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Dynamic Visual Servo Control of Robots: an Adaptive Image-Based Dynamic Visual Servo Control cf Robots: An Adaptive Image-Based Approach Lee Elliot Weiss CMU-RI-TR-84-16 Department of Electrical and Computer Engineering The Robotics Institute Carnegie-Mellon University Pittsburgh, Pennsylvania 152.13 April 1984 Copyright @ 7984 Carnegie-Mellon University i Table of Contents 1. Introduction 3 1.1. Overview 3 1.2. Introduction to Visual Servo Control 3 1.3. Outline of Dissertation 13 1.3.1. Dissertation Goals 13 1.3.2. Design Approach 14 1.3.3. Outline of Dissertation 14 2. Visual Servo Control 19 2.1. Overview 19 2.2. Robot Kinematics and Dynamics 20 2.2.1. Kinematics 21 2.2.2. Rigid Body Dynamics 22 2.3. Control 23 2.3.1. Joint Level Control 24 2.3.1.1. Feed-Formrd Open-Loop Control 25 2.3.1.2. Fixed Linear Servo Control 26 2.3.1.3. Adaptive Feedback Control 28 2.3.2. Kinematic; Control 31 2.3.2.1. Inctemental Motion Control 33 2.4. Visual Servo Control Structures 34 2.4.1. Computer Vision 36 2.4.2. Position Based Visual Control Structures 37 2.4.2.1. Static Position Based "Look and Move" 37 2.4.2.2. Dynamic Position-Based "Look and Move" 39 2.4.2.3. Position Based Visual Servoing 40 2.4.3. Imaged Based Visual Control Structures 41 2.4.3.1. Dynamic Image-Based "Look and Move" 42 2.4.3.2. Image Based Visual Servoing 44 2.5. Control Of Image-BasedSystems 46 2.5.1. Control Apptoach 47 2.5.2. Feature Selection and Assignment 51 2.5.2.1. Feature Assignment Using Diagonal Dominance 51 2.5.2.2. Feature Selection 53 2.5.3. Path Constraint 56 2.6. Summary 60 3. Model Reference Adaptive Control 63 3.1. Overview 63 3.2. MRAC for Systems Without Measurement Delay 63 3.3. MRAC Control With Measi.irement Delay 65 3.3.1. MRAC Controller with Delay 66 3.3.2. Control Penalty 68 3.3.3. Reference Model 68 3.4. Signal Biasing and Gravity Compensation 70 3.4.1. Signal Biasing 70 3.4.2. Gravity Compensation 71 3.5. Linear Control Interpretation 72 3.5.1. FP MRAC 73 3.5.2. SP MRAC 75 3.6. Parameter Specification 78 3.6.1. Model Time Constant Specification 78 3.6.2. Sampling Period Selection 79 3.6.2.1. Ftindaniental Upper Bound 80 3.6.2.2. Performance Margin 80 3.6.2.3. MRAC Identifier Requirements 81 3.6.3. Adaptive Gain Matrix Initialization and Limiting 81 3.6.4. Parameter Vector Initialization 82 3.6.5. Weighting Factor 83 3.6.6. Control Penalty 03 3.7. Summary 83 4. Task Modeling and Simulation 05 4.1. Overvkw 85 4.2. Task Configurations 86 4.2.1. Configuration 1: 2 DOF wi!h linear kinematics and dynamics 86 4.2.2. Configuration 2: 2 DOF with r,onlinesr kinematics t3 dynamics 88 4.2.3. Con;iguration 3. 3 DOF with nonlinear kinematics, and linear and 89 iincoupled dynamics 4.3. Plant Modeling for Translational and Rotational Stages 91 4.3 1. Rotational Stage 91 4.3.2. X-Y Stages 93 4.3.3. X-Y-ThetaStage Parameters 94 4.3.4. Computer Simulation Of Uncoupled Linear Models 96 4.4. Plant Modeling for 2 DOF Robot Arm 97 4.4.1. Kinematic Equations 99 4.4.2. Rigid Body Dynamics 100 4.4.3. Actuator Dynamics 101 4.4.4. Robot Arm Parameters 102 4.4.4.1. Motor 2 Selection 104 4.4.4.2. Motor 1 Selection 105 4.4.5. Computer Simulation of the Robot Arm 106 4.4.5.1. Linear Model 108 4.5. Modeling Picture Taking and Feature Measurement 110 4.5.1. Image Transformations 110 4.5.2. Feature Transtormations 111 4.5.2.1. Two-Dimensional Line 111 4.5.2.2. Polyhedral Objects 115 4.5.2.3. Noise Signal Modeling 118 4.6. Summary 119 iii 5. Evaluation: One DOF Systems 121 5.1. Overview 121 5.2. Baseline MRAC 122 5.2.1. MRAC Without Measurement Delay 123 5.2.2. MRAC With Measurement Delay 124 5.3. Linear IBVS 126 5.3.1. Noise Performance: Fixed vs. Adaptive Control 132 5.4. Nonlinear IBVS 135 5.4.1. Adaptive Control Vs. Fixed 144 5.5. Summary 147 6. Evaluation: Two DOF Systems 149 6.1. Overview 149 6.2. Linear Kinematics and Dynamics 150 6.2.1. Sensitivity Analysis 151 6.2.1 .l.Predicted Path 153 6.2.1.2. FeatiireIJoint Assignment 156 6.2.1.3. Path Constraint 160 6.2.2. Control Evaluation 161 6.2.3. Independent Adaptive Control Problems 171 6.2.3.1. Sign-Sensitivity 171 6.2.3.2. FestureIJoint Reassignment 173 6.3. Nonlinear Kinematics and Dynamics 176 6.3.1. Control of Nonlinear Dynamics 176 6.3.1 .l.Joint-Lsvel Control Examples 178 6.3.2. Sensitivity f..nalysis 186 6.3.2.1. FeaturcIJoint Assignment 189 6.3.2.2. Pdtli Constraint 192 6.3.3. IBVS Evaluation 192 6.3.3.1. Small Motion Trajectories 195 6.3.3.2. Large Motion Travel 199 6.3.3.3. FeatureIJoint Reassignment 20 1 6.4. Summary 203 7. Evaluation: Three DOF 207 7.1. Overview 207 7.2. Candidate Control Features 208 7.2.1. Sensitivity Measurements 209 7.2.2. Feature/Joint Assignment 21 I 7.3. Small Signal Evaluation 21 3 7.4. Large Motion Evaluation 21 8 7.5. Summary 223 8. Conclusions 225 8.1. Overview 225 8.2. Conclusions 225 8.3. Suggestions for Future Research 229 8.3.1. MlMO vs. SlSO Adaptive Control 229 8.3.1.1. On-Line Sensitivity Estimation 230 8.3.2. Implementation 23 1 8.3.2.1. Robot Mechanical Structure 231 iv 8.3.2.2. Sensor Resolution 232 8.3.2.3. Extension to Higher DOF 232 8.3.2.4. Position vs. Image Based Control 233 Appendix A. MRAC Without Measurement Delay 235 A.l. Refererice Model 236 A.2. Plant Model Structure 239 A.3. Controller 239 A.4. Adjustment Mechanism 24 1 A.5. Enhancements 242 Appendix B. Dynamic Equations for 2 DOF Arm 247 Appendix C. 2 DOF Controller Parameters 255 Appendix D. 3 DOF Controller Parameters 257 V List of Figures Figure 1-1: Robot Acquiring Object Using Computer Vision 4 Figure 1-2: Robot Assembling PC Boards Using Computer Vision 5 Figure 1-3: Basic Robot Positioning Control 6 Figure 1-4: Computer Vision 8 Figure 1-5: Static "Look and Move" Control 9 Figure 1-6: Dynamic Visual Servo Control 9 Figure 1-7: Features Change with Motion 11 Figure 2-1: Robot Block Diagram 20 Figure 2-2: Robot Control Block Diagram 25 Figure 2-3: Self - Tu nin g Reg uI a t o r 29 Figure 2-4: Model Reference Adaptive Control 29 Figure 2-5: Open-Loop Kinematic Control 32 Figure 2-6: Incremental Robot System 34 Figure 2-7: Robotic Visual Servo Control 35 Figure 2-8: Computer Based Vision System 36 Figure 2-9: Static Position-Based "Look 8. Move" 38 Figure 2- 10: Dynamic Position-Based "Look 8 Move" 39 Figii re 2- 1 1 : Position-BasedVisual Servoing 40 Figure 2- 1 2: Dynamic Image-Based "Look 8 Move" 43 Figure 2- 13: Image-Based Visual Servoing 45 Figure 2- 14: Small-Signal Image-Based "Look and Move" 47 Figure 2- 15: Small-Signal Image-Based Visual Servoing 48 Figure 2- 16: MRAC Control of an IBVS System 50 Figure 2- 17: Equivalent IBVS Control 51 Figure 2- 18: Control Hierarchy 58 Figure 2- 19: Hierarchical Control Example 59 Figure 2-20: Visual Based Control Structures 61 Figure 3-1: Analog Process Under MRAC Control 64 Figure 3-2: MRAC with Measurement Delay 66 Figure 3-3: Reference Model With Delays 69 Figure 3-4: Reference Model Root-Locus with One Delay 69 Figu re 3-5: FP LMFC Control 73 Figure 3-6: FP Root Locus vs. n 75 Figure 3-7: SP LMFC Control 76 Figure 3-8: SP Root Locus vs. n 78 Figure 4- 1 : Configuration 1 07 Figure 4-2: Configuration 2. 08 Figure 4-3: Configuration 3 90 Figure 4-4: RotatiGnal Stage Model 92 vi Figure 4-5: Translational Stage Model 93 Figure 4-6: Rotational Plant Block Diagram 96 Figure 4-7: Translational Plant Block Diagram 96 Figure 4-8: 2 DOF Robot Arm 98 Figure 4-9: Arm Coordinate Frames 99 Figure 4- 10: Robot Actuator 102 Figure 4- 1 1 : Arm Simulation Block Diagram 109 Figure 4- 12: Line-Image 113 Figure 4- 13: Objects 115 Figure 4- 14: Image Planes 117 Figure 4- 15: Scaled Distribution 118 Figure 5-1 : SP MRAC Without Measurement Delay 125 Figure 5-2: SP MRAC With Measurement Delay 127 Figure 5-3: Linear Time-Invariant Tasks 129 Figure 5-4: Linear Autonomous IBVS 130 Figure 5-5: IBVS with Control Signal Saturation 131 Figure 5-6: MRAC vs. LMFC Noise Performance (SNR = 44 db) 133 Figure 5-7: MRAC vs. LMFC Noise Performance (SNR = 30 db) 134 Figure 5-8: Error index vs. SNR 134 Figure 5-9: 1 DOF Nonlinear Tasks 136 Figu re 5-10: Task D Feature Characteristics 137 Figure 5-1 1 : IBVS With Nonlinear Sensitivity 139 Figure 5-12: Sensitivity Change for TASK C 140 Figure 5-13: IBVS With Large Gain Changes 142 Figure 5-14: IBVS With Varying Sampling-to-BandwidthRatios 143 Figure 5-15: Fixed vs.
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