Distributed Coordination Theory for Robot Teams develops control algorithms to coordinate the motion of autonomous teams of robots in order to achieve some desired collective goal. It provides novel solutions to foundational coordination problems, including distributed algorithms to make quadrotor helicopters rendezvous and to make ground vehicles move in formation along circles or straight lines. The majority of the algorithms presented in this book can be implemented using on-board cameras.
The book begins with an introduction to coordination problems, such as rendezvous of flying robots, and modelling. It then provides a solid theoretical background in basic stability, graph theory and control primitives. The book discusses the algorithmic solutions for numerous distributed control problems, focusing primarily on flying robotics and kinematic unicycles. Finally, the book looks to the future, and suggests areas discussed which could be pursued in further research.This book will provide practitioners, researchers and students in the field of control and robotics new insights in distributed multi-agent systems.
Author(s): Ashton Roza, Manfredi Maggiore, Luca Scardovi
Series: Lecture Notes in Control and Information Sciences, 490
Publisher: Springer
Year: 2022
Language: English
Pages: 152
City: Cham
Contents
Notation and Abbreviations
Notation for Kinematic Unicycle Model
Notation for Flying Robots
Notation in Chaps. 7 and 8
Abbreviations
1 Introduction
1.1 Motivation
1.2 What Is in This Book
1.3 What Is Not in This Book
1.4 Book Organization
References
2 Robot Models
2.1 Attitude Representation and Coordinate Frames
2.2 Models
2.2.1 Kinematic Unicycles
2.2.2 Flying Robots
2.3 Local and Distributed Feedback
References
3 Coordination Problems
3.1 Rendezvous of Flying Robots
3.2 Rendezvous of Kinematic Unicycles
3.3 Formation Control Problems
3.3.1 Parallel Formations That Stop
3.3.2 Parallel Formation Flocking
3.3.3 Parallel Formation Path Following
3.3.4 Circular Formation Flocking
3.3.5 Circular Formation Path Following
Reference
4 Control Primitives
4.1 Control Primitives for Single Integrators
4.1.1 Single Integrator Consensus Controllers
4.1.2 Path Following Controllers
4.2 Control Primitives for Double Integrators
4.2.1 Double Integrator Consensus
4.3 Control Primitives for Rotational Integrators
4.3.1 Rotational Integrator Equilibrium Stabilization
4.3.2 Rotational Integrator Consensus
4.4 Control Primitive for Rotating Bodies in SO(3)
References
5 Rendezvous of Flying Robots
5.1 Review of the Rendezvous Control Problem
5.2 Solution of the Rendezvous Control Problem
5.3 Outline of the Proof of Theorem 5.1
5.4 Remarks on the Proposed Controller
5.5 Simulation Results
5.6 From Rendezvous to Formations
References
6 Rendezvous of Unicycles
6.1 Review of The Rendezvous Control Problem
6.2 Solution of the Rendezvous Control Problem
6.3 Outline of the Proof of Theorem 6.1
6.4 Remarks on the Proposed Controller
6.5 Simulation Results
References
7 Unicycle Formations Coming to Rest
7.1 The Parallel Formation Problem (PP)
7.2 Solution of the Parallel Formation Problem
7.3 Outline of the Proof of Theorem 7.1
7.4 Remarks on the Proposed Controller
7.5 Special Cases: Line Formations and Full Synchronization
7.6 Simulation Results
References
8 Unicycle Formations with Parallel and Circular Motions
8.1 Introduction
8.2 Final Linear Motion
8.3 Proof of Theorem 8.1
8.4 Final Circular Motion
8.5 Proof of Theorem 8.2
8.6 Simulation Results
Reference
9 Unicycle Formation Simulation Trials
9.1 Performance Measures
9.2 Simulation Trials
9.2.1 Variation of the Formation Threshold
9.2.2 Variation of the High-Gain Parameters barα and k
9.2.3 State-Dependent Undirected Graphs
9.2.4 Directed Graphs
9.2.5 Input Saturation
9.2.6 Disturbances and Sampling
10 Bibliographical Notes
10.1 Literature on Multi-agent Coordination
10.1.1 Coordination Problems for Single and Double Integrators
10.1.2 Relative Equilibria for Kinematic Unicycles
10.1.3 Kinematic Unicycle Rendezvous
10.1.4 Flying Robot Attitude Synchronization and Rendezvous
10.1.5 Formations of Kinematic Unicycles
10.1.6 Kinematic Unicycle Formations with Final Collective Motions
References
Appendix A Notions of Stability Theory
A.1 Equilibrium Stability Theorems
A.2 Stability of Gradient Systems
A.3 Stability of Homogeneous Systems
A.4 Exponential Instability of Equilibria
A.5 Stability of Sets: Definitions
A.6 Stability of Sets: Reduction Theorems
Appendix B Notions of Graph Theory
B.0.1 Basic Definitions in Graph Theory
B.0.2 Classes of Graphs
B.0.3 Graph Decomposition
Appendix References
Index
