Path Planning of Cooperative Mobile Robots Using Discrete Event Models

Foreword xi

Preface xv

Acknowledgments xvii

Acronyms xix

1 Introduction 1

1.1 Historical perspective of mobile robotics 1

1.2 Path planning. Definition and historical background 4

1.3 Motion control. Definition and historical background 9

1.4 Motivation for expressive tasks 11

1.5 Assumptions of this monograph 14

1.6 Outline of this monograph 14

2 Robot Motion Toolbox 17

2.1 Introduction 17

2.2 General description of the simulator 20

2.3 Path planning algorithms 25

2.4 Robot kinematic models 26

2.5 Motion control algorithms 29

2.5.1 Pure pursuit algorithm 29

2.5.2 PI controller 32

2.6 Illustrative examples 33

2.6.1 Examples about path planning aspects 33

2.6.2 Examples about motion control aspects 35

2.6.3 Examples about multi-robot systems and high-level tasks 37

2.7 Conclusions 40

3 Cell Decomposition Algorithms 41

3.1 Introduction 41

3.2 Cell decomposition algorithms 42

3.2.1 Hypothesis 42

3.2.2 Trapezoidal decomposition 45

3.2.3 Triangular decomposition 46

3.2.4 Polytopal decomposition 49

3.2.5 Rectangular decomposition 52

3.3 Implementation and extensions 53

3.3.1 Extensions 53

3.3.2 Implemented functions 55

3.4 Comparative analysis 58

3.4.1 Qualitative comparison 58

3.4.2 Quantitative comparison 61

3.5 Conclusions 70

4 Discrete Event System Models 71

4.1 Introduction 71

4.2 Environment abstraction 72

4.3 Transition system models 75

4.3.1 Single robot case 75

4.3.2 Multi-robot case 79

4.4 Petri net models 83

4.5 Petri nets in resource allocation systems models 90

4.6 High-level specifications 96

4.7 Linear temporal logic 100

4.8 Conclusions 106

5 Path Planning by Using Transition System Models 109

5.1 Introduction 109

5.2 Two-step planning for a single robot and reachability specification 110

5.3 Quantitative comparison of two-step approaches 115

5.4 Receding horizon approach for a single robot and reachability specification 119

5.5 Simulations and analysis 123

5.6 Path planning with an LTL

5.7 Collision avoidance using initial delay 132

5.7.1 Problem description 132

5.7.2 Solution for Problem 5.1 (decentralized) 135

5.7.3 Solution for Problem 5.2 (centralized) 137

5.8 Conclusions 139

6 Path and Task Planning Using Petri Net Models 141

6.1 Introduction 141

6.2 Boolean-based specifications for cooperative robots 144

6.2.1 Problem definition and notations 144

6.2.2 Linear restrictions for Boolean-based specifications 146

6.2.3 Solution for constraints on the final state 147

6.2.4 Solution for constraints on trajectory and final state 149

6.2.5 Discussion on the above solutions 151

6.2.6 Suboptimal solution 152

6.2.7 Simulation examples 154

6.3 LTL specifications for cooperative robots 157

6.3.1 Problem definition and solution 157

6.3.2 Simulation examples 167

6.4 A sequencing problem 170

6.4.1 Problem statement 170

6.4.2 Solution 175

6.5 Task gathering problem 180

6.5.1 Problem formulation 180

6.5.2 Solution 181

6.6 Deadlock prevention using resource allocation models 185

6.7 Conclusions 192

7 Concluding Remarks 193

Bibliography 195

Index 211