Distributed Attitude Consensus of Multiple Flexible Spacecraft

Preface
Contents
Part I Preliminaries and Literature Review
1 Graph Theory and Attitude Representations
	1.1 Notations
	1.2 Graph Theory
		1.2.1 Basic Definitions
		1.2.2 Graph Matrices
		1.2.3 Leader-Follower Communication Graph
	1.3 Attitude Representations
		1.3.1 Rotation Matrix
		1.3.2 Euler Angles
		1.3.3 Modified Rodrigues Parameters
		1.3.4 Quaternions
		1.3.5 Kinematic Differential Equations
	1.4 Dynamics Equation of Rigid Spacecraft
	1.5 Dynamics Equation of Flexible Spacecraft
	References
2 Literature Review
	2.1 Background
	2.2 Attitude Consensus Under Various Communication Graphs
		2.2.1 Centralized Attitude Consensus
		2.2.2 Decentralized Attitude Consensus
		2.2.3 Distributed Attitude Consensus
	2.3 Attitude Consensus with Various Attitude Representations
		2.3.1 Euler-Angles-Based Attitude Consensus
		2.3.2 MRPs-Based Attitude Consensus
		2.3.3 Quanternions-Based Attitude Consensus
		2.3.4 Rotation-Matrix-Based Attitude Consensus
		2.3.5 Attitude Consensus Based on Other Attitude Representations
	2.4 Attitude Consensus Under Complicated Conditions
		2.4.1 Attitude Consensus with Input Saturation
		2.4.2 Attitude Consensus with Actuator Faults
		2.4.3 Attitude Consensus with State Constraints
		2.4.4 Experimental Results on Attitude Consensus
	2.5 Attitude Consensus of Multiple Flexible Spacecraft
	2.6 Conclusions
	References
Part II Leader-Follower Attitude Consensus of Networked Flexible Spacecraft
3 Distributed Passivity-Based Control with Attitude-Only Measurements
	3.1 Introduction
	3.2 Problem Formulation
		3.2.1 Dynamic Equation of Undamped Flexible Spacecraft
		3.2.2 Properties of Networked Flexible Spacecraft
	3.3 Distributed Passivity-Based Control
		3.3.1 Control Objective
		3.3.2 Passivity-Based Control Methodology
		3.3.3 Distributed Controller Under Undirected Graph
		3.3.4 Distributed Controller Under Directed Graph
	3.4 Numerical Simulations
		3.4.1 Case I: Leader-Follower Tracking Under Undirected Graph
		3.4.2 Case II: Leader-Follower Tracking Under Directed Graph
	3.5 Conclusions
	References
4 Rotation-Matrix-Based Attitude Tracking Under an Undirected Tree Graph
	4.1 Introduction
	4.2 Dynamics of Flexible Spacecraft Based on Rotation Matrix
	4.3 Coordinated Tracking Control
		4.3.1 Control Objective
		4.3.2 Controller Design
	4.4 Numerical Simulations
		4.4.1 Case I: Fault-Tolerant Control
		4.4.2 Case II: Fault-Tolerant Control from script upper M 1mathcalM1 with Initial Disturbance
		4.4.3 Case III: Response Without Structural Damping Under Controller (4.24)
	4.5 Conclusions
	References
5 Adaptive Fault-tolerant Attitude Tracking on upper S upper O left parenthesis 3 right parenthesisSO(3) Under an Undirected Graph
	5.1 Introduction
	5.2 Problem Formulation
		5.2.1 Kinematics and Dynamics of Flexible Spacecraft
		5.2.2 Control Objective
	5.3 Distributed Attitude Tracking Control
		5.3.1 Finite-time Distributed Observer
		5.3.2 Modal Variable Observer
		5.3.3 Controller Design
	5.4 Numerical Simulations
	5.5 Conclusions
	References
6 Distributed Attitude Tracking and Synchronization on upper S upper O left parenthesis 3 right parenthesisSO(3) Under Directed Graphs
	6.1 Introduction
	6.2 Problem Formulation
		6.2.1 Dynamics Equation of Flexible Spacecraft
		6.2.2 Control Objective
	6.3 Distributed Attitude Tracking and Synchronization Under Directed Graphs
		6.3.1 Distributed Leader Observer
		6.3.2 Distributed Tracking and Synchronization with Full State Feedback
		6.3.3 Distributed Tracking and Synchronization with Partial State Feedback
	6.4 Numerical Simulations
	6.5 Experimental Verification
	6.6 Conclusions
	References
7 Continuous Constrained Attitude Regulation on MathID2SO(3)
	7.1 Introduction
	7.2 Problem Formulation
		7.2.1 Kinematics and Dynamics of Flexible Spacecraft
		7.2.2 Attitude Constraints Based on Rotation Matrix
		7.2.3 Control Objective
	7.3 Centralized Velocity-Free Attitude Regulation
		7.3.1 Repulsive Potential Function
		7.3.2 Centralized Velocity-Free Control
		7.3.3 Undesired Critical Points
		7.3.4 Finite Control Torque
	7.4 Distributed Attitude Regulation Control
		7.4.1 Finite-Time Distributed Observer
		7.4.2 Distributed Velocity-Free Regulation Controller
	7.5 Numerical Simulations
		7.5.1 Centralized Attitude Regulation
		7.5.2 Distributed Attitude Regulation
	7.6 Conclusions
	References
Part III Leaderless Attitude Consensus of Networked Rigid Spacecraft
8 Continuous Leaderless Synchronization Control of Multiple Rigid Spacecraft on MathID2SO(3)
	8.1 Introduction
	8.2 Spacecraft Dynamics
	8.3 Leaderless Consensus with Nonzero Final Angular Velocity
		8.3.1 Control Objective
		8.3.2 Generating an Undirected Tree Graph
		8.3.3 Distributed Observer
		8.3.4 Controller Design
	8.4 Leaderless Consensus with Zero Final Angular Velocity
		8.4.1 Control Objective
		8.4.2 Distributed Observer
		8.4.3 Controller Design
	8.5 Simulations
	8.6 Conclusions
	References
9 Koopman-Operator-Based Attitude Dynamics and Control on SO(3)
	9.1 Introduction
	9.2 Problem Formulation
		9.2.1 Koopman Operator
		9.2.2 Spacecraft Dynamics on SO(3)
	9.3 Koopman Operator for Attitude Dynamics
		9.3.1 Reduced Linear Model
		9.3.2 Simulation Verification
	9.4 Controller Design Based on Koopman Operator
		9.4.1 Controller Design
		9.4.2 Simulation Verification
		9.4.3 Experimental Verification
		9.4.4 Comparison with Traditional Optimal Control
		9.4.5 Application to Leaderless Synchronization
		9.4.6 Experimental Verification
	9.5 Attitude Control with Large Angular Velocities
		9.5.1 Controller Design
		9.5.2 Simulation Verification
		9.5.3 Experimental Verification
	9.6 Conclusions
	References