Distributed Coordination Theory for Robot Teams

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