available on the market. Typically, these precision machined
gyros can cost between $10,000 and $100,000. Lower cost mechanical gyros are usually of lesser
quality in terms of drift rate and accuracy. Mechanical gyroscopes are rapidly being replaced by
modern high-precision — and recently — low-cost fiber-optic gyroscopes. For this reason we will
discuss only a few low-cost mechanical gyros, specifically those that may appeal to mobile robotics
hobbyists.
Chapter 2: Heading Sensors
33
2.1.3.1 Futaba Model Helicopter Gyro
The Futaba FP-G154 [FUTABA] is a lowcost low-accuracy mechanical rate gyro
designed for use in radio-controlled model
helicopters and model airplanes. The Futaba
FP-G154 costs less than $150 and is available at hobby stores, for example [TOWER].
The unit comprises of the mechanical gyroscope (shown in Figure 2.2 with the cover
removed) and a small control amplifier.
Designed for weight-sensitive model helicopters, the system weighs only 102 grams
(3.6 oz). Motor and amplifier run off a 5 V Figure 2.2: The Futaba FP-G154 miniature mechanical
gyroscope for radio-controlled helicopters. The unit costs
DC supply and consume only 120 mA. less than $150 and weighs only 102 g (3.6 oz).
However, sensitivity and accuracy are orders
of magnitude lower than “professional”
mechanical gyroscopes. The drift of radio-control type gyroscopes is on the order of tens of degrees
per minute.
2.1.3.2 Gyration, Inc.
The GyroEngine made by Gyration, Inc.
[GYRATION], Saratoga, CA, is a low-cost
mechanical gyroscope that measures
changes in rotation around two independent axes. One of the original applications
for which the GyroEngine was designed is
the GyroPoint, a three-dimensional pointing device for manipulating a cursor in
three-dimensional computer graphics. The
GyroEngine model GE9300-C has a typical drift rate of about 9/min. It weighs
only 40 grams (1.5 oz) and compares in Figure 2.3: The Gyration GyroEngine compares in size
size with that of a roll of 35 millimeter film favorably with a roll of 35 mm film (courtesy Gyration, Inc.).
(see Figure 2.3). The sensor can be powered with 5 to 15 VDC and draws only 65
to 85 mA during operation. The open collector outputs can be readily interfaced with digital circuits.
A single GyroEngine unit costs $295.
2.2 Piezoelectric Gyroscopes
Piezoelectric vibrating gyroscopes use Coriolis forces to measure rate of rotation. in one typical
design three piezoelectric transducers are mounted on the three sides of a triangular prism. If one
of the transducers is excited at the transducer's resonance frequency (in the Gyrostar it is 8 kHz),
34
Part I Sensors for Mobile Robot Positioning
the vibrations are picked up by the two other transducers at equal intensity. When the prism is
rotated around its longitudinal axis, the resulting Coriolis force will cause a slight difference in the
intensity of vibration of the two measuring transducers. The resulting analog voltage difference is
an output that varies linearly with the measured rate of rotation.
Figure 2.4: The Murata Gyrostar ENV-05H is a piezoelectric
vibrating gyroscope. (Courtesy of [Murata]).
One popular piezoelectric vibrating gyroscope is the ENV-05 Gyrostar from [MURATA], shown
in Fig. 2.4. The Gyrostar is small, lightweight, and inexpensive: the model ENV-05H measures
47×40×22 mm (1.9×1.6×0.9 inches), weighs 42 grams (1.5 oz) and costs $300. The drift rate, as
quoted by the manufacturer, is very poor: 9/s. However, we believe that this number is the worst
case value, representative for extreme temperature changes in the working environment of the
sensor. When we tested a Gyrostar Model ENV-05H at the University of Michigan, we measured
drift rates under typical room temperatures of 0.05/s to 0.25/s, which equates to 3 to 15/min (see
[Borenstein and Feng, 1996]). Similar drift rates were reported by Barshan and Durrant-Whyte
[1995], who tested an earlier model: the Gyrostar ENV-05S (see Section 5.4.2.1 for more details on
this work). The scale factor, a measure for the useful sensitivity of the sensor, is quoted by the
manufacturer as 22.2 mV/deg/sec.
2.3 Optical Gyroscopes
Optical rotation sensors have now been under development as replacements for mechanical gyros
for over three decades. With little or no moving parts, such devices are virtually maintenance free
and display no gravitational sensitivities, eliminating the need for gimbals. Fueled by a large
Chapter 2: Heading Sensors
35
market in the automotive industry, highly linear fiber-optic versions are now evolving that have wide
dynamic range and very low projected costs.
The principle of operation of the optical gyroscope, first discussed by Sagnac [1913], is
conceptually very simple, although several significant engineering challenges had to be overcome
before practical application was possible. In fact, it was not until the demonstration of the heliumneon laser at Bell Labs in 1960 that Sagnac’s discovery took on any serious implications; the first
operational ring-laser gyro was developed by Warren Macek of Sperry Corporation just two years
later [Martin, 1986]. Navigation quality ring-laser gyroscopes began routine service in inertial
navigation systems for the Boeing 757 and 767 in the early 1980s, and over half a million fiber-optic
navigation systems have been installed in Japanese automobiles since 1987 [Reunert, 1993]. Many
technological improvements since Macek’s first prototype make the optical rate gyro a potentially
significant influence on mobile robot navigation in the future.
The basic device consists of two laser beams traveling in opposite directions (i.e., counter
propagating) around a closed-loop path. The constructive and destructive interference patterns
formed by splitting off and mixing parts of the two beams can be used to determine the rate and
direction of rotation of the device itself.
Schulz-DuBois [1966] idealized the ring laser as a hollow doughnut-shaped mirror in which light
follows a closed circular path. Assuming an ideal 100-percent reflective mirror surface, the optical
energy inside the cavity is theoretically unaffected by any rotation of the mirror itself. The counterpropagating light beams mutually reinforce each other to create a stationary standing wave of
intensity peaks and nulls as depicted in Figure 2.5, regardless of whether the gyro is rotating [Martin,
1986].
A simplistic visualization based on the Schulz-DuBois idealization is perhaps helpful at this point in
understanding the fundamental concept of operation before more detailed treatment of the subject
is presented. The light and dark fringes of the nodes are analogous to the reflective stripes or slotted
holes in the rotating disk of an incremental optical encoder, and can be theoretically counted in similar
fashion by a light detector mounted on the cavity wall. (In this analogy, however, the standing-wave
“disk” is fixed in the inertial reference frame, while the normally stationary detector revolves around
it.) With each full rotation of the mirrored doughnut, the detector would see a number of node peaks
equal to twice the optical path length of the beams divided by the wavelength of the light.
Lossless
cylindrical
mirror
Nodes
Observer moves
around ring
with rotation
EM field pattern
is stationary in
inertial frame
Figure 2.5: Standing wave created by counter-propagating light beams in
an idealized ring-laser gyro. (Adapted from [Schulz-DuBois, 1966].)
36
Part I Sensors for Mobile Robot Positioning
Obviously, there is no practical way to implement this theoretical arrangement, since a perfect
mirror cannot be realized in practice. Furthermore, the introduction of light energy into the cavity
(as well as the need to observe and count the nodes on the standing wave) would interfere with the
mirror's performance, should such an ideal capability even exist. However, many practical
embodiments of optical rotation sensors have been developed for use as rate gyros in navigation
applications. Five general configurations will be discussed in the following subsections:
Active optical resonators (2.3.1).
Passive optical resonators (2.3.2).
Open-loop fiber-optic interferometers (analog) (2.3.3).
Closed-loop fiber-optic interferometers (digital) (2.3.4).
Fiber-optic resonators (2.3.5).
Aronowitz [1971], Menegozzi and Lamb [1973], Chow et al. [1985], Wilkinson [1987], and Udd
[1991] provide in-depth discussions of the theory of the ring-laser gyro and its fiber-optic
derivatives. A comprehensive treatment of the technologies and an extensive bibliography of
preceding works is presented by Ezekial and Arditty [1982] in the proceedings of the First
International Conference on Fiber-Optic Rotation Sensors held at MIT in November, 1981. An
excellent treatment of the salient features, advantages, and disadvantages of ring laser gyros versus
fiber optic gyros is presented by Udd [1985, 1991].
2.3.1 Active Ring Laser Gyros
The active optical resonator configuration, more commonly known as the ring laser gyro, solves the
problem of introducing light into the doughnut by filling the cavity itself with an active lazing
medium, typically helium-neon. There are actually two beams generated by the laser, which travel
around the ring in opposite directions. If the gyro cavity is caused to physically rotate in the
counterclockwise direction, the counterclockwise propagating beam will be forced to traverse a
slightly longer path than under stationary conditions. Similarly, the clockwise propagating beam will
see its closed-loop path shortened by an identical amount. This phenomenon, known as the Sagnac
effect, in essence changes the length of the resonant cavity. The magnitude of this change is given
by the following equation [Chow et al., 1985]:
2
L 4%r 6
c
(2.2)
where
L = change in path length
r = radius of the circular beam path
6 = angular velocity of rotation
c = speed of light.
Note that the change in path length is directly proportional to the rotation rate 6 of the cavity.
Thus, to measure gyro rotation, some convenient means must be established to measure the induced
change in the optical path length.
This requirement to measure the difference in path lengths is where the invention of the laser in
the early 1960s provided the needed technological breakthrough that allowed Sagnac’s observations
to be put to practical use. For lazing to occur in the resonant cavity, the round-trip beam path must
Chapter 2: Heading Sensors
37
be precisely equal in length to an integral number of wavelengths at the resonant frequency. This
means the wavelengths (and therefore the frequencies) of the two counter- propagating beams must
change, as only oscillations with wavelengths satisfying the resonance condition can be sustained
in the cavity. The frequency difference between the two beams is given by [Chow et al., 1985]:
f 2f r 6
2r6
c
(2.3)
where
f = frequency difference
r = radius of circular beam path
6 = angular velocity of rotation
= wavelength.
In practice, a doughnut-shaped ring cavity would be hard to realize. For an arbitrary cavity
geometry, the expression becomes [Chow et al., 1985]:
f 4A 6
P
(2.4)
where
f = frequency difference
A = area enclosed by the closed-loop beam path
6 = angular velocity of rotation
P = perimeter of the beam path
= wavelength.
For single-axis gyros, the ring is generally formed by aligning three highly reflective mirrors to
create a closed-loop triangular path as shown in Figure 2.6. (Some systems, such as Macek’s early
prototype, employ four mirrors to create a square path.) The mirrors are usually mounted to a
monolithic glass-ceramic block with machined ports for the cavity bores and electrodes. Most
modern three-axis units employ a square block cube with a total of six mirrors, each mounted to the
center of a block face as shown in Figure 2.6. The most stable systems employ linearly polarized light
and minimize circularly polarized components to avoid magnetic sensitivities [Martin, 1986].
The approximate quantum noise limit for the ring-laser gyro is due to spontaneous emission in the
gain medium [Ezekiel and Arditty, 1982]. Yet, the ring-laser gyro represents the “best-case” scenario
of the five general gyro configurations outlined above. For this reason the active ring-laser gyro
offers the highest sensitivity and is perhaps the most accurate implementation to date.
The fundamental disadvantage associated with the active ring laser is a problem called frequency
lock-in, which occurs at low rotation rates when the counter-propagating beams “lock” together in
frequency [Chao et al., 1984]. This lock-in is attributed to the influence of a very small amount of
backscatter from the mirror surfaces, and results in a deadband region (below a certain threshold of
rotational velocity) for which there is no output signal. Above the lock-in threshold, output
approaches the ideal linear response curve in a parabolic fashion.
The most obvious approach to solving the lock-in problem is to improve the quality of the mirrors
to reduce the resulting backscatter. Again, however, perfect mirrors do not exist, and some finite
38
Part I Sensors for Mobile Robot Positioning
amount of backscatter will always be present. Martin [1986] reports a representative value as 10 -12
of the power of the main beam; enough to induce frequency lock-in for rotational rates of several
hundred degrees per hour in a typical gyro with a 20-centimeter (8-in) perimeter.
A
B
C
D
Figure 2.6: Six-mirror configuration of three-axis ring-laser
gyro. (Adapted from [Koper, 1987].)
An additional technique for reducing lock-in is to incorporate some type of biasing scheme to shift
the operating point away from the deadband zone. Mechanical dithering is the least elegant but most
common biasing means, introducing the obvious disadvantages of increased system complexity and
reduced mean time between failures due to the moving parts. The entire gyro assembly is rotated
back and forth about the sensing axis in an oscillatory fashion. State-of-the-art dithered active ring
laser gyros have a scale factor linearity that far surpasses the best mechanical gyros.
Dithered biasing, unfortunately, is too slow for high-performance systems (i.e., flight control),
resulting in oscillatory instabilities [Martin, 1986]. Furthermore, mechanical dithering can introduce
crosstalk between axes on a multi-axis system, although some unibody three-axis gyros employ a
common dither axis to eliminate this possibility [Martin, 1986].
Buholz and Chodorow [1967], Chesnoy [1989], and Christian and Rosker [1991] discuss the use
of extremely short duration laser pulses (typically 1/15 of the resonator perimeter in length) to
reduce the effects of frequency lock-in at low rotation rates. The basic idea is to reduce the crosscoupling between the two counter-propagating beams by limiting the regions in the cavity where the
two pulses overlap. Wax and Chodorow [1972] report an improvement in performance of two orders
of magnitude through the use of intracavity phase modulation. Other techniques based on non-linear
optics have been proposed, including an approach by Litton that applies an external magnetic field
to the cavity to create a directionally dependent phase shift for biasing [Martin, 1986]. Yet another
solution to the lock-in problem is to remove the lazing medium from the ring altogether, effectively
forming what is known as a passive ring resonator.
Chapter 2: Heading Sensors
39
2.3.2 Passive Ring Resonator Gyr os
Light source
Highly
reflective
mirror
Partially
transmissive
mirror
Detector
Figure 2.7: Passive ring resonator gyro with laser source
external to the ring cavity. (Adapted from [Udd, 1991].)
The passive ring resonator gyro makes use of a laser source external to the ring cavity
(Figure 2.7), and thus avoids the frequency lock-in problem which arises when the gain medium is
internal to the cavity itself. The passive configuration also eliminates problems arising from changes
in the optical path length within the interferometer due to variations in the index of refraction of the
gain medium [Chow et al., 1985]. The theoretical quantum noise limit is determined by photon shot
noise and is slightly higher (i.e., worse) than the theoretical limit seen for the active ring-laser gyro
[Ezekiel and Arditty, 1982].
The fact that these devices use mirrored resonators patterned after their active ring predecessors
means that their packaging is inherently bulky. However, fiber-optic technology now offers a low
volume alternative. The fiber-optic derivatives also allow longer length multi-turn resonators, for
increased sensitivity in smaller, rugged, and less expensive packages. As a consequence, the Resonant
Fiber-Optic Gyro (RFOG), to be discussed in Section 2.1.2.5, has emerged as the most popular of
the resonator configurations [Sanders, 1992].
2.3.3 Open-Loop Inter fer ometr ic Fiber Optic Gyr os
The concurrent development of optical fiber technology, spurred mainly by the communications
industry, presented a potential low-cost alternative to the high-tolerance machining and clean-room
assembly required for ring-laser gyros. The glass fiber in essence forms an internally reflective
waveguide for optical energy, along the lines of a small-diameter linear implementation of the
doughnut-shaped mirror cavity conceptualized by Schulz-DuBois [1966].
Recall the refractive index n relates the speed of light in a particular medium to the speed of light
in a vacuum as follows:
n
c
cm
(2.5)
40
Part I Sensors for Mobile Robot Positioning
where
n = refractive index of medium
c = speed of light in a vacuum
cm = speed of light in medium.
Step-index multi-mode fiber (Figure 2.8) is made up of a core region of glass with index of
refraction nco, surrounded by a protective cladding with a lower index of refraction ncl [Nolan and
Blaszyk, 1991]. The lower refractive index in the cladding is necessary to ensure total internal
reflection of the light propagating through the core region. The terminology step index refers to this
“stepped” discontinuity in the refractive index that occurs at the core-cladding interface.
Referring now to Figure 2.8, as long as the entry angle (with respect to the waveguide axis) of an
incoming ray is less than a certain critical angle c, the ray will be guided down the fiber, virtually
without loss. The numerical aperture of the fiber quantifies this parameter of acceptance (the lightcollecting ability of the fiber) and is defined as follows [Nolan and Blaszyk, 1991]:
NA
sin
2
c
2
nco ncl
ncl
nco
(2.6)
where
NA = numerical aperture of the fiber
= critical angle of acceptance
c
nco = index of refraction of glass core
ncl = index of refraction of cladding.
Waveguide
axis
Figure 2.8: Step-index multi-mode fiber. (Adapted from
[Nolan et al., 1991].)
As illustrated in Figure 2.9, a number of rays following different-length paths can simultaneously
propagate down the fiber, as long as their respective entry angles are less than the critical angle of
acceptance c. Multiple-path propagation of this nature occurs where the core diameter is much larger
than the wavelength of the guided energy, giving rise to the term multi-mode fiber. Such multi-mode
operation is clearly undesirable in gyro applications, where the objective is to eliminate all nonreciprocal conditions other than that imposed by the Sagnac effect itself. As the diameter of the core
is reduced to approach the operating wavelength, a cutoff condition is reached where just a single
mode is allowed to propagate, constrained to travel only along the waveNumerical aperture
guide axis [Nolan and Blaszyk, 1991].
Light can randomly change polariza
tion states as it propagates through standard single-mode fiber. The use of special
Waveguide
polarization-maintaining fiber, such as
axis
PRSM Corning, maintains the original
2
polarization state of the light along the
path of travel [Reunert, 1993]. This is 1
important, since light of different polarization states travels through an optical fiber Figure 2.9: Entry angles of incoming rays 1 and 2
determine propagation paths in fiber core. (Adapted from
at different speeds.
[Nolan et al., 1991].)
Chapter 2: Heading Sensors
41
A typical block diagram of the “minimum-reciprocal” IFOG configuration is presented in
Figure 2.10. Polarization-maintaining single-mode fiber [Nolan and Blaszyk, 1991] is employed to
ensure the two counter-propagating beams in the loop follow identical paths in the absence of
rotation.
An interesting characteristic of the IFOG is the absence of any laser source [Burns et al., 1983],
the enabling technology allowing the Sagnac effect to reach practical implementation in the first place.
A low-coherence source, such as a super-luminescent diode (SLD), is typically employed instead to
reduce the effects of noise [Tai et al., 1986], the primary source of which is backscattering within the
fiber and at any interfaces. As a result, in addition to the two primary counter-propagating waves in
the loop, there are also a number of parasitic waves that yield secondary interferometers [Lefevre,
1992]. The limited temporal coherence of the broadband SLD causes any interference due to
backscattering to average to zero, suppressing the contrast of these spurious interferometers. The
detection system becomes sensitive only to the interference between waves that followed identical
paths [Ezekiel and Arditty, 1982; Lefevre, 1992].
The Sagnac phase shift introduced by rotation is given by [Ezekiel and Arditty, 1982]
=
2 LD
c
(2.7)
where
= measured phase shift between counter-propagating beams
L = length of fiber-optic cable in loop
D = diameter of loop
= wavelength of optical energy
c = speed of light in a vacuum.
The stability of the scale factor relating
to the rotational velocity in the equation above is thus
limited to the stability of L, D, and [Ezekiel and Arditty, 1982]. Practical implementations usually
operate over plus or minus half a fringe (i.e., ± rad of phase difference), with a theoretical sensitivity
of 10-6 radians or less of phase shift [Lefevre, 1992].
IFOG sensitivity may be improved by increasing L (i.e., adding turns of fiber in the sensing loop).
This effect peaks at an optimal length of several kilometers, after which the fiber attenuation (typically
1 dB/km) begins to degrade performance. This large amount of fiber represents a significant
percentage of overall system cost.
Source splitter
Coil splitter
Source
Polarizer
Filter
Detector
Fiber coil
Phase modulator
Figure 2.10: Block diagram of “minimum-reciprocal” integrated fiber-optic gyro. (Adapted
from [Lefevre, 1992].)
42
Part I Sensors for Mobile Robot Positioning
In summary, the open-loop IFOG is attractive from the standpoint of reduced manufacturing
costs. Additional advantages include high tolerance to shock and vibration, insensitivity to gravity
effects, quick start-up, and good sensitivity in terms of bias drift rate and the random walk
coefficient. Coil geometry is not critical, and no path length control is needed. Some disadvantages
are that a long optical cable is required, dynamic range is limited with respect to active ring-laser
gyros, and the scale factor is prone to vary [Adrian, 1991]. Open-loop configurations are therefore
most suited to the needs of low-cost systems in applications that require relatively low accuracy (i.e.,
automobile navigation).
For applications demanding higher accuracy, such as aircraft navigation (0.01 to 0.001/hr), the
closed-loop IFOG to be discussed in the next section offers significant promise.
2.3.4 Closed-Loop Interferometric Fiber Optic Gyros
This new implementation of a fiber-optic gyro provides feedback to a frequency or phase shifting
element. The use of feedback results in the cancellation of the rotationally induced Sagnac phase
shift. However, closed-loop digital signal processing is considerably more complex than the analog
signal processing employed on open-loop IFOG configurations [Adrian, 1991]. Nonetheless, it now
seems that the additional complexity is justified by the improved stability of the gyro: closed-loop
IFOGs are now under development with drifts in the 0.001 to 0.01/hr range, and scale-factor
stabilities greater than 100 ppm (parts per million) [Adrian, 1991].
2.3.5 Resonant Fiber Optic Gyros
The resonant fiber optic gyro (RFOG) evolved as a solid-state derivative of the passive ring
resonator gyro discussed in Section 2.1.2.2. In the solid-state implementation, a passive resonant
cavity is formed from a multi-turn closed loop of optical fiber. An input coupler provides a means
for injecting frequency-modulated light from a laser source into the resonant loop in both the
clockwise and counterclockwise directions. As the frequency of the modulated light passes through
a value such that the perimeter of the loop precisely matches an integral number of wavelengths at
that frequency, input energy is strongly coupled into the loop [Sanders, 1992]. In the absence of loop
rotation, maximum coupling for both beam directions occurs in a sharp peak centered at this
resonant frequency.
If the loop is caused to rotate in the clockwise direction, of course, the Sagnac effect causes the
perceived loop perimeter to lengthen for the clockwise-traveling beam, and to shorten for the
counterclockwise-traveling beam. The resonant frequencies must shift accordingly, and as a result,
energy is coupled into the loop at two different frequencies and directions during each cycle of the
sinusoidal FM sweep. An output coupler samples the intensity of the energy in the loop by passing
a percentage of the two counter-rotating beams to their respective detectors. The demodulated
output from these detectors will show resonance peaks, separated by a frequency difference f given
by the following [Sanders, 1992]:
D
f = n 6
where
f = frequency difference between counter-propagating beams
D = diameter of the resonant loop
(2.8)
Chapter 2: Heading Sensors
43
$
= rotational velocity
n
= refractive index of the fiber.
= freespace wavelength of laser
Like the IFOG, the all-solid-state RFOG is attractive from the standpoint of high reliability, long
life, quick start-up, and light weight. The principle advantage of the RFOG, however, is that it
requires significantly less fiber (from 10 to 100 times less) in the sensing coil than the IFOG
configuration, while achieving the same shot-noise-limited performance [Sanders, 1992]. Sanders
attributes this to the fact that light traverses the sensing loop multiple times, as opposed to once in
the IFOG counterpart. On the down side are the requirements for a highly coherent source and
extremely low-loss fiber components [Adrian, 1991].
2.3.6 Commercially Available Optical Gyroscopes
Only recently have optical fiber gyros become commercially available at a price that is suitable for
mobile robot applications. In this section we introduce two such systems.
2.3.6.1 The Andrew “Autogyro"
Andrew Corp. [ANDREW] offers the low-cost Autogyro, shown in Figure 2.11, for terrestrial
navigation. It is a single-axis interferometric fiber-optic gyroscope (see Sec. 2.1.2.3) based on
polarization-maintaining fiber and precision
fiber-optic gyroscope technology. Model
3ARG-A ($950) comes with an analog
output, while model 3ARG-D ($1,100) has
an RS-232 output for connection to a computer. Technical specifications for the
3ARG-D are given in Table 2.1. Specifications for the 3ARG-A are similar. A more
detailed discussion of the Autogyro is given
Table 2.1: Selected specifications for the Andrew
Autogyro Model 3ARG-D. (Courtesy of [Andrew
Corp].)
Parameter
Value Units
Input rotation rate
±100 /s
Minimum detectable
rotation rate
±0.05 /s
±180 /hr
Rate bandwidth
Bias drift (at stabilized
temperature) — RMS
100 Hz
0.005 /s rms
18 /hr rms
Size
(excluding connector)
Weight (total)
Power
77 dia × 88 mm
3.0 dia × 3.5 in
0.63
1.38
9 to 18
630
kg
lb
VDC
mA
Figure 2.11: The Andrew Autogyro Model 3ARG.
(Courtesy of [Andrew Corp].)
44
Part I Sensors for Mobile Robot Positioning
Table 2.1: Selected specifications for the Andrew
Autogyro Navigator (Courtesy of [Andrew Corp].)
Parameter
Value Units
Input rotation rate
±100 /s
Instantaneous
bandwidth
Bias drift (at stabilized
temperature) — RMS
Size
(excluding connector)
Weight (total)
Power Analog
Power Digital
100 Hz
0.005 /s rms
18 /hr rms
115×90×41 mm
4.5×3.5×1.6 in
0.25
0.55
<2
<3
kg
lb
W
W
in [Allen et al., 1994; Bennett and Emge,
1994].
In fall 1995 Andrew Corporation announced a newer model, called the AUTOGYRO Navigator. This laser gyro, shown in
Fig. 2.12, is only one third the weight, consume only half the power, and cost 15% less
than its predecessor, the AUTOGYRO.
Figure 2.12: The Andrew AUTOGYRO Navigator.
(Courtesy of [Andrew Corp].)
2.3.6.2 Hitachi Cable Ltd. OFG-3
Hitachi Cable Ltd. markets an optical fiber gyroscope called OFG-3 (see Figure 2.13). Komoriya and
Oyama [1994] tested that sensor and found its drift rate to be quite linear with 0.00317/s (11.4/hr).
This result is close to the advertised specification of 10/hr. This low drift rate is substantially better
than that provided by conventional (mechanical) gyros. Table 2.2 shows technical specifications of
the OFG-3 gyro, as reported by Komoriya and Oyama [1994].
One point to keep in mind when considering the use of fiber optic gyros in mobile robot
applications is the minimum detectable rotation rate. This rate happens to be the same for both the
Andrew 3ARG-A and the Hitachi OFG-3 gyros: 0.05/s. If either gyro was installed on a robot with
a systematic error (e.g., due to unequal wheel diameters; see Sec. 5.1 for more details) of 1 degree
per 10 meter linear travel, then neither gyro would detect this systematic error at speeds lower than
0.5 m/s.
Chapter 2: Heading Sensors
45
Table 2.2: Selected specifications for the Hitachi
Cable Ltd. OFG-3 fiber optic gyroscope.
(Reprinted with permission from [Komoriya and
Oyama, 1994].)
Parameter
Value Units
Input rotation rate
Minimum
detectable rotation
rate
±100 /s
±0.05 /s
±60 /hr
Min. sampl. interval
Zero drift (rate
integration)
Size
10 ms
0.0028
10
88(W)×88(L)×65(H)
3.5(W)×3.5(L)×2.5(H)
Weight (total)
Power
/s
/hr
mm
in
0.48 kg
1.09 lb
12 VDC
150-250 mA
Figure 2.13: The OFG-3 optical fiber gyro made
by Hitachi Cable Ltd. (Courtesy of Hitachi Cable
America, Inc. [HITACHI].)
2.4 Geomagnetic Sensors
Vehicle heading is the most significant of the navigation parameters (x, y, and ) in terms of its
influence on accumulated dead-reckoning errors. For this reason, sensors which provide a measure
of absolute heading or relative angular velocity are extremely important in solving the real world
navigation needs of an autonomous platform. The most commonly known sensor of this type is
probably the magnetic compass. The terminology normally used to describe the intensity of a
magnetic field is magnetic flux density B, measured in Gauss (G). Alternative units are the Tesla (T),
and the gamma (), where 1 Tesla = 10 4 Gauss = 10 9 gamma.
The average strength of the earth’s magnetic field is 0.5 Gauss and can be represented as a dipole
that fluctuates both in time and space, situated roughly 440 kilometers off center and inclined 11
degrees to the planet’s axis of rotation [Fraden, 1993]. This difference in location between true north
and magnetic north is known as declination and varies with both time and geographical location.
Corrective values are routinely provided in the form of declination tables printed directly on the
maps or charts for any given locale.
Instruments which measure magnetic fields are known as magnetometers. For application to
mobile robot navigation, only those classes of magnetometers which sense the magnetic field of the
earth are of interest. Such geomagnetic sensors, for purposes of this discussion, will be broken down
into the following general categories:
Mechanical magnetic compasses.
Fluxgate compasses.
Hall-effect compasses.
Magnetoresistive compasses.
Magnetoelastic compasses.
46
Part I Sensors for Mobile Robot Positioning
Before we introduce different types of compasses, a word of warning: the earth's magnetic field
is often distorted near power lines or steel structures [Byrne et al., 1992]. This makes the
straightforward use of geomagnetic sensors difficult for indoor applications. However, it may be
possible to overcome this problem in the future by fusing data from geomagnetic compasses with
data from other sensors.
2.4.1 Mechanical Magnetic Compasses
The first recorded use of a magnetic compass was in 2634 B.C., when the Chinese suspended a piece
of naturally occurring magnetite from a silk thread and used it to guide a chariot over land [Carter,
1966]. Much controversy surrounds the debate over whether the Chinese or the Europeans first
adapted the compass for marine applications, but by the middle of the 13 th century such usage was
fairly widespread around the globe. William Gilbert [1600] was the first to propose that the earth
itself was the source of the mysterious magnetic field that provided such a stable navigation
reference for ships at sea.
The early marine compasses were little more that magnetized needles floated in water on small
pieces of cork. These primitive devices evolved over the years into the reliable and time proven
systems in use today, which consist of a ring magnet or pair of bar magnets attached to a graduated
mica readout disk. The magnet and disk assembly floats in a mixture of water and alcohol or
glycerine, such that it is free to rotate around a jeweled pivot. The fluid acts to both support the
weight of the rotating assembly and to dampen its motion under rough conditions.
The sealed vessel containing the compass disk and damping fluid is typically suspended from a
2-degree-of-freedom gimbal to decouple it from the ship’s motion. This gimbal assembly is mounted
in turn atop a floor stand or binnacle. On either side of the binnacle are massive iron spheres that,
along with adjustable permanent magnets in the base, are used to compensate the compass for
surrounding magnetic abnormalities that alter the geomagnetic lines of flux. The error resulting from
such external influences (i.e., the angle between indicated and actual bearing to magnetic north) is
known as compass deviation, and along with local declination, must be added or subtracted as
appropriate for true heading:
Ht = Hi ± CFdev ± CFdec
(2.9)
where
Ht
= true heading
Hi
= indicated heading
CFdev = correction factor for compass deviation
CFdec = correction factor for magnetic declination.
Another potential source of error which must be taken into account is magnetic dip, a term arising
from the “dipping” action observed in compass needles attributed to the vertical component of the
geomagnetic field. The dip effect varies with latitude, from no impact at the equator where the flux
lines are horizontal, to maximum at the poles where the lines of force are entirely vertical. For this
reason, many swing-needle instruments have small adjustable weights that can be moved radially to
balance the needle for any given local area of operation. Marine compasses ensure alignment in the
horizontal plane by floating the magnet assembly in an inert fluid.
Chapter 2: Heading Sensors
47
Dinsmore Starguide Magnetic Compass
An extremely low-cost configuration of the mechanical magnetic compass suitable for robotic
applications is seen in a product recently announced by the Dinsmore Instrument Company, Flint,
MI. The heart of the Starguide compass is the Dinsmore model 1490 digital sensor [Dinsmore
Instrument Company, 1991], which consists of a miniaturized permanent-magnet rotor mounted in
low-friction jeweled bearings. The sensor is internally damped such that if momentarily displaced
90 degrees, it will return to the indicated direction in 2.5 seconds, with no overshoot.
Four Hall-effect switches corresponding to the cardinal headings (N, E, W, S) are arranged
around the periphery of the rotor and activated by the south pole of the magnet as the rotor aligns
itself with the earth’s magnetic field. Intermediate headings (NE, NW, SE, SW) are indicated through
simultaneous activation of the adjacent cardinal-heading switches. The Dinsmore Starguide is not
a true Hall-effect compass (see Sec. 2.4.3), in that the Hall-effect devices are not directly sensing
the geomagnetic field of the earth, but rather the angular position of a mechanical rotor.
The model 1490 digital sensor measures 12.5 millimeters (0.5 in) in diameter by 16 millimeters
(0.63 in) high, and is available separately from Dinsmore for around $12. Current consumption is
30 mA, and the open-collector NPN outputs can sink 25 mA per channel. Grenoble [1990] presents
a simple circuit for interfacing the device to eight indicator LEDs. An alternative analog sensor
(model 1525) with a ratiometric sine-cosine output is also available for around $35. Both sensors
may be subjected to unlimited magnetic flux without damage.
2.4.2 Fluxgate Compasses
There currently is no practical alternative to the popular fluxgate compass for portability and long
missions [Fenn et al., 1992]. The term fluxgate is actually a trade name of Pioneer Bendix for the
saturable-core magnetometer, derived from the gating action imposed by an AC-driven excitation
coil that induces a time varying permeability in the sensor core. Before discussing the principle of
operation, it is probably best to review briefly the subject of magnetic conductance, or permeability.
The permeability µ of a given material is a measure of how well it serves as a path for magnetic
lines of force, relative to air, which has an assigned permeability of one. Some examples of highpermeability materials are listed in Table 2.3.
Permeability is the magnetic circuit analogy to electrical conductivity, and relates Table 2.3: Permeability ranges for selected materials.
magnetic flux density to the magnetizing Values vary with proportional make-up, heat treatment, and
force as follows:
mechanical working of the material [Bolz and Tuve, 1979].
B=µ H
(2.10)
Material
Supermalloy
Permeability µ
100,000 - 1,000,000
where
Pure iron
25,000 - 300,000
B = magnetic flux density
Mumetal
20,000 - 100,000
µ = permeability
Permalloy
2,500 - 25,000
H = magnetizing force.
Cast iron
100 - 600
Since the magnetic flux in a magnetic circuit
is analogous to current I in an electrical
circuit, it follows that magnetic flux density B is the parallel to electrical current density.
A graphical plot of the above equation is known as the normal magnetizing curve, or B-H curve,
and the permeability µ is the slope. An example plot is depicted in Figure 2.14 for the case of mild
48
Part I Sensors for Mobile Robot Positioning
steel. In actuality, due to hysteresis, µ depends not only on the current value of H, but also the
history of previous values and the sign of dH/dt, as will be seen later. The important thing to note
at this point in the discussion is the B-H curve is not linear, but rather starts off with a fairly steep
slope, and then flattens out suddenly as H reaches a certain value. Increasing H beyond this “knee”
of the B-H curve yields little increase in B; the material is effectively saturated, with a near-zero
permeability.
Figure 2.14: The slope of the B-H curve, shown here for cast iron and
sheet steel, describes the permeability of a magnetic material, a
measure of its ability (relative to air) to conduct a magnetic flux.
(Adapted from [Carlson and Gisser, 1981].)
When a highly permeable material is introduced into a uniform magnetic field, the lines of force
are drawn into the lower resistance path presented by the material as shown in Figure 2.15.
However, if the material is forced into saturation by some additional magnetizing force H, the lines
of flux of the external field will be relatively unaffected by the presence of the saturated material,
as indicated in Figure 2.15b. The fluxgate magnetometer makes use of this saturation phenomenon
in order to directly measure the strength of a surrounding static magnetic field.
Various core materials have been employed in different fluxgate designs over the past 50 years,
with the two most common being permalloy (an alloy of iron and nickel) and mumetal (iron, nickel,
Chapter 2: Heading Sensors
Drive
a.
49
Sense
Drive
Sense
b.
Figure 2.15: External lines of flux for: a. unsaturated core, b. saturated core. (Adapted from [Lenz,
1990].)
copper, and chromium). The permeable core is driven into and out of saturation by a gating signal
applied to an excitation coil wound around the core. For purposes of illustration, let’s assume for the
moment a square-wave drive current is applied. As the core moves in and out of saturation, the flux
lines from the external B field to be measured are drawn into and out of the core, alternating in turn
between the two states depicted in Figure 2.15. (This is somewhat of an oversimplification, in that
the B-H curve does not fully flatten out with zero slope after the knee.) These expanding and
collapsing flux lines will induce positive and negative EMF surges in a sensing coil properly oriented
around the core. The magnitude of these surges will vary with the strength of the external magnetic
field, and its orientation with respect to the axis of the core and sensing coil of the fluxgate
configuration. The fact that the permeability of the sensor core can be altered in a controlled fashion
by the excitation coil is the underlying principle which enables the DC field being measured to induce
a voltage in the sense coil. The greater the differential between the saturated and unsaturated states
(i.e., the steeper the slope), the more sensitive the instrument will be.
An idealized B-H curve for an alternating H-field is shown in Figure 2.16. The permeability (i.e.,
slope) is high along the section b-c of the curve, and falls to zero on either side of the saturation
points Hs and -Hs, along segments c-d and a-b, respectively. Figure 2.16 shows a more representative
situation: the difference between the left- and right-hand traces is due to hysteresis caused by some
finite amount of permanent magnetization of the material. When a positive magnetizing force Hs is
applied, the material will saturate with flux density Bs at point P1 on the curve. When the magnetizing
force is removed (i.e., H = 0), the flux density drops accordingly, but does not return to zero. Instead,
there remains some residual magnetic flux density Br , shown at point P2, known as the retentivity.
A similar effect is seen in the application of an H-field of opposite polarity. The flux density goes
into saturation at point P3, then passes through point P4 as the field reverses. This hysteresis effect
can create what is known as a zero offset (i.e., some DC bias is still present when the external B-field
is zero) in fluxgate magnetometers. Primdahl (1970) provides an excellent mathematical analysis of
the actual gating curves for fluxgate devices.
The effective permeability µa of a material is influenced to a significant extent by its geometry.
Bozorth and Chapin [1942] showed how µa for a cylindrical rod falls off with a decrease in the
length-to-diameter ratio. This relationship can be attributed to the so-called demagnetization factor
[Hine, 1968]. When a ferrous rod is coaxially aligned with the lines of flux of a magnetic field, a
magnetic dipole is developed in the rod itself. The associated field introduced by the north and south
poles of this dipole opposes the ambient field, with a corresponding reduction of flux density through
the rod. The lowered value of µa results in a less sensitive magnetometer, in that the “flux-gathering"
50
Part I Sensors for Mobile Robot Positioning
Figure 2.16: a. Ideal B-H curve.
b. Some minor hysteresis in the actual curve results in a residual non-zero
value of B when H is reduced to zero, known as the retentivity. (Adapted from
Halliday and Resnick, 1974; Carlson and Gisser, 1981).
capability of the core is substantially reduced.
Consider again the cylindrical rod sensor presented in Figure 2.17, now in the absence of any
external magnetic field Be. When the drive coil is energized, there will be a strong coupling between
the drive coil and the sense coil. Obviously, this will be an undesirable situation since the output signal
is supposed to be related to the strength of the external field only.
One way around this problem is seen in the Vacquier configuration developed in the early 1940s,
where two parallel rods collectively form the core, with a common sense coil [Primdahl, 1979] as
illustrated in Figure 2.17. The two rods are simultaneously forced into and out of saturation, excited
in antiphase by identical but oppositely
wound solenoidal drive windings. In this
Core
fashion, the magnetization fluxes of the two
Sensitive
drive windings effectively cancel each other,
axis
with no net effect on the sense coil.
Bridges of magnetic material may be
S
employed to couple the ends of the two coils
together in a closed-loop fashion for more
complete flux linkage through the core. This
configuration is functionally very similar to
Sense
the ring-core design first employed in 1928
coil
by Aschenbrenner and Goubau [Geyger,
1957]. An alternative technique for decoupling the pickup coil from the drive coil is to
arrange the two in an orthogonal fashion. In
S
practice, there are a number of different
D
implementations of various types of sensor
D
cores and coil configurations as described by Figure 2.17: Identical but oppositely wound drive
Stuart [1972] and Primdahl [1979]. These windings in the Vacquier configuration cancel the net
are generally divided into two classes, paral- effect of drive coupling into the surrounding sense coil,
lel and orthogonal, depending on whether the while still saturating the core material. (Adapted from
[Primdahl, 1979].)
Chapter 2: Heading Sensors
51
excitation H-field is parallel or perpendicular
to the external B-field being measured. Alternative excitation strategies (sine wave,
square wave, sawtooth ramp) also contribute
to the variety of implementations seen in the
literature. Hine [1968] outlines four different
classifications of saturable inductor magnetometers based on the method of readout
(i.e., how the output EMF is isolated for
evaluation):
Fundamental frequency.
Second harmonic.
Peak output.
Pulse difference.
Sensing
winding 1
Drive
winding
Toroidal
core
Sensing
winding 2
Drive
winding
Figure 2.18: Two channel ring core fluxgate with
toroidal excitation. (Adapted from [Acuna and Pellerin,
1969].)
Unambiguous 360-degree resolution of
the earth’s geomagnetic field requires two
sensing coils at right angles to each other. The ring-core geometry lends itself to such dual-axis
applications in that two orthogonal pickup coils can be configured in a symmetrical fashion around
a common core. A follow-up version developed by Gordon and Lundsten [1970] employed a toroidal
excitation winding as shown in Figure 2.19. Since there are no distinct poles in a closed-ring design,
demagnetization effects, although still present [Stuart, 1972], are less severe. The use of a ring
geometry also leads to more complete flux linkage throughout the core, implying less required drive
excitation for lower power operation, and the zero offset can be minimized by rotating the circular
core. For these reasons, along with ease of manufacture, toroidal ring-core sensors are commonly
employed in many of the low-cost fluxgate compasses available today.
The integrated DC output voltages Vx and Vy of the orthogonal sensing coils vary as sine and
cosine functions of , where is the angle of the sensor unit relative to the earth’s magnetic field.
The instantaneous value of can be easily derived by performing two successive A/D conversions
on these voltages and taking the arctangent of their quotient:
S
120o
He
Hx sin wt
S
P
Primary
He
S
Figure 2.19: The Sperry Flux Valve consisted of a common drive winding P in the center of
three sense windings S symmetrically arranged 120 apart. (Adapted from [Hine, 1968].)
52
Part I Sensors for Mobile Robot Positioning
arctan
Vx
Vy
.
(2.11)
Another popular two-axis core design is seen in the Flux Valve magnetometer developed by
Sperry Corp. [SPERRY] and shown in Figure 2.19. This three-legged spider configuration employs
three horizontal sense coils 120 degrees apart, with a common vertical excitation coil in the middle
[Hine, 1968]. Referring to Figure 2.20, the upper and lower “arms” of the sense coil S are excited
by the driving coil D, so that a magnetizing force H x developed as indicated by the arrows. In the
absence of an external field He, the flux generated in the upper and lower arms by the excitation coil
is equal and opposite due to symmetry.
When this assembly is placed in an axial magnetic field He, however, the instantaneous excitation
field Hx complements the flow in one arm, while opposing the flow in the other. This condition is
periodically reversed in the arms, of course, due to the alternating nature of the driving function. A
second-harmonic output is induced in the sensing coil S, proportional to the strength and orientation
of the ambient field. By observing the relationships between the magnitudes of the output signals from
each of the three sense coils (see Figure 2.20), the angular relationship of the Flux Valve with respect
to the external field can be unambiguously determined.
a
b
Figure 2.20: The Flux Valve magnetometer developed by Sperry Corporation uses a
spider-core configuration. (Adapted from [Lenz, 1990].)
When maintained in a level attitude, the fluxgate compass will measure the horizontal component
of the earth’s magnetic field, with the decided advantages of low power consumption, no moving
parts, intolerance to shock ad vibration, rapid start-up, and relatively low cost. If the vehicle is
expected to operate over uneven terrain, the sensor coil should be gimbal-mounted and mechanically
dampened to prevent serious errors introduced by the vertical component of the geomagnetic field.
2.4.2.1 Zemco Fluxgate Compasses
The Zemco fluxgate compass [ZEMCO] was used in earlier work by Everett et al. [1990] on their
robot called ROBART II. The sensor was a fluxgate compass manufactured by Zemco Electronics,
San Ramon, CA, model number DE-700. This very low-cost (around $40) unit featured a rotating
analog dial and was originally intended for 12 VDC operation in automobiles.
Chapter 2: Heading Sensors
53
A system block diagram is presented in Figure 2.21. The sensor consists of two orthogonal pickup
coils arranged around a toroidal excitation coil, driven in turn by a local oscillator. The outputs V x
and Vy of amplifier channels A and B are applied across an air-core resolver to drive the display
indicator. The standard resolver equations [ILC Corporation, 1982] for these two voltages are
Vx = Kx sin sin(%t + ax)
(2.12a)
Vy = Ky cos sin(%t + ay)
(2.12b)
where
= the resolver shaft angle
% = 2f, where f is the excitation frequency.
K x and Ky are ideally equal transfer-function constants, and ax and ay are ideally zero time-phase
shifts.
Thus, for any static spatial angle , the equations reduce to
Vx = Kx sin
(2.13a)
Vy = Ky cos
(2.13b)
which can be combined to yield
sin tan .
cos
VY
Vx
(2.14)
The magnetic heading therefore is simply the
arctangent of Vx over Vy.
Everett [1995] recounts
his experience with two models of the Zemco fluxgate
compass on ROBART II as
follows:
Problems associated with
the use of this particular
fluxgate
compass
on
ROBART, however, included
a fairly high current consumption (250 mA), and
stiction in the resolver reflecting back as a load into
the drive circuitry, introducing some error for minor
Amplifier
Fluxgate
sensor
Driver
Oscillator
Air
core
resolver
Driver
Amplifier
Driver
Figure 2.21: Block diagram of ZEMCO Model DE-700 fluxgate compass.
(Courtesy of ZEMCO, Inc.)
54
Part I Sensors for Mobile Robot Positioning
changes in vehicle heading. In addition, the sensor itself was affected by surrounding magnetic
anomalies, some that existed on board the robot (i.e., current flow in nearby cable runs, drive and
head positioning motors), and some present in the surrounding environment (metal desks,
bookcases, large motors, etc.).
The most serious interference turned out to be the fluctuating magnetic fields due to power
cables in close proximity — on the order of 30 centimeters (12 in) — to the fluxgate sensor. As
various auxiliary systems on board the robot were turned on when needed and later deactivated
to save power, the magnetic field surrounding the sensor would change accordingly. Serious errors
could be introduced as well by minor changes in the position of cable runs, which occurred as a
result of routine maintenance and trouble shooting. These problems were minimized by securing
all cable runs with plastic tie-downs, and adopting a somewhat standardized protocol regarding
which auxiliary systems would be activated when reading the compass.
There was no solution, however, for the interference effects of large metallic objects within the
operating environment, and deviations of approximately four degrees were observed when passing
within 30 centi-meters (12 in) of a large metal cabinet, for example. A final source of error was
introduced by virtue of the fact that the fluxgate compass had been mounted on the robot’s head,
so as to be as far away as possible from the effects of the drive motors and power distribution lines
discussed above. The exact head position could only be read to within 0.82 degrees due to the
limited resolution of the 8-bit A/D converter. In any event, an overall system error of ±10 degrees
was typical, and grossly insufficient for reliable dead-reckoning calculations, which was not the
original intent of the compass.
This analog compass was later replaced by a newer digital version produced by Zemco, model
DE-710, which cost approximately $90. The system block diagram is shown in Figure 2.22. This
unit contained a built-in ADC0834 A/D converter to read the amplified outputs of the two sensor
channels, and employed its own COP 421-MLA microprocessor, which drove a liquid crystal
display (LCD). All communication between the A/D converter, microprocessor, and display driver
was serial in nature, with a resulting slow update rate of 0.25 Hz. The built-in LCD simulated an
analog dial with an extremely coarse resolution of 20 between display increments, but provision
Amplifier
Fluxgate
sensor
Driver
Oscillator
Analog
to
digital
convertor
Microprocessor
Display
Driver
Amplifier
Driver
Figure 2.22: Block diagram of ZEMCO model DE-710 fluxgate compass (courtesy ZEMCO, Inc.).
Chapter 2: Heading Sensors
55
was made for serial output to an optional external shift register and associated three-digit
numerical display.
All things considered, it was determined to be more practical to discard the built-in
microprocessor, A/D converter, and LCD display, and interface an external A/D converter directly
to the amplifier outputs as before with the analog version. This resulted in a decrease in supply
current from 168 to 94 mA. Power consumption turned out to be less of a factor when it was
discovered the circuitry could be powered up for a reading, and then deactivated afterwards with
no noticeable effect on accuracy.
Overall system accuracy for this configuration was typically ±6 degrees, although a valid
comparison to the analog version is not possible since the digital model was mounted in a different
location to minimize interference from nearby circuitry. The amount of effort put into the
calibration of the two systems must also be taken into account; the calibration procedure as
performed was an iterative process not easily replicated from unit to unit with any quantitative
measure.
2.4.2.2 Watson Gyrocompass
A combination fluxgate compass and solid-state rate gyro package (part number FGM-G100DHSRS232) is available from Watson Industries, Eau Claire, WI [WATSON]. The system contains its
own microprocessor that is intended to integrate the information from both the rate gyro and the
compass to provide a more stable output less susceptible to interference, with an update rate of
40 Hz. An overall block diagram is presented in Figure 2.23.
HDG
select
HDG
A/D
Angular
rate
sensor
Damping
function
D/A
Bias
Fluxgate
sensor
HDG Hold
HDG Trim (+)
HDG Trim (-)
RS-232
interface
Error
A/D
3 /sec
Figure 2.22: Block diagram of Watson fluxgate compass and rate gyro combination. (Courtesy of
[WATSON].)
56
Part I Sensors for Mobile Robot Positioning
The Watson fluxgate/rate gyro combination balances the shortcomings of each type of device:
the gyro serves to filter out the effects of magnetic anomalies in the surrounding environment, while
the compass counters the long-term drift of the gyro. Furthermore, the toroidal ring-core fluxgate
sensor is gimbal-mounted for improved accuracy.
The Watson unit measures 6.3×4.4×7.6 centimeters (2.5×1.75×3.0 in) and weighs only 275 grams
(10 oz). This integrated package is a much more expensive unit ($2,500) than the low-cost Zemco
fluxgate compass, but is advertised to have higher accuracy (±2). Power supply requirements are
12 VDC at 200 mA, and the unit provides an analog voltage output as well as a 12-bit digital output
over a 2400-baud RS-232 serial link.
2.4.2.3 KVH Fluxgate Compasses
KVH Industries, Inc., Middletown, RI, offers a complete line of fluxgate compasses and related
accessories, ranging from inexpensive units targeted for the individual consumer up through
sophisticated systems intended for military applications [KVH]. The C100 COMPASS ENGINE (see
Figure 2.24) is a versatile low-cost (less than $700) developer's kit that includes a microprocessorcontrolled stand-alone fluxgate sensor subsystem based on a two-axis toroidal ring-core sensor.
Figure 2.24: The C-100 fluxgate compass engine was tested at the
University of Michigan in a flying robot prototype. (Courtesy of
[KVH].)
Two different sensor options are offered with the C-100: 1) the SE-25 sensor, recommended for
applications with a tilt range of ±16 degrees and 2) the SE-10 sensor, for applications anticipating
a tilt angle of up to ±45 degrees. The SE-25 sensor provides internal gimballing by floating the sensor
coil in an inert fluid inside the lexan housing.The SE-10 sensor provides an additional 2-degree-offreedom pendulous gimbal in addition to the internal fluid suspension. The SE-25 sensor mounts on
top of the sensor PC board, while the SE-10 is suspended beneath it. The sensor PC board can be
Chapter 2: Heading Sensors
57
separated as much as 122 centimeters (48 in) from the detachable electronics PC board with an
optional cable if so desired.
The resolution of the C100 is ±0.1 degrees, with an advertised accuracy of ±0.5 degrees (after
compensation, with the sensor card level) and a repeatability of ±0.2 degrees. Separate ±180 degree
adjustments are provided for declination as well as index offset (in the event the sensor unit cannot
be mounted in perfect alignment with the vehicle’s axis of travel). System damping can be userselected, anywhere in the range of 0.1 to 24 seconds settling time to final value.
An innovative automatic compensation algorithm employed in the C100 is largely responsible for
the high accuracy obtained by such a relatively low-priced system. This software routine runs on the
controlling microprocessor mounted on the electronics board and corrects for magnetic anomalies
associated with the host vehicle. Three alternative user-selectable procedures are offered:
Eight-Point Auto-Compensation — starting from an arbitrary heading, the platform turns full
circle, pausing momentarily at approximately 45-degree intervals. No known headings are
required.
Circular Auto-Compensation — Starting from an arbitrary position, the platform turns slowly
through a continuous 360-degree circle. No known headings are required.
Three-Point Auto-Compensation — Starting from an arbitrary heading, the platform turns and
pauses on two additional known headings approximately 120 degrees apart.
Correction values are stored in a look-up table in non-volatile EEPROM memory. The automatic
compensation routine also provides a quantitative indicator of the estimated quality of the current
compensation and the magnitude of any magnetic interference present [KVH Industries, 1993].
The C100 configured with an SE-25 coil assembly weighs just 62 grams (2.25 oz) and draws
40 mA at 8 to 18 VDC (or 18 to 28 VDC). The combined sensor and electronics boards measure
4.6×11 centimeters (1.8×4.5 in). RS-232 (300 to 9600 baud) and NMEA 0183 digital outputs are
provided, as well as linear and sine/cosine analog voltage outputs. Display and housing options are
also available.
2.4.3 Hall-Effect Compasses
Hall-effect sensors are based on E. H. Hall's observation (in 1879) that a DC voltage develops across
a conductor or semiconductor when in the presence of an external magnetic field. One advantage
of this technology (i.e., relative to the fluxgate) is the inherent ability to directly sense a static flux,
resulting in much simpler readout electronics. Early Hall magnetometers could not match the
sensitivity and stability of the fluxgate [Primdahl, 1979], but the sensitivity of Hall devices has
improved significantly. The more recent indium-antimonide devices have a lower sensitivity limit
of 10-3 Gauss [Lenz, 1990].
The U.S. Navy in the early 1960s showed considerable interest in a small solid-state Hall-effect
compass for low-power extended operations in sonobuoys [Wiley, 1964]. A number of such
prototypes were built and delivered by Motorola for evaluation. The Motorola Hall-effect compass
employed two orthogonal Hall elements for temperature-nulled non-ambiguous resolution of the
geomagnetic field vector. Each sensor element was fabricated from a 2×2×0.1 millimeter indiumarsenide-ferrite sandwich, and inserted between two wing-like mumetal flux concentrators as shown
in Figure 2.25. It is estimated the 5 centimeter (2 in) magnetic concentrators increased the flux
density through the sensing elements by two orders of magnitude [Wiley, 1964]. The output of the
Motorola unit was a variable-width pulse train, the width of the pulse being proportional to the
58
Part I Sensors for Mobile Robot Positioning
Fe
Fe
Indium
arsenide
Fe
Fe
Indium
arsenide
Figure 2.25: A pair of indium-arsenide-ferrite Hall-effect sensors (one
shown) are positioned between flux concentrating wings of mumetal in
this early Motorola prototype. (Adapted from [Wiley, 1964].)
sensed magnetic heading. Excellent response linearity was reported down to flux densities of 0.001
Gauss [Willey, 1962].
Maenaka et al. [1990] report on the development of a monolithic silicon magnetic compass at the
Toyohashi University of Technology in Japan, based on two orthogonal Hall-effect sensors. Their use
of the terminology “magnetic compass” is perhaps an unfortunate misnomer in that the prototype
device was tested with an external field of 1,000 Gauss. Contrast this with the strength of the earth’s
magnetic field, which varies from only about 0.1 Gauss at the equator to about 0.9 Gauss at the poles.
Silicon-based Hall-effect sensors have a lower sensitivity limit of around 10 Gauss [Lenz, 1990]. It
is likely the Toyohashi University device was intended for other than geomagnetic applications, such
as remote position sensing of rotating mechanical assemblies.
This prototype Hall-effect magnetometer is still of interest in that it represents a fully selfcontained implementation of a two-axis magnetometer in integrated circuit form. Two vertical Hall
cells [Maenaka et al., 1987] are arranged at right angles (see Figure 2.25) on a 4.7 mm² chip, with
their respective outputs coupled to a companion signal processing IC of identical size. (Two separate
chips were fabricated for the prototype instead of a single integrated unit to enhance production
yield.) The sensor and signal processing ICs are interconnected (along with some external variable
resistors for calibration purposes) on a glass-epoxy printed circuit board.
The dedicated signal-processing circuitry converts the B-field components Bx and By measured by
the Hall sensors into an angle by means of the analog operation [Maenaka et al., 1990]:
arctan
Bx
By
(2.15)
where
= angle between B-field axis and sensor
Bx = x-component of B-field
By = y-component of B-field.
The analog output of the signal-processing IC is a DC voltage which varies linearly with vector
orientation of the ambient magnetic field in a plane parallel to the chip surface. Reported test results
show a fairly straight-line response (i.e., ± 2 percent full scale) for external field strengths ranging
from 8,000 Gauss down to 500 Gauss; below this level performance begins to degrade rapidly
[Maenaka et al., 1990]. A second analog output on the IC provides an indication of the absolute value
of field intensity.
Chapter 2: Heading Sensors
59
While the Toyohashi “magnetic compass” prototype based on silicon Hall-effect technology is
incapable of detecting the earth’s magnetic field, it is noteworthy nonetheless. A two-axis monolithic
device of a similar nature employing the more sensitive indium-antimonide Hall devices could
potentially have broad appeal for low-cost applications on mobile robotic platforms. An alternative
possibility would be to use magnetoresistive sensor elements, which will be discussed in the next
section.
2.4.4 Magnetoresistive Compasses
The general theory of operation for AMR and GMR magnetoresistive sensors for use in short-range
proximity detection is beyond the scope of this text. However, there are three specific properties of
the magnetoresistive magnetometer that make it well suited for use as a geomagnetic sensor: 1) high
sensitivity, 2) directionality, and, in the case of AMR sensors, 3) the characteristic “flipping” action
associated with the direction of internal magnetization.
AMR sensors have an open-loop sensitivity range of 10 -2 Gauss to 50 Gauss (which easily covers
the 0.1 to 1.0 Gauss range of the earth’s horizontal magnetic field component), and limitedbandwidth closed-loop sensitivities approaching 10 -6 Gauss [Lenz, 1990]. Excellent sensitivity, low
power consumption, small package size, and decreasing cost make both AMR and GMR sensors
increasingly popular alternatives to the more conventional fluxgate designs used in robotic vehicle
applications.
2.4.4.1 Philips AMR Compass
One of the earliest magnetoresistive sensors to be applied to a magnetic compass application is the
KMZ10B offered by Philips Semiconductors BV, The Netherlands [Dibburn and Petersen, 1983;
Kwiatkowski and Tumanski, 1986; Petersen, 1989]. The limited sensitivity of this device
(approximately 0.1 mV/A/m with a supply voltage of 5 VDC) in comparison to the earth’s maximum
horizontal magnetic field (15 A/m) means that considerable attention must be given to error-inducing
effects of temperature and offset drift [Petersen, 1989].
One way around these problems is to exploit the “flipping” phenomenon by driving the device
back and forth between its two possible magnetization states with square-wave excitation pulses
applied to an external coil (Figure 2.26). This switching action toggles the sensor’s axial magnetic
field as shown in Figure 2.26a, resulting in the alternating response characteristics depicted in
Figure 2.26b. Since the sensor offset remains unchanged while the signal output due to the external
magnetic field Hy is inverted (Figure 2.26a), the undesirable DC offset voltages can be easily isolated
from the weak AC signal.
A typical implementation of this strategy is shown in Figure 2.27. A 100 Hz square wave
generator is capacitively coupled to the external excitation coil L which surrounds two orthogonally
mounted magnetoresistive sensors. The sensors' output signals are amplified and AC-coupled to a
60
Part I Sensors for Mobile Robot Positioning
Vo
Magnetizing current
I
Time
Magnetization
Offset
Hy
M
Time
Sensor signal
V
a.
b.
Offset
Time
Figure 2.26: External current pulses set and reset the direction of magnetization,
resulting in the “flipped” response characteristics shown by the dashed line. Note
the DC offset of the device remains constant, while the signal output is inverted.
(Adapted from [Petersen, 1989].)
synchronous detector driven by the same square-wave source. The rectified DC voltages VH1 and VH2
are thus proportional to the measured magnetic field components H1 and H2 . The applied field
direction is dependant on the ratio of V to H, not their absolute values. This means that as long as the
two channels are calibrated to the same sensitivity, no temperature correction is required [Fraden,
1993].
2.4.5 Magnetoelastic Compasses
A number of researchers have recently investigated the use of magnetoelastic (also known as
magnetostrictive) materials as sensing elements for high-resolution magnetometers. The principle of
operation is based on the changes in Young’s modulus experienced by magnetic alloys when exposed
to an external magnetic field. The modulus of elasticity E of a given material is basically a measure
of its stiffness, and directly relates stress to strain as follows:
E
(2.16)
where
E = Young’s modulus of elasticity
= applied stress
= resulting strain.
Any ferromagnetic material will experience some finite amount of strain (expansion or shrinkage)
in the direction of magnetization due to this magnetostriction phenomenon. It stands to reason that
if the applied stress remains the same, strain will vary inversely with any change in Young’s
modulus E. In certain amorphous metallic alloys, this effect is very pronounced.
Barrett et al. [1973] proposed a qualitative explanation, wherein individual atoms in the crystal
lattice are treated as tiny magnetic dipoles. The forces exerted by these dipoles on one another depend
upon their mutual orientation within the lattice; if the dipoles are aligned end to end, the opposite
Chapter 2: Heading Sensors
61
H1
Sensors
H2
R
VB
Square-wave
generator
C
L
Coil L
V(H)1
Sensor
Amplifier
Synchronous
detector
V(H)2
Figure 2.27: Block diagram of a two-axis magnetic compass system
based on a commercially available anisotropic magnetoresistive
sensor from Philips [Petersen, 1989].
poles attract, and the material shrinks ever so slightly. The crystal is said to exhibit a negative
magnetostriction constant in this direction. Conversely, if the dipoles are rotated into side-by-side
alignment through the influence of some external field, like poles will repel, and the result is a small
expansion.
It follows that the strength of an unknown magnetic field can be accurately measured if a suitable
means is employed to quantify the resulting change in length of some appropriate material displaying
a high magnetostriction constant. There are currently at least two measurement technologies with the
required resolution allowing the magnetoelastic magnetometer to be a realistic contender for highsensitivity low-cost performance: 1) interferometric displacement sensing, and 2) tunneling-tip
displacement sensing.
Lenz [1990] describes a magnetoelastic magnetometer which employs a Mach-Zender fiber-optic
interferometer to measure the change in length of a magnetostrictive material when exposed to an
external magnetic field. A laser source directs a beam of light along two optical fiber paths by way
of a beam splitter as shown in Figure 2.28. One of the fibers is coated with a material (nickel iron was
used) exhibiting a high magnetostrictive constant. The length of this fiber is stretched or compressed
Optical
fiber
Laser
diode
Sensing leg
Light coupler
Photodetectors
Reference leg
Figure 2.28: Fiber-optic magnetometers, basically a Mach-Zender interferometer with one
fiber coated or attached to a magnetoelastic material, have a sensitivity range of 10 -7 to 10
Gauss. (Adapted from [Lenz, 1990].)
62
Part I Sensors for Mobile Robot Positioning
in conjunction with any magnetoelastic expansion or contraction of its coating. The output beam from
this fiber-optic cable is combined in a light coupler with the output beam from the uncoated reference
fiber and fed to a pair of photodetectors.
Constructive and destructive interferences caused by differences in path lengths associated with
the two fibers will cause the final output intensity as measured by the photodetectors to vary
accordingly. This variation is directly related to the change in path length of the coated fiber, which
in turn is a function of the magnetic field strength along the fiber axis. The prototype constructed by
Lenz [1990] at Honeywell Corporation measured 10×2.5 centimeters (4×1 in) and was able to detect
fields ranging from 10-7 Gauss up to 10 Gauss.
Researchers at the Naval Research Laboratory (NRL) have developed a prototype magnetoelastic
magnetometer capable of detecting a field as small as 6×10-5 Gauss [Brizzolara et al., 1989] using the
tunneling-tip approach. This new displacement sensing technology, invented in 1982 at IBM Zürich,
is based on the measurement of current generated by quantum mechanical tunneling of electrons
across a narrow gap (Figure 2.29). An analog feedback circuit compares the measured tunnel current
with a desired value and outputs a drive signal to suitably adjust the distance between the tunneling
electrodes with an electromechanical actuator [Kenny et al., 1991]. The instantaneous tunneling
current is directly proportional to the exponential of electrode displacement. The most common
actuators employed in this role are piezoelectric and electrostatic, the latter lending itself more readily
to silicon micro-machining techniques.
Cantilever
Tip
Surface
Figure 2.29: Scanning tunneling microscopy, invented at IBM Zürich in
1982, uses quantum mechanical tunneling of electrons across a barrier
to measure separation distance at the gap. (Courtesy of T. W. Kenny,
NASA JPL).
The active sense element in the NRL magnetometer is a 10 centimeter (4 in) metallic glass ribbon
made from METGLAS 2605S2, annealed in a transverse magnetic field to yield a high
magnetomechanical coupling [Brizzolara et al., 1989]. (METGLAS is an alloy of iron, boron, silicon,
and carbon, and is a registered trademark of Allied Chemical.) The magnetoelastic ribbon elongates
when exposed to an axial magnetic field, and the magnitude of this displacement is measured by a
tunneling transducer as illustrated in Figure 2.30.
An electrochemically etched gold tip is mounted on a tubular piezoelectric actuator and positioned
within about one nanometer of the free end of the METGLAS ribbon. The ribbon and tip are
electrically biased with respect to each other, establishing a tunneling current that is fed back to the
piezo actuator to maintain a constant gap separation. The degree of magnetically induced elongation
of the ribbon can thus be inferred from the driving voltage applied to the piezoelectric actuator. The
solenoidal coil shown in the diagram supplies a bias field of 0.85 oersted to shift the sensor into its
region of maximum sensitivity.
Chapter 2: Heading Sensors
63
High
voltage
amps
Electronics
feedback
It
Vbias
Lecroy
scope
Solenoid coils
Tunneling
tip
piezo
Quartz tube
Approach Tunneling tip
mechanism
Magnetostrictive
ribbon
Figure 2.30: The NRL tunneling-transducer magnetometer employed a 10 cm (4 in)
magnetoelastic ribbon vertically supported in a quartz tube [Brizzolara et al., 1989].
Fenn et al. [1992] propose an alternative tunneling-tip magnetoelastic configuration with a
predicted sensitivity of 2×10-11 Gauss, along the same order of magnitude as the cryogenically cooled
SQUID. A small cantilevered beam of METGLAS 2605S2, excited at its resonant frequency by a
gold-film electrostatic actuator, is centered between two high-permeability magnetic flux
concentrators as illustrated in Figure 2.31. Any changes in the modulus of elasticity of the beam will
directly affect its natural frequency; these changes in natural frequency can then be measured and
directly related to the strength of the ambient magnetic field. The effective shift in natural frequency
is rather small, however (Fenn et al. [1992] report only a 6 Hz shift at saturation), again necessitating
a very precise method of measurement.
0.7 mm
0.7 mm
NS
Metglas
cantilever
Flux
guide
Flux
guide
Substrate
NS
1or 5 cm
Figure 2.31: Top view of the single cantilevered design. (Adapted from [Fenn, et al., 1992].)
A second (non-magnetic) cantilever element is employed to track the displacement of the
METGLAS reed with sub-angstrom resolution using tunneling-tip displacement sensing as illustrated
in Figure 2.32. A pair of electrostatic actuator plates dynamically positions the reed follower to
maintain a constant tunneling current in the probe gap, thus ensuring a constant lateral separation
between the probe tip and the vibrating reed. The frequency of the excitation signal applied to the
reed-follower actuator is therefore directly influenced by any resonant frequency changes occurring
in the METGLAS reed. The magnetometer provides an analog voltage output which is proportional
to this excitation frequency, and therefore indicative of the external magnetic field amplitude.
Excitation
actuator
Metglas reed
Tunneling tip
cantelever
Reed following
actuator
Figure 2.32: Side view of the double cantilevered design. (Adapted from
[Fenn et al., 1992].)
Chapter 3: Active Beacons
65
CHAPTER 3
GROUND-BASED RF-BEACONS AND GPS
In this chapter we discuss sensors used for active beacon navigation. Active beacons have been
used for many centuries as a reliable and accurate means for navigation. Stars can be considered as
active beacons with respect to navigation; and lighthouses were early man-made beacon systems.
Typical non-robotics applications for active beacon navigation include marine navigation, aircraft
navigation, race car performance analysis, range instrumentation, unmanned mobile target control,
mine localization, hazardous materials mapping, dredge positioning, geodetic surveys, and most
recently, position location and range information for golfers [Purkey, 1994].
Modern technology has vastly enhanced the capabilities of active beacon systems with the
introduction of laser, ultrasonic, and radio-frequency (RF) transmitters. It should be noted, though,
that according to our conversations with manufacturers, none of the RF systems can be used reliably
in indoor environments. Ground-based RF systems will be discussed in Section 3.1.
However, the most revolutionary technology for outdoor navigation is the recently completed Global
Positioning System (GPS). Because of the rapidly increasing popularity of GPSs we have dedicated
a large portion of this chapter to this subject. Section 3.2 explains GPS technology, Section 3.3
includes a major comparative study of five different GPS receivers [Byrne, 1993], and Section 3.4
presents some state-of-the-art commercially available systems.
3.1 Ground-Based RF Systems
Ground-based RF position location systems are typically of two types:
Passive hyperbolic line-of-position phase-measurement systems that compare the time-of-arrival
phase differences of incoming signals simultaneously emitted from surveyed transmitter sites.
Active radar-like trilateration systems that measure the round-trip propagation delays for a
number of fixed-reference transponders. Passive systems are generally preferable when a large
number of vehicles must operate in the same local area, for obvious reasons.
3.1.1 Loran
An early example of the first category is seen in Loran (short for long range navigation).
Developed at MIT during World War II, such systems compare the time of arrival of two identical
signals broadcast simultaneously from high-power transmitters located at surveyed sites with a
known separation baseline. For each finite time difference (as measured by the receiver) there is an
associated hyperbolic line of position as shown in Figure 3.1. Two or more pairs of master/slave
stations are required to get intersecting hyperbolic lines resulting in a two-dimensional (latitude and
longitude) fix.
The original implementation (Loran A) was aimed at assisting convoys of liberty ships crossing
the North Atlantic in stormy winter weather. Two 100 kW slave transmitters were located about 200
miles on either side of the master station. Non-line-of-sight ground-wave propagation at around 2
MHz was employed, with pulsed as opposed to continuous-wave transmissions to aid in sky-wave
66
Part I Sensors for Mobile Robot Positioning
Vehicle
C
A
Master
Transmitter
B
Slave
Transmitter
Figure 3.1: For each hyperbolic line-of-position, length
ABC minus length AC equals some constant K. (Adapted
from [Dodington, 1989].)
discrimination. The time-of-arrival difference was simply measured as the lateral separation of the
two pulses on an oscilloscope display, with a typical accuracy of around 1 µs. This numerical value
was matched to the appropriate line of position on a special Loran chart of the region, and the
procedure then repeated for another set of transmitters. For discrimination purposes, four different
frequencies were used, 50 kHz apart, with 24 different pulse repetition rates in the neighborhood of
20 to 35 pulses per second [Dodington, 1989]. In situations where the hyperbolic lines intersected
more or less at right angles, the resulting (best-case) accuracy was about 1.5 kilometers.
Loran A was phased out in the early ‘80s in favor of Loran C, which achieves much longer overthe-horizon ranges through use of 5 MW pulses radiated from 400-meter (1300 ft) towers at a lower
carrier frequency of 100 kHz. For improved accuracy, the phase differences of the first three cycles
of the master and slave pulses are tracked by phase-lock-loops in the receiver and converted to a
digital readout, which is again cross-referenced to a preprinted chart. Effective operational range is
about 1000 miles, with best-case accuracies in the neighborhood of 100 meters (330 ft). Coverage
is provided by about 50 transmitter sites to all U.S. coastal waters and parts of the North Atlantic,
North Pacific, and the Mediterranean.
3.1.2 Kaman Sciences Radio Frequency Navigation Grid
The Unmanned Vehicle Control Systems Group of Kaman Sciences Corporation, Colorado Springs,
CO, has developed a scaled-down version of a Loran-type hyperbolic position-location system
known as the Radio Frequency Navigation Grid (RFNG). The original application in the late 1970s
involved autonomous route control of unmanned mobile targets used in live-fire testing of the laserguided Copperhead artillery round [Stokes, 1989]. The various remote vehicles sense their position
by measuring the phase differences in received signals from a master transmitter and two slaves
situated at surveyed sites within a 30 km2 (18.75 mi2) area as shown in Figure 3.2. System resolution
is 3 centimeters (1.5 in) at a 20 Hz update rate, resulting in a vehicle positioning repeatability of 1
meter (3.3 ft).
Path trajectories are initially taught by driving a vehicle over the desired route and recording the
actual phase differences observed. This file is then played back at run time and compared to
Chapter 3: Active Beacons
67
measured phase difference values, with vehicle steering servoed in an appropriate manner to null
any observed error signal. Velocity of advance is directly controlled by the speed of file playback.
Vehicle speeds in excess of 50 km/h (30 mph) are supported over path lengths of up to 15 kilometers
(9.4 mi) [Stokes, 1989]. Multiple canned paths can be stored and changed remotely, but vehicle
travel must always begin from a known start point due to an inherent 6.3 meters (20 ft) phase
ambiguity interval associated with the grid [Byrne et al., 1992].
The Threat Array Control and Tracking Information Center (TACTIC) is offered by Kaman
Sciences to augment the RFNG by tracking and displaying the location and orientation of up to 24
remote vehicles [Kaman, 1991]. Real-time telemetry and recording of vehicle heading, position,
velocity, status, and other designated parameters (i.e., fuel level, oil pressure, battery voltage) are
supported at a 1 Hz update rate. The TACTIC operator has direct control over engine start,
automatic path playback, vehicle pause/resume, and emergency halt functions. Non-line-of-sight
operation is supported through use of a 23.825 MHz grid frequency in conjunction with a 72 MHz
control and communications channel.
Figure 3.2: Kaman Sciences 1500 W navigation grid is a scaled-down version of the LORAN concept,
covering an area 8 to 15 km on a side with a position-location repeatability of 1 m. (Courtesy of Kaman
Sciences Corporation.)
3.1.3 Precision Location Tracking and Telemetry System
Precision Technology, Inc., of Saline, MI, has recently introduced to the automotive racing world
an interesting variation of the conventional phase-shift measurement approach (type 1 RF system).
The company’s Precision Location tracking and telemetry system employs a number of receive-only
antennae situated at fixed locations around a racetrack to monitor a continuous sine wave
transmission from a moving vehicle. By comparing the signals received by the various antennae to
a common reference signal of identical frequency generated at the base station, relative changes in
vehicle position with respect to each antenna can be inferred from resulting shifts in the respective
68
Part I Sensors for Mobile Robot Positioning
phase relationships. The 58 MHz VHF signal allows for non-line-of-sight operation, with a resulting
precision of approximately 1 to 10 centimeters (0.4 to 4 in) [Duchnowski, 1992]. From a robotics
perspective, problems with this approach arise when more than one vehicle must be tracked. The
system costs $200,000 to $400,000, depending on the number of receivers used. According to
Duchnowski, the system is not suitable for indoor operations.
3.1.4 Motorola Mini-Ranger Falcon
An example of the active transponder category of ground-based RF position-location techniques is
seen in the Mini-Ranger Falcon series of range positioning systems offered by the Government and
Systems Technology Group of Motorola, Inc, Scottsdale, AZ [MOTOROLA]. The Falcon 484
configuration depicted in Figure 3.3 is capable of measuring line-of-sight distances from 100 meters
(328 ft) out to 75 kilometers (47 miles). An initial calibration is performed at a known location to
determine the turn-around delay (TAD) for each transponder (i.e., the time required to transmit a
response back to the interrogator after receipt of interrogation). The actual distance between the
interrogator and a given transponder is found by [Byrne et al., 1992]:
Display transceiver
unit
Site 1
Site 4
Range processor
Optional
computer
Optional
plotter
Site 2
Site 3
Figure 3.7: Motorola's Mini-Ranger Falcon 484 R position-location system provides 2 m (6.5 ft) accuracy over
ranges of 100 m to 75 km (328 ft to 47 mi). (Courtesy of [MOTOROLA].)
D (Te Td)c
(3.1)
2
where
D = separation distance
Te = total elapsed time
Td = transponder turn-around delay
c = speed of light.
The MC6809-based range processor performs a least-squares position solution at a 1-Hz update
rate, using range inputs from two, three, four, or 16 possible reference transponders. The individual
reference stations answer only to uniquely coded interrogations and operate in C-band (5410 to 5890
MHz) to avoid interference from popular X-band marine radars [Motorola, undated]. Up to 20
Chapter 3: Active Beacons
69
mobile users can time share the Falcon 484 system (50 ms per user maximum). System resolution
is in tenths of units (m, ft, or yd) with a range accuracy of 2 meters (6.5 ft) probable.
Power requirements for the fixed-location reference stations are 22 to 32 VDC at 13 W nominal,
8.5 W standby, while the mobile range processor and its associated transmitter-receiver and display
unit draw 150 W at 22 to 32 VDC. The Falcon system comes in different, customized configurations.
Complete system cost is $75,000 to $100,000.
3.1.5 Harris Infogeometric System
Harris Technologies, Inc., [HTI], Clifton, VA, is developing a ground-based R position location and
communications strategy wherein moderately priced infogeometric (IG) devices cooperatively form
self-organizing instrumentation and communication networks [Harris, 1994]. Each IG device in the
network has full awareness of the identity, location, and orientation of all other IG devices and can
communicate with other such devices in both party-line and point-to-point communication modes.
The IG devices employ digital code-division-multiple-access (CDMA) spread-spectrum R
hardware that provides the following functional capabilities:
Network level mutual autocalibration.
Associative location and orientation tracking.
Party-line and point-to-point data communications (with video and audio options).
Distributed sensor data fusion.
Precision position location on the move is based on high-speed range trilateration from fixed
reference devices, a method commonly employed in many instrumentation test ranges and other
tracking system applications. In this approach, each beacon has an extremely accurate internal clock
that is carefully synchronized with all other beacon clocks. A time-stamped (coded) R signal is
periodically sent by each transmitter. The receiver is also equipped with a precision clock, so that
it can compare the timing information and time of arrival of the incoming signals to its internal clock.
This way, the system is able to accurately measure the signals' time of flight and thus the distance
between the receiver and the three beacons. This method, known as “differential location
regression” [Harris, 1994] is essentially the same as the locating method used in global positioning
systems (GPS).
To improve accuracy over current range-lateration schemes, the HTI system incorporates mutual
data communications, permitting each mobile user access to the time-tagged range measurements
made by fixed reference devices and all other mobile users. This additional network-level range and
timing information permits more accurate time synchronization among device clocks, and automatic
detection and compensation for uncalibrated hardware delays.
Each omnidirectional CDMA spread-spectrum “geometric” transmission uniquely identifies the
identity, location, and orientation of the transmitting source. Typically the available geometric
measurement update rate is in excess of 1000 kHz. Harris quotes a detection radius of 500 meters
(1640 ft) with 100 mW peak power transmitters. Larger ranges can be achieved with stronger
transmitters. Harris also reports on “centimeter-class repeatability accuracy” obtained with a
modified transmitter called an “Interactive Beacon.” Tracking and communications at operating
ranges of up to 20 kilometers (12.5 mi) are also supported by higher transmission power levels of 1
to 3 W. Typical “raw data” measurement resolution and accuracies are cited in Table 3.1.
Enhanced tracking accuracies for selected applications can be provided as cited in Table 3.2. This
significant improvement in performance is provided by sensor data fusion algorithms that exploit the
70
Part I Sensors for Mobile Robot Positioning
high degree of relational redundancy that is characteristic for infogeometric network measurements
and communications.
Infogeometric enhancement algorithms also provide the following capabilities:
Enhanced tracking in multipath and clutter — permits precision robotics tracking even when
operating indoors.
Enhanced near/far interference reduction — permits shared-spectrum operations in potentially
large user networks (i.e., hundreds to thousands).
Table 3.1: Raw data measurement
resolution and accuracy [Everett, 1995].
Parameter
Range
Table 3.2: Enhanced tracking resolution
and accuracies obtained through sensor
data fusion [Everett, 1995].
Resolution
Biasing
1
3.3
5m
16.4 ft
Bearing (Az, El)
2
2
Orientation (Az)
2
2
Parameter
Resolutio
n
Biasing
Range
0.1 - 0.3
0.3 - 0.9
0.1 - 0.3 m
0.3 - 0.9 ft
Bearing
0.5 - 1.0
0.5 - 1.0 Orientation
0.5 - 1.0
0.5 - 1.0 Operationally, mobile IG networks support precision tracking, communications, and command
and control among a wide variety of potential user devices. A complete Infogeometric Positioning
System is commercially available from [HTI], at a cost of $30,000 or more (depending on the
number of transmitters required). In conversation with HTI we learned that the system requires an
almost clear “line of sight” between the transmitters and receivers. In indoor applications, the
existence of walls or columns obstructing the path will dramatically reduce the detection range and
may result in erroneous measurements, due to multi-path reflections.
3.2 Overview of Global Positioning Systems (GPSs)
The recent Navstar Global Positioning System (GPS) developed as a Joint Services Program by the
Department of Defense uses a constellation of 24 satellites (including three spares) orbiting the earth
every 12 hours at a height of about 10,900 nautical miles. Four satellites are located in each of six
planes inclined 55 degrees with respect to the plane of the earth’s equator [Getting, 1993]. The
absolute three-dimensional location of any GPS receiver is determined through simple trilateration
techniques based on time of flight for uniquely coded spread-spectrum radio signals transmitted by
the satellites. Precisely measured signal propagation times are converted to pseudoranges
representing the line-of-sight distances between the receiver and a number of reference satellites in
known orbital positions. The measured distances have to be adjusted for receiver clock offset, as will
be discussed later, hence the term pseudoranges. Knowing the exact distance from the ground
receiver to three satellites theoretically allows for calculation of receiver latitude, longitude, and
altitude.
Although conceptually very simple (see [Hurn, 1993]), this design philosophy introduces at least
four obvious technical challenges:
Time synchronization between individual satellites and GPS receivers.
Precise real-time location of satellite position.
Chapter 3: Active Beacons
71
Accurate measurement of signal propagation time.
Sufficient signal-to-noise ratio for reliable operation in the presence of interference and possible
jamming.
The first of these problems is addressed through the use of atomic clocks (relying on the vibration
period of the cesium atom as a time reference) on each of the satellites to generate time ticks at a
frequency of 10.23 MHz. Each satellite transmits a periodic pseudo-random code on two different
frequencies (designated L1 and L2) in the internationally assigned navigational frequency band. The
L1 and L2 frequencies of 1575.42 and 1227.6 MHz are generated by multiplying the cesium-clock
time ticks by 154 and 128, respectively. The individual satellite clocks are monitored by dedicated
ground tracking stations operated by the Air Force, and continuously advised of their measured
offsets from the ground master station clock. High precision in this regard is critical since electromagnetic radiation propagates at the speed of light, roughly 0.3 meters (1 ft) per nanosecond.
To establish the exact time required for signal propagation, an identical pseudocode sequence is
generated in the GPS receiver on the ground and compared to the received code from the satellite.
The locally generated code is shifted in time during this comparison process until maximum
correlation is observed, at which point the induced delay represents the time of arrival as measured
by the receiver’s clock. The problem then becomes establishing the relationship between the atomic
clock on the satellite and the inexpensive quartz-crystal clock employed in the GPS receiver. This
T is found by measuring the range to a fourth satellite, resulting in four independent trilateration
equations with four unknowns. Details of the mathematics involved are presented by Langley
[1991].
The precise real-time location of satellite position is determined by a number of widely distributed
tracking and telemetry stations at surveyed locations around the world. Referring to Figure 3.4, all
measured and received data are forwarded to a master station for analysis and referenced to
universal standard time. Change orders and signal-coding corrections are generated by the master
station and then sent to the satellite control facilities for uploading [Getting, 1993]. In this fashion
the satellites are continuously advised of their current position as perceived by the earth-based
tracking stations, and encode this ephemeris information into their L1 and L2 transmissions to the
GPS receivers. (Ephemeris is the space vehicle orbit characteristics, a set of numbers that precisely
describe the vehicle's orbit when entered into a specific group of equations.)
In addition to its own timing offset and orbital information, each satellite transmits data on all
other satellites in the constellation to enable any ground receiver to build up an almanac after a “cold
start.” Diagnostic information with respect to the status of certain onboard systems and expected
range-measurement accuracy is also included. This collective “housekeeping” message is
superimposed on the pseudo-random code modulation at a very low (50 bits/s) data rate, and
requires 12.5 minutes for complete downloading [Ellowitz, 1992]. Timing offset and ephemeris
information is repeated at 30 second intervals during this procedure to facilitate initial pseudorange
measurements.
To further complicate matters, the sheer length of the unique pseudocode segment assigned to
each individual Navstar Satellite (i.e., around 6.2 trillion bits) for repetitive transmission can
potentially cause initial synchronization by the ground receiver to take considerable time. For this
and other reasons, each satellite broadcasts two different non-interfering pseudocodes. The first of
these is called the coarse acquisition, or C/A code, and is transmitted on the L1 frequency to assist
in acquisition. There are 1023 different C/A codes, each having 1023 chips (code bits) repeated 1000
times a second [Getting, 1993] for an effective chip rate of 1.023 MHz (i.e., one-tenth the cesium
clock rate). While the C/A code alone can be employed by civilian users to obtain a fix, the resultant
72
Part I Sensors for Mobile Robot Positioning
SPACE
CONTROL
USER
Monitor
Stations
Uploading
Station
Master
Station
Figure 3.4: The Navstar Global Positioning System consists of three fundamental segments: Space, Control,
and User. (Adapted from [Getting, 1993].)
positional accuracy is understandably somewhat degraded. The Y code (formerly the precision or
P code prior to encryption on January 1st, 1994) is transmitted on both the L1 and L2 frequencies
and scrambled for reception by authorized military users only with appropriate cryptographic keys
and equipment. This encryption also ensures bona fide recipients cannot be “spoofed” (i.e., will not
inadvertently track false GPS-like signals transmitted by unfriendly forces).
Another major difference between the Y and C/A code is the length of the code segment. While
the C/A code is 1023 bits long and repeats every millisecond, the Y code is 2.35×10 14 bits long and
requires 266 days to complete [Ellowitz, 1992]. Each satellite uses a one-week segment of this total
code sequence; there are thus 37 unique Y codes (for up to 37 satellites) each consisting of
6.18×1012 code bits set to repeat at midnight on Saturday of each week. The higher chip rate of 10.23
MHz (equal to the cesium clock rate) in the precision Y code results in a chip wavelength of 30
meters for the Y code as compared to 300 meters for the C/A code [Ellowitz, 1992], and thus
facilitates more precise time-of-arrival measurement for military purposes.
Brown and Hwang [1992] discuss a number of potential pseudorange error sources as summarized
below in Table 3.3. Positional uncertainties related to the reference satellites are clearly a factor,
introducing as much as 3 meters (9.8 ft) standard deviation in pseudo-range measurement accuracy.
As the radiated signal propagates downward toward the earth, atmospheric refraction and multi-path
reflections (i.e., from clouds, land masses, water surfaces) can increase the perceived time of flight
beyond that associated with the optimal straight-line path (Figure 3.5).
Additional errors can be attributed to group delay uncertainties introduced by the processing and
passage of the signal through the satellite electronics. Receiver noise and resolution must also be
Chapter 3: Active Beacons
73
taken into account. Motazed [1993] reports fairly significant differences of 0.02 to 0.07 arc minutes
in calculated latitudes and longitudes for two identical C/A-code receivers placed side by side. And
finally, the particular dynamics of the mobile vehicle that hosts the GPS receiver plays a noteworthy
role, in that best-case conditions are associated with a static platform, and any substantial velocity and
acceleration will adversely affect the solution.
For commercial applications using Table 3.3: Summary of potential error sources for measured
the C/A code, small errors in timing pseudoranges [Brown and Hwang, 1992].
Error Source
Standard Deviation
and satellite position have been delib[m]
[ft]
erately introduced by the master staSatellite position
3
29
tion to prevent a hostile nation from
Ionospheric refraction
5
16.4
using GPS in support of precision
Tropospheric refraction
2
6.6
weapons delivery. This intentional
Multipath reflection
5
16.4
degradation in positional accuracy to
Selective availability
30
98.4
around 100 meters (328 ft) best case
and 200 meters (656 ft) typical spherical error probable (SEP) is termed
selective availability [Gothard, 1993]. Selective availability has been on continuously (with a few
exceptions) since the end of Operation Desert Storm. It was turned off during the war from August
1990 until July 1991 to improve the accuracy of commercial hand-held GPS receivers used by
coalition ground forces.
There are two aspects of selective availability: epsilon and dither. Epsilon is intentional error in
the navigation message regarding the location (ephemeris) of the satellite. Dither is error in the timing
source (carrier frequency) that creates uncertainty in velocity measurements (Doppler). Some GPS
receivers (for example, the Trimble ENSIGN) employ running-average filtering to statistically reduce
the epsilon error over time to a reported value of 15 meters SEP [Wormley, 1994].
At another occasion (October 1992) SA was also turned off for a brief period while the Air Force
was conducting tests. Byrne [1993] conducted tests at that time to compare the accuracy of GPS with
SA turned on and off. The static measurements of the GPS error as a function of time shown in
Figure 3.6 were taken before the October 1992 test, i.e., with SA "on" (note the slowly varying error
in Figure 3.6, which is caused by SA). By contrast, Figure 3.7 shows measurements from the October
1992 period when SA was briefly "off."
a
b
Figure 3.5: Contributing factors to pseudorange measurement errors:
a. atmospheric refraction; b. multi-path reflections [Everett, 1995].
74
Part I Sensors for Mobile Robot Positioning
Figure 3.6: Typical GPS static position error with SA "On." (Courtesy of [Byrne,
1993].)
Figure 3.7: Typical GPS static position error with SA "Off". (Courtesy of Byrne
[1993]).
Chapter 3: Active Beacons
75
All of the error sources listed in Table 3.3 are further influenced by the particular geometry of the
four reference satellites at time of sighting. Ignoring time synchronization needs for the moment (i.e.,
so only three satellites are required), the most accurate three-dimensional trilater-ation solutions will
result when the bearing or sight lines extending from the receiver to the respective satellites are
mutually orthogonal. If the satellites are spaced close together in a tight cluster or otherwise arranged
in a more or less collinear fashion with respect to the receiver as shown in Figure 3.8, the desired
orthogonality is lost and the solution degrades accordingly.
Terms used to describe the strength of the position fix based on the geometry include: Dilution
of Precision (DOP), Horizontal Dilution of Precision (HDOP), Geometric Dilution of Precision
(GDOP), Position Dilution of Precision (PDOP), Time Dilution of Precision (TDOP), and Vertical
Dilution of Precision (VDOP). The various DOPs are error multipliers that indicate the accuracy
of a particular type of position fix based on a certain pseudo-range error. For instance, if the pseudorange measurements are accurate to 10 meters (33 ft) and the HDOP is equal to 3.5, the horizontal
position accuracy would be 10 × 3.5 = 35 meters (100 ft). A PDOP of 2 or 3 is fairly good, while a
PDOP of 10 is not so good. Certain geometries can cause the DOP to become very large (infinite).
Two useful DOP identities are shown in Equations (3.2) and (3.3).
PDOP2 = VDOP2 + HDOP2
(3.2)
GDOP2 = PDOP2 + TDOP 2
(3.3)
Acronyms used in this section
DOP
dilution of precision
GDOP geometric dilution of
precision
HDOP horizontal dilution of precision
PDOP position dilution of precision
TDOP Time dilution of precision
VDOP vertical dilution of precision
SA
selective availability
Kihara and Okada [1984] show that the minimum
achievable (best-case) value for GDOP is 1.5811. This
optimal constellation occurs when the four required GPS
satellites are symmetrically located with an angle of 109.47
degrees between adjacent bearing lines as shown in
Figure 3.9.
With the exception of multi-path effects, all of the error
sources listed in Table 3.3 above can be essentially eliminated through use of a practice known as
differential GPS (DGPS). The concept is based on the premise that a second GPS receiver in fairly
close proximity (i.e., within 10 km — 6.2 mi) to the first will experience basically the same error
effects when viewing the same reference satellites. If this second receiver is fixed at a precisely
Figure 3.8: Worst-case geometric dilution of precision (GDOP) errors
occur when the receiver and satellites approach a collinear configuration as
shown [Everett, 1995].
76
Part I Sensors for Mobile Robot Positioning
surveyed location, its calculated solution can be
compared to the known position to generate a
Z
composite error vector representative of prevailing
conditions in that immediate locale. This differen_
tial correction can then be passed to the first
e
4
receiver to null out the unwanted effects, effec_
tively reducing position error for commercial
e3
systems to well under 10 meters.
The fixed DGPS reference station transmits
these correction signals every two to four minutes
to any differential-capable receiver within range.
Y
_
Many commercial GPS receivers are available with
e2
differential capability, and most now follow the
_
RTCM-104 standard developed by the Radio
e1
Technical Commission for Maritime Services to
X
promote interoperability. Prices for DGPS-capable Figure 3.9: GDOP error contribution is minimal for
mobile receivers run about $2K, while the refer- four GPS satellites symmetrically situated with
ence stations cost somewhere between $10K and respect to the receiver (at origin) along bearing
o
$20K. Magnavox is working with CUE Network lines 109.47 apart [Kihara and Okada, 1984].
Corporation to market a nationwide network to
pass differential corrections over an FM link to paid subscribers [GPS Report, 1992].
Typical DGPS accuracies are around 4 to 6 meters (13 to 20 ft) SEP, with better performance
seen as the distance between the mobile receivers and the fixed reference station is decreased. For
example, the Coast Guard is in the process of implementing differential GPS in all major U.S.
harbors, with an expected accuracy of around 1 meter (3.3 ft) SEP [Getting, 1993]. A differential
GPS system already in operation at O’Hare International Airport in Chicago has demonstrated that
aircraft and service vehicles can be located to 1 meter (3.3 ft). Surveyors use differential GPS to
achieve centimeter accuracy, but this practice requires significant postprocessing of the collected
data [Byrne, 1993].
An interesting variant of conventional DGPS is reported by Motazed [1993] in conjunction with
the Non-Line-of-Sight Leader/Follower (NLOSLF) program underway at RedZone Robotics, Inc.,
Pittsburgh, PA. The NLOSLF operational scenario involves a number of vehicles in a convoy
configuration that autonomously follow a lead vehicle driven by a human operator, both on-road and
off-road at varying speeds and separation distances. A technique to which Motazed refers as
intermittent stationary base differential GPS is used to provide global referencing for purposes of
bounding the errors of a sophisticated Kalman-filter-based GPS/INS position estimation system.
Under this innovative concept, the lead and final vehicle in the convoy alternate as fixedreference differential GPS base stations. As the convoy moves out from a known location, the final
vehicle remains behind to provide differential corrections to the GPS receivers in the rest of the
vehicles. After traversing a predetermined distance in this fashion, the convoy is halted and the lead
vehicle assumes the role of a differential reference station, providing enhanced accuracy to the
trailing vehicle as it catches up to the pack. During this time, the lead vehicle takes advantage of onsite dwell to further improve the accuracy of its own fix. Once the last vehicle joins up with the rest,
the base-station roles are reversed again, and the convoy resumes transit in “inchworm” fashion
along its intended route. Disadvantages to this approach include the need for intermittent stops and
the accumulating ambiguity in actual location of the appointed reference station.
Chapter 3: Active Beacons
77
Recall the Y-code chip rate is directly equal to the satellite cesium clock rate, or 10.23 MHz.
Since the L1 carrier frequency of 1575.42 MHz is generated by multiplying the clock output by 154,
there are consequently 154 carrier cycles for every Y-code chip. This implies even higher
measurement precision is possible if the time of arrival is somehow referenced to the carrier instead
of the pseudocode itself. Such codeless interferometric differential GPS schemes measure the phase
of the L1 and L2 carrier frequencies to achieve centimeter accuracies, but they must start at a
known geodetic location and typically require long dwell times. The Army’s Engineer Topographic
Laboratories (ETL) is in the process of developing a carrier-phase-differential system of this type
that is expected to provide 1 to 3 centimeters (0.4 to 1.2 in) accuracy at a 60-Hz rate when finished
sometime in 1996 [McPherson, 1991].
A reasonable extraction from the open literature of achievable position accuracies for the various
GPS configurations is presented in Table 3.4. The Y code has dual-frequency estimation for
atmospheric refraction and no S/A error component, so accuracies are better than stand-alone singlefrequency C/A systems. Commercial DGPS accuracy, however, exceeds stand-alone military Y-code
accuracy, particularly for small-area applications such as airports. Differential Y code is currently
under consideration and may involve the use of a satellite to disseminate the corrections over a wide
area.
Table 3.4: Summary of achievable position accuracies for various
implementations of GPS.
GPS Implementation Method
Position Accuracy
C/A-code stand alone
100 m SEP
(328 ft)
Y-code stand alone
16 m SEP
(52 ft)
3 m SEP
(10 ft)
Differential (C/A-code)
Differential (Y-code)
unknown (TBD)
Phase differential (codeless)
1 cm SEP
(0.4 in)
A typical non-differential GPS was tested by Cooper and Durrant-White [1994] and yielded an
accumulated position error of over 40 meters (131 ft) after extensive filtering.
Systems likely to provide the best accuracy are those that combine GPS with Inertial Navigation
Systems (INS), because the INS position drift is bounded by GPS corrections [Motazed, 1993].
Similarly, the combination of GPS with odometry and a compass was proposed by Byrne [1993].
In summary, the fundamental problems associated with using GPS for mobile robot navigation
are as follows:
Periodic signal blockage due to foliage and hilly terrain.
Multi-path interference.
Insufficient position accuracy for primary (stand-alone) navigation systems.
Arradondo-Perry [1992] provides a comprehensive listing of GPS receiver equipment, while
Byrne [1993] presents a detailed evaluation of performance for five popular models. Parts of Byrne's
performance evaluation has been adapted from the original report for inclusion in this survey as
Section 3.3.
78
Part I Sensors for Mobile Robot Positioning
3.3 Evaluation of Five GPS Receivers by Byrne [1993]
In 1992 and 1993 Raymond H. Byrne at the Advanced Vehicle Development Department, Sandia
National Laboratories, Albuquerque, New Mexico conducted a series of in-depth comparison tests
with five different GPS receivers. His results were originally published in September 1993 as Sandia
Report SAND93-0827 UC-515. With permission of the author we have reproduced and adapted
parts of that report in this section.
3.3.1 Project Goals
The intent of Byrne's study was to compare the performance of a particular two-channel,
sequencing GPS receiver (a 10 year old, outdated Magnavox 6400) to that of newer five- and sixchannel parallel receivers. The parallel channel receivers used in this study were selected based upon
availability, cost, size, and receiver specifications.
The receivers tested are listed in Table 3.5. The "original equipment manufacturer" (OEM)
receivers are single board GPS devices that are meant to be integrated into a system or product. The
Trimble and Magnavox 6400 receivers are "integrated" commercial products.
Table 3.5: GPS receivers tested. (Courtesy of Byrne [1993]).
Receiver
Description
Magnavox 6400 (10-year old
system, outdated)
2-channel, sequencing receiver, receiver in
current system, integrated system
Magellan OEM GPS Module
5-channel GPS receiver, OEM type
Magnavox GPS Engine
6-channel GPS receiver, OEM type
Rockwell NavCore V
5-channel GPS receiver, OEM type
Trimble Placer
6-channel receiver, Integrated System
The performance of the current GPS receiver was tested along with four commercially available
receivers. The experiments included static as well as dynamic testing. The results of these tests are
presented in the following section.
3.3.2 Test Methodology
Many parameters may be measured when comparing GPS receivers. Section 3.3.2.1 discusses the
parameters that were chosen to compare the performance of Sandia's old Magnavox 6400 GPS
receiver to newer commercial off the-shelf units. Section 3.3.2.2 describes the test fixture hardware
developed to gather GPS data from the five different receivers, and the post processing of the
gathered data is discussed in Section 3.3.2.3.
Chapter 3: Active Beacons
79
3.3.2.1 Parameters tested
In the experiments performed at Sandia National Laboratories testing focused on receiver sensitivity,
static accuracy, dynamic accuracy, number of satellites tracked, and time-to-first-fix. The tests
aimed at evaluating the five different GPS receivers in both static and dynamic environments. This
section discusses the parameters tested and the rationalization for choosing these parameters.
For many navigation applications time-to-first-fix is an important parameter. The older Magnavox
6400 receiver can take up to 30 minutes to initialize and lock onto the satellite signals before it starts
navigating. However, all of the newer receivers advertise fast position fixes, usually under one
minute, if the receiver knows its position to within several hundred miles. This is often referred to
as a "warm start." The difference between a 30-second first fix and a 2-minute first fix is not that
important for most applications. However, 1 to 2 minutes is a great improvement over 30 minutes.
Although this parameter was not explicitly measured, attention was paid to time-to-first-fix to
confirm that the newer receivers were meeting the quoted specification.
The number of satellites tracked and receiver sensitivity are also important parameters. The more
satellites tracked, the less likely an obstruction of one or more satellites will result in a loss of
navigation. Also, a more sensitive receiver is less likely to be affected by foliage and other
obstructions that reduce signal strengths. The receiver sensitivity is affected by the type of antenna
used and the type of cabling. Some antennas have higher gains than others, different cables have
different attenuation characteristics, and longer cables cause greater signal attenuation. The
navigation mode, two-dimensional (2D-mode) or three-dimensional (3D-mode), is affected by the
number of satellites visible. Provided that the geometry results in an acceptable DOP, a minimum
of four satellites are necessary for three-dimensional navigation. Additional satellites may be used
to achieve a more robust position fix. If four satellites are in view, but the DOP is higher than a
certain threshold, many receivers will switch to two-dimensional navigation.
Ideally, measuring the signal-to-noise ratio in the receiver and the number of satellites being
tracked would yield the most insight into receiver performance. However, this information is usually
buried in several different data packets for any given receiver. For some receivers, this information
is not always available (the Trimble Placer does not output signal-to-noise ratio or the number of
satellites tracked for example). Therefore, a compromise was made and packets were requested that
contained the position fix as well as the navigation mode or number of satellites tracked. Usually this
data was contained in the same data packet. This reduced the amount of data stored and simplified
the data analysis. The information gathered from each receiver is listed in Table 3.6.
Differences in navigation modes can be caused by several factors; these include differences in
number of satellites being tracked, differences in the DOP value that cause a switch from 3D-mode
to 2D-mode navigation, and differences in satellite mask angles and receiver/antenna sensitivity. The
DOP settings and mask angles are known for each receiver, so the navigation mode data will allow
comparing the number of satellites tracked and receiver/antenna sensitivity as one performance
criterion. Although the navigation mode data lumps several factors together, it does give a
comparison of overall receiver/antenna performance.
As mentioned in the previous section, the antenna and cable choice affects the performance of
the GPS receiver. The antennas used for the GPS testing were supplied with the receiver or OEM
evaluation kit, The cabling was also supplied with the exception of the Magnavox GPS Engine.
Therefore, the performance of the antenna and cabling was lumped together with the overall GPS
system because each manufacturer recommends (or provides) antennas and cabling.
80
Part I Sensors for Mobile Robot Positioning
Table 3.6: Summary of data analyzed (Courtesy of [Byrne, 1993].)
Receiver
Data Gathered
Magellan
Latitude, longitude.
Number of satellites used - implies navigation mode (none, 2-D, or 3-D).
Magnavox GPS Engine
Latitude, longitude.
Navigation Mode (none, 2-D, or 3-D).
Rockwell NavCore V
Latitude, longitude, navigation mode (none, 2-D, or 3-D).
Number of satellites tracked also available from raw data.
Magnavox 6400
Latitude, longitude
Number of satellites tracked.
Trimble Placer
Latitude, longitude.
Navigation Mode (none, 2-D, or 3-D).
Other performance factors include the amount of filtering in a GPS receiver. Excessive filtering
reduces the amount of variance in the position and velocity data, but also slows the response of the
receiver. Excessive filtering will cause a receiver to output incorrect positions when starting,
stopping, or turning sharply. In applications where the GPS data is processed off board and needs
to be transmitted via RF-link to a central computer, this type of error is not very important because
the delay introduced by the communication link will probably be much greater than the delay
introduced by filtering in the receiver.
Parameters that were not analyzed in the Sandia experiments are velocity and heading accuracy,
because in Sandia's application (and many other typical mobile robot navigation tasks) accurate
velocity information was already available from odometry. Heading information that would be
required for dead reckoning is not needed while GPS is functional.
Another easy-to-measure performance criterion is static position accuracy. This parameter was
measured by placing the GPS receivers at a surveyed location and taking data for approximately 24
hours. Although in typical application the receivers are moving most of the time, the static accuracy
does give a good idea of the receivers' position accuracy capabilities. The parameters measured and
the performance insights gained from these measurements are summarized in Table 3.7.
In summary, the GPS testing performed for this project consisted of storing position and
navigation mode data from five different GPS receivers for both static and dynamic tests. The static
testing provides information about the static position accuracy as well as the sensitivity of the
receiver and antenna if DOP switching is taken into account. The dynamic testing mostly provides
information about the receiver/antenna sensitivity and the receiver's ability to recover from
temporary obstructions (taking into account DOP switching). The dynamic testing also provides
some qualitative information about position accuracy by comparing plots of the data points from the
various receivers.
Chapter 3: Active Beacons
81
Table 3.7: Summary of parameters measured and performance areas evaluated. (Courtesy of [Byrne, 1993].)
Parameter measured
Performance evaluated by that parameter
Time-to-first-fix
How quickly a receiver starts navigating. Not explicitly measured, but
qualitatively considered.
Static position accuracy
Static accuracy and insight into overall accuracy.
Static navigation mode —
Number of satellites tracked
Taking into account DOP switching, gives insight into receiver/antenna
sensitivity.
Dynamic position plots
Some accuracy information is obtained by comparing different data plots
taken while driving down the same section of road. Most of this analysis is
qualitative though because there is no ground-truth data for comparison.
Dynamic navigation mode
Taking DOP switching into account gives insight into the sensitivity of the
receiver/antenna and the rate with which the receiver recovers from
obstructions.
3.3.2.2 Test hardware
The GPS receivers tested use a serial interface for communicating position information. The
Magnavox 6400 receiver communicates using RS-422 serial communications, while the other four
receivers use the RS-232 communications standard. The RS-422 and RS-232 standards for data
transmission are compared in Table 3.8.
For the short distances involved in transmitting GPS data from the receiver to a computer, the
type of serial communications is not important. In fact, even though RS-232 communications are
inferior in some ways to RS422, RS-232 is easier to work with because it is a more common standard
(especially for PC-type computers).
A block diagram of the overall GPS test system is shown in Figure 3.10. Figure 3.10 depicts the
system used for dynamic testing where power was supplied from a 12-Volt battery. For the static
testing, AC power was available with an extension cord. Therefore, the computer supply was
connected directly to AC, while the +12 Volts for the GPS receivers was generated using an AC-DC
power supply for the static test.
The GPS test fixture was set up in a Chevrolet van with an extended rear for additional room. The
GPS antennas were mounted on aluminum plates that where attached to the van with magnets. The
Rockwell antenna came with a magnetic mount so it was attached directly to the roof. The five
antennas were within one meter of each other near the rear of the van and mounted at the same
height so that no antenna obstructed the others.
82
Part I Sensors for Mobile Robot Positioning
Battery backup
Data
acquisition
computer
RS-232
RS-232
Magellan OEM
Interface circuit
RS-232
Magnavox Eng.
Rockwell NavCore
RS-422
Magnavox 6400
RS-232
Trimble Placer
AC power
supply
GPS receivers
DC-AC
inverter
12 Volt battery
byr02_01.cdr,.wpg
Figure 3.10: Block diagram of the GPS test fixture. (Courtesy of [Byrne, 1993].)
For the dynamic testing, power was supplied from a 60 Amp-Hour lead acid battery. The battery
was used to power the AC-DC inverter as well as the five receivers. The van's electrical system was
tried at first, but noise caused the computer to lock up occasionally. Using an isolated battery solved
this problem. An AC-powered computer monitor was used for the static testing because AC power
was available. For the dynamic testing, the low power LCD display was used.
3.3.2.3 Data post processing
The GPS data was stored in raw form and post processed to extract position and navigation data.
This was done so that the raw data could be analyzed again if there were any questions with the
results. Also, storing the data as it came in from the serial ports required less computational effort
and reduced the chance of overloading the data acquisition computer. This section describes the
software used to post process the data.
Table 3.9 shows the minimum resolution (I..e, the smallest change in measurement the unit can
output) of the different GPS receivers. Note, however, that the resolution of all tested receivers is
still orders of magnitude smaller than the typical position error of up to 100 meters. Therefore, this
parameter will not be an issue in the data analysis.
Table 3.8: Comparison of RS-232 and RS-422 serial communications. (Courtesy of [Byrne, 1993].)
RS-232 Communications
RS-422 Communications
Single-ended data transmission
Differential data transmissions
Relatively slow data rates (usually < 20 kbs),
short distances up to 50 feet, most widely used.
Very high data rates (up to I0 Mbs), long distances
(up to 4000 feet at I00 Kbs), good noise immunity.
Chapter 3: Active Beacons
83
Once the raw data was converted to files with latitude, longitude, and navigation mode in
columnar form, the data was prepared for analysis. Data manipulations included obtaining the
position error from a surveyed location, generating histograms of position error and navigation mode,
and plotting dynamic position data. The mean and variance of the position errors were also obtained.
Degrees of latitude and longitude were converted to meters using the conversion factors listed below.
Latitude Conversion Factor
Longitude Conversion Factor
11.0988×104 m/ latitude
9.126×104 m/ longitude
3.3.3 Test Results
Sections 3.3.3.1 and 3.3.3.2 discuss the test results for the static and dynamic tests, respectively,
and a summary of these results is given in Section 3.3.3.3. The results of the static and dynamic tests
provide different information about the overall performance of the GPS receivers. The static test
compares the accuracy of the different receivers as they navigate at a surveyed location. The static
test also provides some information about the receiver/antenna sensitivity by comparing navigation
modes (3D-mode, 2D-mode, or not navigating) of the different receivers over the same time period.
Differences in navigation mode may be caused by several factors. One is that the receiver/antenna
operating in a plane on ground level may not be able to track a satellite close to the horizon. This
reflects receiver/antenna sensitivity. Another reason is that different receivers have different DOP
limits that cause them to switch to two dimensional navigation when four satellites are in view but
the DOP becomes too high. This merely reflects the designer's preference in setting DOP switching
masks that are somewhat arbitrary.
Dynamic testing was used to compare relative receiver/antenna sensitivity and to determine the
amount of time during which navigation was not possible because of obstructions. By driving over
different types of terrain, ranging from normal city driving to deep canyons, the relative sensitivity
of the different receivers was observed. The navigation mode (3D-mode, 2D-mode, or not
navigating) was used to compare the relative performance of the receivers. In addition, plots of the
data taken give some insight into the accuracy by qualitatively observing the scatter of the data.
Table 3.9: Accuracy of receiver data formats. (Courtesy of [Byrne, 1993].)
Receiver
Data format resolution
(degrees)
Minimum resolution
(meters)
Magellan
10-7
0.011
1.7×l0-6
0.19
5.73×l0-10
6.36×l0-5
10-8 5.73×l0-7
6.36×l0-2
10-5
1.11
Magnavox GPS Engine
Rockwell NavCore V
Magnavox 6400
Trimble Placer
84
Part I Sensors for Mobile Robot Positioning
3.3.3.1 Static test results
Static testing was conducted at a surveyed location at Sandia National Laboratories' Robotic Vehicle
Range (RVR). The position of the surveyed location is described in Table 3.10.
Table 3.10: Location of the surveyed point at the Sandia Robotic Vehicle
Range. (Courtesy of [Byrne, 1993].)
Surveyed Latitude
Surveyed Longitude
35 02 27.71607 (deg min sec)
106 31 16.14169 (deg min sec)
35.0410322 (deg)
106.5211505 (deg)
The data for the results presented here was gathered on October 7 and 8, 1992, from 2:21 p.m.
to 2:04 p.m. Although this is the only static data analyzed in this report, a significant amount of
additional data was gathered when all of the receivers were not functioning simultaneously. This
previously gathered data supported the trends found in the October 7 and 8 test.The plots of the
static position error for each receiver are shown in Figure 3.11. A summary of the mean and standard
deviation () of the position error for the different receivers appears in Table 3.11.
Table 3.11: Summary of the static position error mean and variance for different receivers.
(Courtesy of [Byrne, 1993].)
Receiver
Mean position error
(meters)
Position error standard
deviation
(feet)
(meters)
(feet)
Magellan
33.48
110
23.17
76
Magnavox GPS Engine
22.00
72
16.06
53
Rockwell NavCore V
30.09
99
20.27
67
Magnavox 6400
28.01
92
19.76
65
Trimble Placer
29.97
98
23.58
77
It is evident from Table 3.11 that the Magnavox GPS Engine was noticeably more accurate when
comparing static position error. The Magellan, Rockwell, Magnavox 6400, and Trimble Placer all
exhibit comparable, but larger, average position errors. This trend was also observed when SA was
turned off. However, a functioning Rockwell receiver was not available for this test so the data will
not be presented. It is interesting to note that the Magnavox 6400 unit compares well with the newer
receivers when looking at static accuracy. This is expected: since the receiver only has two channels,
it will take longer to reacquire satellites after blockages; one can also expect greater difficulties with
dynamic situations. However, in a static test, the weaknesses of a sequencing receiver are less
noticeable.
Chapter 3: Active Beacons
85
a. Magellan
b. Magnavox GPS Engine.
c. Rockwell NavCore V.
d. Magnavox 6400.
Figure 3.11: Static position error plots for all five
GPS receivers. (Courtesy of Byrne [1993]).
e. Trimble Placer.
86
Part I Sensors for Mobile Robot Positioning
The histogramic error distributions for the data taken during the static test are shown in
Figure 3.12. One can see from Fig. 3.12 that the Magnavox GPS Engine has the most data points
within 20 meters of the surveyed position. This corresponds with the smallest mean position error
exhibited by the Magnavox receiver. The error distributions for the other four receivers are fairly
similar. The Magnavox 6400 unit has slightly more data points in the 10 to 20 meter error bin, but
otherwise there are no unique features. The Magnavox GPS Engine is the only receiver of the five
tested that had a noticeably superior static position error distribution. Navigation mode data for the
different receivers is summarized in Figure 3.13 for the static test.
Number of
samples
1000
800
600
400
200
0
10
20
30
40
50
60
Position
error bins (in meters)
70
80
90
100
Figure 3.12: Histogramic error distributions for the data taken during the static test, for all five tested GPS
receivers. (Adapted from [Byrne, 1993].)
In order to analyze the data in Figure 3.13, one needs to take into account the DOP criterion for
the different receivers. As mentioned previously, some receivers switch from 3D-mode navigation
to 2D-mode navigation if four satellites are visible but the DOP is above a predetermined threshold.
The DOP switching criterion for the different receivers are outlined in Table 3.12. As seen in
Table 3.12, the different receivers use different DOP criteria. However, by taking advantage of
Equations (3.1) and (3.2), the different DOP criteria can be compared.
Chapter 3: Active Beacons
87
97.7
100.0
90.0
97.3
96.2
93.3
82.2
80.0
70.0
60.0
50.0
40.0
30.0
17.8
20.0
10.0
0.0
0.0 2.4
0.0
Magellan
% No Navigation
0.0
Magnavox Engine
% 2-D Navigation
2.7
Rockwell NavCore
6.7
1.6 2.2
Magnavox 6400
0.0
Trimble Placer
% 3-D Navigation
Figure 3.13: Navigation mode data for the static test. (Adapted from [Byrne, 1993].)
Table 3.12 relates all of the different DOP criteria to the PDOP. Based on the information in
Table 3.12, several comments can be made about the relative stringency of the various DOP
criterions. First, the Magnavox GPS Engine VDOP criterion is much less stringent than the Magellan
VDOP criterion (these two can be compared directly). The Magellan unit also incorporates
hysteresis, which makes the criterion even more stringent. Comparing the Rockwell to the Trimble
Placer, the Rockwell criterion is much less stringent. A TDOP of 10.2 would be required to make
the two criteria equivalent. The Rockwell and Magnavox GPS Engine have the least stringent DOP
requirements.
Taking into account the DOP criterions of the different receivers, the significant amount of twodimensional navigation exhibited by the Magellan receiver might be attributed to a more stringent
DOP criterion. However, this did not improve the horizontal (latitude-longitude) position error. The
Magnavox GPS Engine still exhibited the most accurate static position performance. The same can
Table 3.12: Summary of DOP - navigation mode switching criteria. (Courtesy of [Byrne, 1993].)
Receiver
2-D/3-D DOP criterion
PDOP equivalent
Magellan
If 4 satellites visible and VDOP >7, will
switch to 2-D navigation.
Enters 3-D navigation when VDOP<5.
PDOP > (HDOP2 + 72)½
Magnavox GPS
Engine
If 4 satellites visible and VDOP>10,
switches to 2-D navigation.
If HDOP>10, suspends 2-D navigation
PDOP < (HDOP2 + 52)½
PDOP > (HDOP2 + 102)½
Rockwell NavCore V
If 4 satellites visible and GDOP>13,
switches to 2-D navigation.
PDOP > (132 - TDOP2)½
Magnavox 6400
Data Not Available in MX 5400 manual
provided
Trimble Placer
If 4 satellites visible and PDOP>8, switches to 2-D
navigation. If PDOP>12, receiver stops navigating.
PDOP > 8
88
Part I Sensors for Mobile Robot Positioning
be said for the Trimble Placer unit. Although is has a stricter DOP requirement than the Magnavox
Engine, its position location accuracy was not superior. The static navigation mode results don't
conclusively show that any receiver has superior sensitivity. However, the static position error results
do show that the Magnavox GPS Engine is clearly more accurate than the other receivers tested. The
superior accuracy of the Magnavox receiver in the static tests might be attributed to more filtering
in the receiver. It should also be noted that the Magnavox 6400 unit was the only receiver that did
not navigate for some time period during the static test.
3.3.3.2 Dynamic test results
The dynamic test data was obtained by driving the instrumented van over different types of
terrain. The various routes were chosen so that the GPS receivers would be subjected to a wide
variety of obstructions. These include buildings, underpasses, signs, and foliage for the city driving.
Rock cliffs and foliage were typical for the mountain and canyon driving. Large trucks, underpasses,
highway signs, buildings, foliage, as well as small canyons were found on the interstate and rural
highway driving routes.
The results of the dynamic testing are presented in Figures 3.14 through 3.18. The dynamic test
results as well as a discussion of the results appear on the following pages.
Several noticeable differences exist between Figure 3.13 (static navigation mode) and Figure 3.14.
The Magnavox 6400 unit is not navigating a significant portion of the time. This is because
sequencing receivers do not perform as well in dynamic environments with periodic obstructions.
The Magellan GPS receiver also navigated in 2D-mode a larger percentage of the time compared
with the other receivers. The Rockwell unit was able to navigate in 3D-mode the largest percentage
of the time. Although this is also a result of the Rockwell DOP setting discussed in the previous
section, it does seem to indicate that the Rockwell receiver might have slightly better sensitivity
(Rockwell claims this is one of the receiver's selling points). The Magnavox GPS Engine also did not
navigate a small percentage of the time. This can be attributed to the small period of time when the
receiver was obstructed and the other receivers (which also were obstructed) might not have been
outputting data (caused by asynchronous sampling).
The Mountain Driving Test actually yielded less obstructions than the City Driving Test. This
might be a result of better satellite geometries during the test period. However, the Magnavox 6400
unit once again did not navigate for a significant portion of the time. The Magellan receiver
navigated in 2D-mode a significant portion of the time, but this can be attributed to some degree to
the stricter DOP limits. The performance of the Rockwell NavCore V, Trimble Placer, and
Magnavox GPS Engine are comparable.
Chapter 3: Active Beacons
89
98.9
100.0
94.8
91.2
89.4
90.0
80.0
74.2
70.0
60.0
50.0
40.0
25.8
30.0
20.0
10.0
10.3
3.4 5.3
0.0
5.2
0.0 1.1
0.2
0.0
0.0
Magellan
% No Navigation
Magnavox Engine
Rockwell Nav V
% 2-D Navigation
Magnavox 6400
Trimble Placer
% 3-D Navigation
Figure 3.14: Summary of City Driving Results. (Adapted from [Byrne, 1993]).
100.0
99.0
100.0
98.7
95.5
87.7
90.0
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
12.3
0.0 1.0
0.0
4.6
0.0 0.0
0.0 1.3
0.0
0.0
Magellan
% No Navigation
Magnavox Engine
Rockwell Nav V
% 2-D Navigation
Magnavox 6400
Trimble Placer
% 3-D Navigation
Figure 3.15: Summary of mountain driving results. (Adapted from [Byrne, 1993]).
100.0
90.0
100.0
98.8
94.6
84.3
80.0
69.8
70.0
60.0
50.0
40.0
30.2
30.0
15.7
20.0
10.0
0.0
0.0
Magellan
% No Navigation
1.1
4.4
Magnavox Engine
% 2-D Navigation
1.2 0.0
0.0
Rockwell Nav V
Magnavox 6400
% 3-D Navigation
Figure 3.16: Summary of Canyon Driving Results. (Adapted from [Byrne, 1993]).
0.0 0.0
Trimble Placer
90
Part I Sensors for Mobile Robot Positioning
99.6
99.3
100.0
95.8
90.0
79.9
80.0
67.2
70.0
60.0
50.0
40.0
32.8
30.0
20.1
20.0
10.0
0.4 0.4
0.0
0.2 0.2
0.0
0.0
4.2
0.0
Magellan
% No Navigation
Magnavox Engine
Rockwell Nav V
% 2-D Navigation
Magnavox 6400
Trimble Placer
% 3-D Navigation
Figure 3.17: Summary of Interstate Highway Results. (Adapted from [Byrne, 1993]).
98.5
100.0
97.8
96.1
92.7
87.8
90.0
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
10.4
7.4
0.0
1.6 0.5
0.3 1.3
1.8
0.0
3.9
0.0
Magellan
% No Navigation
Magnavox Engine
Rockwell Nav V
% 2-D Navigation
Magnavox 6400
Trimble Placer
% 3-D Navigation
Figure 3.18. Summary of Rural Highway Results. (Adapted from [Byrne, 1993]).
The Canyon Driving Test exposed the GPS receivers to the most obstructions. The steep canyon
walls and abundant foliage stopped the current receiver from navigating over 30 percent of the time.
The Magnavox GPS Engine and Rockwell receiver were also not navigating a small percentage of
the time. This particular test clearly shows the superiority of the newer receivers over the older
sequencing receiver. Because the newer receivers are able to track extra satellites and recover more
quickly from obstructions, they are better suited for operation in dynamic environments with
periodic obstructions. The Trimble Placer and Rockwell receiver performed the best in this particular
test, followed closely by the Magnavox GPS Engine.
During the Interstate Highway Driving tests, the Magnavox 6400 unit did not navigate over
20 percent of the time. This is consistent with the sometimes poor performance exhibited by the
current navigation system. The other newer receivers did quite well, with the Trimble Placer,
Magnavox GPS Engine, and Rockwell NavCore V exhibiting similar performance. Once again, the
Chapter 3: Active Beacons
91
Magellan unit navigated in 2D-mode a significant portion of the time. This can probably be attributed
to the stricter DOP limits.
During the Rural Highway Driving test the Magnavox 6400 unit once again did not navigate a
significant portion of the time. All of the newer receivers had similar performance results. The
Magellan receiver navigated in 2D-mode considerably less in this test compared to the other dynamic
tests.
3.3.3.3 Summary of test results
Both static and dynamic tests were used to compare the performance of the five different GPS
receivers. The static test results showed that the Magnavox GPS Engine was the most accurate (for
static situations). The other four receivers were slightly less accurate and exhibited similar static
position error performance. The static navigation mode results did not differentiate the sensitivity
of the various receivers significantly. The Magellan unit navigated in 2D-mode much more
frequently than the other receivers, but some of this can be attributed to stricter DOP limits.
However, the stricter DOP limits of the Magellan receiver and Trimble Placer did not yield better
static position accuracies. All four of the newer GPS receivers obtained a first fix under one minute,
which verifies the time to first-fix specifications stated by the manufacturers.
The dynamic tests were used to differentiate receiver sensitivity and the ability to recover quickly
from periodic obstructions. As expected, the Magnavox 6400 unit did not perform very well in the
dynamic testing. The Magnavox 6400 was unable to navigate for some period of each dynamic test.
This was most noticeable in the Canyon route, where the receiver did not navigate over 30 percent
of the time. The newer receivers performed much better in the dynamic testing, navigating almost
all of the time. The Magnavox GPS Engine, Rockwell NavCore V, and Trimble Placer exhibited
comparable receiver/antenna sensitivity during the dynamic testing based on the navigation mode
data. The Magellan unit navigated in 2D-mode significantly more than the other receivers in the
dynamic tests. Most of this can probably be attributed to a more stringent DOP requirement. It
should also be noted that the Magellan receiver was the only receiver to navigate in 2D-mode or 3Dmode 100 percent of the time in all of the dynamic tests.
Overall, the four newer receivers performed significantly better than the Magnavox 6400 unit in
the dynamic tests. In the static test, all of the receivers performed satisfactorily, but the Magnavox
GPS Engine exhibited the most accurate position estimation. Recommendations on choosing a GPS
receiver are outlined in the next section.
3.3.4 Recommendations
In order to discuss some of the integration issues involved with GPS receivers, a list of the
problems encountered with the receivers tested is outlined in Section 3.3.4.1. The problems
encountered with the Magnavox 6400 unit (there were several) are not listed because the Magnavox
6400 unit is not comparable to the newer receivers in performance.
Based on the problems experienced testing the GPS receivers as well as the requirements of the
current application, a list of critical issues is outlined in Section 3.3.4.2.
One critical integration issue not mentioned in Section 3.3.4.2 is price. Almost any level of
performance can be purchased, but at a significantly increased cost. This issue will be addressed
further in the next section. Overall, the Magellan OEM Module, the Magnavox GPS Engine,
Rockwell NavCore V, and Trimble Placer are good receivers. The Magnavox GPS Engine exhibited
superior static position accuracy. During dynamic testing, all of the receivers were able to navigate
92
Part I Sensors for Mobile Robot Positioning
a large percentage of the time, even in hilly wooded terrain. Based on the experimental results, other
integration issues such as price, software flexibility, technical support, size, power, and differential
capability are probably the most important factors to consider when choosing a GPS receiver.
3.3.4.1 Summary of problems encountered with the tested GPS receivers
Magellan OEM Module
No problems, unit functioned correctly out of the box. However, the current drain on the battery
for the battery backed RAM seemed high. A 1-AmpHour 3.6-Volt Lithium battery only lasted a
few months.
The binary position packet was used because of the increased position resolution. Sometimes the
receiver outputs a garbage binary packet (about I percent of the time).
Magnavox GPS Engine
The first unit received was a pre-production unit. It had a difficult time tracking satellites. On one
occasion it took over 24 hours to obtain a first fix. This receiver was returned to Magnavox.
Magnavox claimed that upgrading the software fixed the problem. However, the EEPROM failed
when trying to load the oscillator parameters. A new production board was shipped and it
functioned flawlessly out of the box.
The RF connector for the Magnavox GPS Engine was also difficult to obtain. The suppliers
recommended in the back of the GPS Engine Integration Guide have large minimum orders. A
sample connector was finally requested. It never arrived and a second sample had to be
requested.
Rockwell NavCore V
The first Rockwell receiver functioned for a while, and then began outputting garbage at 600
baud (9600 baud is the only selectable baud rate). Rockwell claims that a Gallium Arsenide IC
that counts down a clock signal was failing because of contamination from the plastic package
of the IC (suppliers fault). This Rockwell unit was returned for repair under warranty.
The second Rockwell unit tested output data but did not navigate. Power was applied to the unit
with reverse polarity (Sandia's fault) and an internal rectifier bridge allowed the unit to function,
but not properly. Applying power in the correct manner (positive on the outside contact) fixed
the problem.
Trimble Placer
No problems, unit functioned correctly out of the box.
3.3.4.2 Summary of critical integration issues
Flexible software interface Having the flexibility to control the data output by the receiver is
important. This includes serial data format (TTL, RS-232, RS-422). baud rates, and packet data rates.
It is desirable to have the receiver output position data at fixed data rate, that is user selectable. It
is also desirable to be able to request other data packets when needed. All of the receivers with the
exception of the Rockwell unit were fairly flexible. The Rockwell unit on the other hand outputs
position data at a fixed 1-Hz rate and fixed baud rate of 9600 baud.
The format of the data packets is also important. ASCII formats are easier to work with because
the raw data can be stored and then analyzed visually. The Rockwell unit uses an IEEE floating point
Chapter 3: Active Beacons
93
format. Although Binary data formats and the Rockwell format might be more efficient, it is much
easier to troubleshoot a problem when the data docs not have to be post processed just to take a
quick look.
Differential capability The capability to receive differential corrections is important if increased
accuracy is desired. Although a near-term fielded system might not use differential corrections, the
availability of subscriber networks that broadcast differential corrections in the future will probably
make this a likely upgrade.
Time to first fix A fast time-to-first-fix is important. However, all newer receivers usually advertise
a first fix in under one minute when the receiver knows its approximate position. The difference
between a 30-second first fix and a one-minute first fix is probably not that important. This
parameter also affects how quickly the receiver can reacquire satellites after blockages.
Memory back up Different manufacturers use different approaches for providing power to back
up the static memory (which stores the last location, almanac, ephemeris, and receiver parameters)
when the receiver is powered down. These include an internal lithium battery, an external voltage
supplied by the integrator, and a large capacitor. The large capacitor has the advantage of never
needing replacement. This approach is taken on the Rockwell NavCore V. However, the capacitor
charge can only last for several weeks. An internal lithium battery can last for several years, but will
eventually need replacement. An external voltage supplied by the integrator can come from a
number of sources, but must be taken into account when doing the system design.
Size, Power, and packaging Low power consumption and small size are advantageous for vehicular
applications. Some manufacturers also offer the antenna and receiver integrated into a single
package. This has some advantages, but limits antenna choices.
Active/passive antenna Active antennas with built-in amplifiers allow longer cable runs to the
receiver. Passive antennas require no power but can not be used with longer cabling because of
losses.
Cable length and number of connectors The losses in the cabling and connectors must be taken
into account when designing the cabling and choosing the appropriate antenna.
Receiver/antenna sensitivity Increased receiver/antenna sensitivity will reduce the affects of
foliage and other obstructions. The sensitivity is affected by the receiver, the cabling, as well as the
antenna used.
Position accuracy Both static and dynamic position accuracy are important. However, the effects
of SA reduce the accuracy of all receivers significantly. Differential accuracy will become an
important parameter in the future.
Technical Support Good technical support, including quick turn around times for repairs, is very
important. Quick turn around for failed units can also be accomplished by keeping spares in stock.
94
Part I Sensors for Mobile Robot Positioning
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CHAPTER 4
SENSORS FOR MAP-BASED POSITIONING
Most sensors used for the purpose of map building involve some kind of distance measurement.
There are three basically different approaches to measuring range:
Sensors based on measuring the time of flight (TOF) of a pulse of emitted energy traveling to a
reflecting object, then echoing back to a receiver.
The phase-shift measurement (or phase-detection) ranging technique involves continuous wave
transmission as opposed to the short pulsed outputs used in TOF systems.
Sensors based on frequency-modulated (FM) radar. This technique is somewhat related to the
(amplitude-modulated) phase-shift measurement technique.
4.1 Time-of-Flight Range Sensors
Many of today's range sensors use the time-of-flight (TOF) method. The measured pulses typically
come from an ultrasonic, RF, or optical energy source. Therefore, the relevant parameters involved
in range calculation are the speed of sound in air (roughly 0.3 m/ms — 1 ft/ms), and the speed of
light (0.3 m/ns — 1 ft/ns). Using elementary physics, distance is determined by multiplying the
velocity of the energy wave by the time required to travel the round-trip distance:
d=vt
(4.1)
where
d = round-trip distance
v = speed of propagation
t = elapsed time.
The measured time is representative of traveling twice the separation distance (i.e., out and back)
and must therefore be reduced by half to result in actual range to the target.
The advantages of TOF systems arise from the direct nature of their straight-line active sensing.
The returned signal follows essentially the same path back to a receiver located coaxially with or in
close proximity to the transmitter. In fact, it is possible in some cases for the transmitting and
receiving transducers to be the same device. The absolute range to an observed point is directly
available as output with no complicated analysis required, and the technique is not based on any
assumptions concerning the planar properties or orientation of the target surface. The missing parts
problem seen in triangulation does not arise because minimal or no offset distance between
transducers is needed. Furthermore, TOF sensors maintain range accuracy in a linear fashion as long
as reliable echo detection is sustained, while triangulation schemes suffer diminishing accuracy as
distance to the target increases.
Potential error sources for TOF systems include the following:
Variations in the speed of propagation, particularly in the case of acoustical systems.
Uncertainties in determining the exact time of arrival of the reflected pulse.
96
Part I Sensors for Mobile Robot Positioning
Inaccuracies in the timing circuitry used to measure the round-trip time of flight.
Interaction of the incident wave with the target surface.
Each of these areas will be briefly addressed below, and discussed later in more detail.
a. Propagation Speed For mobile robotics applications, changes in the propagation speed of
electromagnetic energy are for the most part inconsequential and can basically be ignored, with the
exception of satellite-based position-location systems as presented in Chapter 3. This is not the case,
however, for acoustically based systems, where the speed of sound is markedly influenced by
temperature changes, and to a lesser extent by humidity. (The speed of sound is actually proportional
to the square root of temperature in degrees Rankine.) An ambient temperature shift of just 30 o F
can cause a 0.3 meter (1 ft) error at a measured distance of 10 meters (35 ft) [Everett, 1985].
b. Detection Uncertainties So-called time-walk errors are caused by the wide dynamic range
in returned signal strength due to varying reflectivities of target surfaces. These differences in
returned signal intensity influence the rise time of the detected pulse, and in the case of fixedthreshold detection will cause the more reflective targets to appear closer. For this reason, constant
fraction timing discriminators are typically employed to establish the detector threshold at some
specified fraction of the peak value of the received pulse [Vuylsteke et al., 1990].
c. Timing Considerations Due to the relatively slow speed of sound in air, compared to light,
acoustically based systems face milder timing demands than their light-based counterparts and as a
result are less expensive. Conversely, the propagation speed of electromagnetic energy can place
severe requirements on associated control and measurement circuitry in optical or RF implementations. As a result, TOF sensors based on the speed of light require sub-nanosecond timing circuitry
to measure distances with a resolution of about a foot [Koenigsburg, 1982]. More specifically, a
desired resolution of 1 millimeter requires a timing accuracy of 3 picoseconds (3×10 -12 s) [Vuylsteke
et al., 1990]. This capability is somewhat expensive to realize and may not be cost effective for
certain applications, particularly at close range where high accuracies are required.
d. Surface Interaction When light, sound, or radio waves strike an object, any detected echo
represents only a small portion of the original signal. The remaining energy reflects in scattered
directions and can be absorbed by or pass through the target, depending on surface characteristics
and the angle of incidence of the beam. Instances where no return signal is received at all can occur
because of specular reflection at the object's surface, especially in the ultrasonic region of the energy
spectrum. If the transmission source approach angle meets or exceeds a certain critical value, the
reflected energy will be deflected outside of the sensing envelope of the receiver. In cluttered
environments soundwaves can reflect from (multiple) objects and can then be received by other
sensors. This phenomenon is known as crosstalk (see Figure 4.1). To compensate, repeated
measurements are often averaged to bring the signal-to-noise ratio within acceptable levels, but at
the expense of additional time required to determine a single range value. Borenstein and Koren
[1995] proposed a method that allows individual sensors to detect and reject crosstalk.
Chapter 4: Sensors for Map-Based Positioning
97
Using this method much faster firing
rates — under 100 ms for a complete
scan with 12 sonars — are feasible.
4.1.1 Ultrasonic TOF Systems
y X
y
y
y
Ultrasonic TOF ranging is today the
y
y
most common technique employed on
indoor mobile robotics systems, priMobile
Direction
robot
of motion
marily due to the ready availability of
low-cost systems and their ease of
Xy y y y
interface. Over the past decade, much
y
research has been conducted investiy
gating applicability in such areas as
Mobile
world modeling and collision avoida.
b. robot
ance, position estimation, and motion
detection. Several researchers have Figure 4.1: Crosstalk is a phenomenon in which one sonar picks
more recently begun to assess the up the echo from another. One can distinguish between a. direct
effectiveness of ultrasonic sensors in crosstalk and b. indirect crosstalk.
exterior settings [Pletta et al., 1992;
Langer and Thorpe, 1992; Pin and Watanabe, 1993; Hammond, 1994]. In the automotive industry,
BMW now incorporates four piezoceramic transducers (sealed in a membrane for environmental
protection) on both front and rear bumpers in its Park Distance Control system [Siuru, 1994]. A
detailed discussion of ultrasonic sensors and their characteristics with regard to indoor mobile robot
applications is given in [Jörg, 1994].
Two of the most popular commercially available ultrasonic ranging systems will be reviewed in
the following sections.
\eeruf\crostalk.ds4, crostalk.w mf
4.1.1.1 Massa Products Ultrasonic Ranging Module Subsystems
Massa Products Corporation, Hingham, MA, offers a full line of ultrasonic ranging subsystems with
maximum detection ranges from 0.6 to 9.1 meters (2 to 30 ft) [MASSA]. The E-201B series sonar
operates in the bistatic mode with separate transmit and receive transducers, either side by side for
echo ranging or as an opposed pair for unambiguous distance measurement between two uniquely
defined points. This latter configuration is sometimes used in ultrasonic position location systems and
provides twice the effective operating range with respect to that advertised for conventional echo
ranging. The E-220B series (see Figure 4.2) is designed for monostatic (single transducer) operation
but is otherwise functionally identical to the E-201B. Either version can be externally triggered on
command, or internally triggered by a free-running oscillator at a repetition rate determined by an
external resistor (see Figure 4.3).
Selected specifications for the four operating frequencies available in the E-220B series are listed
in Table 4.1 below. A removable focusing horn is provided for the 26- and 40-kHz models that
decreases the effective beamwidth (when installed) from 35 to 15 degrees. The horn must be in place
to achieve the maximum listed range.
98
Part I Sensors for Mobile Robot Positioning
Transmit
driver
Receiver
Internal
oscillator
Threshold
AC
AMP
Analog
Trig in
Trig out
PRR
Vcc
+V
GND
D
Digital
timing
Filter
Latch
G
S
Figure 4.2: The single-transducer Massa E-220B-series ultrasonic ranging module
can be internally or externally triggered, and offers both analog and digital outputs.
(Courtesy of Massa Products Corp.)
Pulse repetition rate period
Trigger
Ring down
1st echo
2nd echo
Analog
Digital
Figure 4.3: Timing diagram for the E-220B series ranging module showing
analog and digital output signals in relationship to the trigger input. (Courtesy
of Massa Products Corp.)
Table 4.1: Specifications for the monostatic E-220B Ultrasonic Ranging Module Subsystems. The E-201
series is a bistatic configuration with very similar specifications. (Courtesy of Massa Products Corp.)
Parameter
E-220B/215
E-220B/150
E-220B/40
Beamwidth
10 - 61
4 - 24
10
20 - 152
8 - 60
10
61 - 610
24 - 240
35 (15)
Frequency
215
150
40
Max rep rate
Resolution
150
0.076
0.03
100
0.1
0.04
25
0.76
0.3
Power
8 - 15
8 - 15
8 - 15
8 - 15 VDC
Weight
4-8
4-8
4-8
4 - 8 oz
Range
E-220B/26 Units
61 - 914 cm
24 - 360 in
35 (15) 26 kHz
20 Hz
1 cm
0.4 in
Chapter 4: Sensors for Map-Based Positioning
99
4.1.1.2 Polaroid Ultrasonic Ranging Modules
The Polaroid ranging module is
an active TOF device developed
for automatic camera focusing,
which determines the range to
target by measuring elapsed
time between the transmission
of an ultrasonic waveform and
the detected echo [Biber et al.,
1987, POLAROID]. This system is the most widely found in
mobile
robotics literature
[Koenigsburg, 1982; Moravec
and Elfes, 1985; Everett, 1985;
Kim, 1986; Moravec, 1988;
Elfes, 1989; Arkin, 1989;
Borenstein and Koren, 1990;
1991a; 1991b; 1995; Borenstein Figure 4.4: The Polaroid OEM kit included the transducer and a small
et al., 1995], and is representa- electronics interface board.
tive of the general characteristics of such ranging devices. The most basic configuration consists of two fundamental components:
1) the ultrasonic transducer, and 2) the ranging module electronics. Polaroid offers OEM kits with
two transducers and two ranging module circuit boards for less than $100 (see Figure 4.4).
A choice of transducer types is now available. In the original instrument-grade electrostatic
version, a very thin metal diaphragm mounted on a machined backplate formed a capacitive
transducer as illustrated in Figure 4.5 [POLAROID, 1991]. The system operates in the monostatic
transceiver mode so that only a single transducer is necessary to acquire range data. A smaller
diameter electrostatic transducer (7000-series) has also
been made available, developed
for the Polaroid Spectra camera
[POLAROID, 1987]. A more
rugged piezoelectric (9000-series) environmental transducer
for applications in severe environmental conditions including
vibration is able to meet or exceed the SAE J1455 January
1988 specification for heavyduty trucks. Table 4.2 lists the
technical specifications for the
different Polaroid transducers.
The original Polaroid ranging
module functioned by transmit- Figure 4.5: The Polaroid instrument grade electrostatic transducer
ting a chirp of four discrete fre- consists of a gold-plated plastic foil stretched across a machined
backplate. (Reproduced with permission from Polaroid [1991].)
100
Part I Sensors for Mobile Robot Positioning
quencies at about of 50 kHz. The SN28827 module was later developed with reduced parts count,
lower power consumption, and simplified computer interface requirements. This second-generation
board transmits only a single frequency at 49.1 kHz. A third-generation board (6500 series)
introduced in 1990 provided yet a further reduction in interface circuitry, with the ability to detect
and report multiple echoes [Polaroid, 1990]. An Ultrasonic Ranging Developer’s Kit based on the
Intel 80C196 microprocessor is now available for use with the 6500 series ranging module that
allows software control of transmit frequency, pulse width, blanking time, amplifier gain, and
maximum range [Polaroid, 1993].
The range of the Polaroid system runs from about 41 centimeters to 10.5 meters (1.33 ft to 35 ft).
However, using custom circuitry suggested in [POLAROID, 1991] the minimum range can be
reduced reliably to about 20 centimeters (8 in) [Borenstein et al., 1995]. The beam dispersion angle
is approximately 30 degrees. A typical operating cycle is as follows.
1. The control circuitry fires the transducer and waits for indication that transmission has begun.
2. The receiver is blanked for a short period of time to prevent false detection due to ringing from
residual transmit signals in the transducer.
3. The received signals are amplified with increased gain over time to compensate for the decrease
in sound intensity with distance.
4. Returning echoes that exceed a fixed threshold value are recorded and the associated distances
calculated from elapsed time.
Table 4.2: Specifications for the various Polaroid ultrasonic ranging modules. (Courtesy of
Polaroid.)
Parameter
Original
SN28827
Maximum range
10.5
35
10.5
35
Minimum range*
25
10.5
56
20
6
16
20 cm
6 in
16
1.6
2.38
2.38 ms
Number of pulses
Blanking time
Resolution
Gain steps
Multiple echo
Programmable frequency
Power
1
2
16
no
12
yes
no
no
4.7 - 6.8
200
4.7 - 6.8
100
6500 Units
10.5 m
35 ft
1 %
12
yes
yes
4.7 - 6.8 V
100 mA
* with custom electronics (see [Borenstein et al., 1995].)
Figure 4.6 [Polaroid, 1990] illustrates the operation of the sensor in a timing diagram. In the
single-echo mode of operation for the 6500-series module, the blank (BLNK) and blank-inhibit
(BINH) lines are held low as the initiate (INIT) line goes high to trigger the outgoing pulse train. The
internal blanking (BLANKING) signal automatically goes high for 2.38 milliseconds to prevent
transducer ringing from being misinterpreted as a returned echo. Once a valid return is received, the
echo (ECHO) output will latch high until reset by a high-to-low transition on INIT.
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