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2023 | Book

Distributed Attitude Consensus of Multiple Flexible Spacecraft

Authors: Ti Chen, Jinjun Shan, Hao Wen

Publisher: Springer Nature Singapore

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About this book

This book mainly presents the authors' recent studies on the distributed attitude consensus of multiple flexible spacecraft. Modified Rodrigues parameters and rotation matrix are used to represent spacecraft attitude. Several distributed adaptive controllers are presented with theoretical analyses, numerical simulations and experimental verifications. The authors intend to provide a manual that allows researchers, engineers and students in the field of aerospace engineering and mechanics to learn a theoretical and practical approach to the design of attitude consensus algorithms.

Table of Contents

Frontmatter

Preliminaries and Literature Review

Frontmatter
Chapter 1. Graph Theory and Attitude Representations
Abstract
The communication between the networked spacecraft can be described by algebraic graphs. This chapter presents some basic knowledge of graph theory. Furthermore, the configuration space of the rigid-body rotation is the special Lie group SO(3). Attitude parameterizations are important to solve the attitude consensus problem. Hence, various attitude representation methods are introduced in this chapter.
Ti Chen, Jinjun Shan, Hao Wen
Chapter 2. Literature Review
Abstract
In the past two decades, spacecraft attitude coordination has gained significant developments. This chapter aims to present a survey of recent research on the spacecraft attitude consensus problem, paying particular attention to the papers published in major aerospace, dynamics, automation and robotics journals.
Ti Chen, Jinjun Shan, Hao Wen

Leader-Follower Attitude Consensus of Networked Flexible Spacecraft

Frontmatter
Chapter 3. Distributed Passivity-Based Control with Attitude-Only Measurements
Abstract
This chapter focuses on the leader-follower attitude consensus of multiple under-actuated flexible spacecraft without system damping based on attitude measurements only. By constructing two different kinds of auxiliary Euler-Lagrange systems, passivity-based controllers are designed under undirected or directed communication graphs to achieve the distributed attitude tracking and vibration suppression simultaneously. For the leader-follower consensus under directed graphs, only the controller’s generalized coordinates and the spacecraft attitudes are exchanged among the followers with the help of an extended state observer. The Lyapunov theory is adopted for the stability analysis of the overall system. Finally, numerical simulations are conducted to verify the effectiveness of the proposed controllers.
Ti Chen, Jinjun Shan, Hao Wen
Chapter 4. Rotation-Matrix-Based Attitude Tracking Under an Undirected Tree Graph
Abstract
This chapter studies the distributed leader-follower consensus for multiple flexible spacecraft with actuator faults under an undirected tree graph. The attitudes of the networked flexible spacecraft are represented on the special orthogonal group SO(3) globally and uniquely. A fault-tolerant tracking controller is proposed to protect against the partial loss of actuator effectiveness based on sign function. Then the saturation function with an adaptive parameter is introduced to replace the sign function. Rigorous Lyapunov analyses are presented to prove the stability of the overall system. Finally, numerical simulations are conducted to verify the effectiveness of the proposed controllers.
Ti Chen, Jinjun Shan, Hao Wen
Chapter 5. Adaptive Fault-tolerant Attitude Tracking on SO(3) Under an Undirected Graph
Abstract
This chapter presents the distributed adaptive fault-tolerant control for the attitude tracking of multiple flexible spacecraft on SO(3) without modal variable measurement. Assume that the communication graph among the followers are undirected and connected and there exists at least one follower linked to the leader. To deal with the distributed tracking on SO(3), a finite-time observer is designed to estimate the leader’s information for the followers. A distributed adaptive fault-tolerant controller is proposed to achieve the attitude tracking based on the estimation of the unmeasurable modal variables. The separation principle between the finite-time observer and the proposed controller is adopted to prove the controller convergence. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed control protocols.
Ti Chen, Jinjun Shan, Hao Wen
Chapter 6. Distributed Attitude Tracking and Synchronization on SO(3) Under Directed Graphs
Abstract
Distributed adaptive controllers are developed for attitude tracking and synchronization on SO(3) of multiple flexible spacecraft under a directed graph. Since not all spacecraft can receive the virtual leader’s information, a finite-time observer is designed for each follower spacecraft to estimate the moving virtual leader’s information. An adaptive controller is then proposed to realize the distributed attitude tracking synchronously and achieve the bounded flexible vibration. A rigorous theoretical proof is presented based on the separation principle. Furthermore, an adaptive controller with a modal variable observer is designed for the case without the measurements of the modal variables. Finally, numerical and experimental verifications are presented.
Ti Chen, Jinjun Shan, Hao Wen
Chapter 7. Continuous Constrained Attitude Regulation on SO(3)
Abstract
In this chapter, both the centralized and distributed attitude regulation of multiple flexible spacecraft are studied on SO(3) with attitude constraints in the absence of the measurements of the angular velocities and modal coordinates. For centralized regulation, each spacecraft knows the desired attitude. A repulsive potential function is constructed to handle attitude constraints. Then a continuous controller is designed without the measurements of angular velocities. With the assumption that only some spacecraft know the desired attitude, a finite-time observer is introduced to estimate the leader’s information under fixed or switching communication graphs. A continuous control law is proposed for the distributed attitude regulation with the estimate of the leader as the reference signal.
Ti Chen, Jinjun Shan, Hao Wen

Leaderless Attitude Consensus of Networked Rigid Spacecraft

Frontmatter
Chapter 8. Continuous Leaderless Synchronization Control of Multiple Rigid Spacecraft on SO(3)
Abstract
This chapter presents a solution to the leaderless consensus of multiple spacecraft on SO(3) under a connected undirected graph. An algorithm is proposed to generate an undirected tree graph from a communication topology. A distributed observer is designed to estimate the desired attitude and angular velocity of each spacecraft under the generated tree graph. An adaptive controller with a general connected undirected graph is developed to complete the synchronization task. Cases with zero and nonzero final angular velocities are considered. Theoretical proofs and numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.
Ti Chen, Jinjun Shan, Hao Wen
Chapter 9. Koopman-Operator-Based Attitude Dynamics and Control on SO(3)
Abstract
This chapter presents an attitude control method based on Koopman operator theory. A set of observables is discovered to represent the nonlinear attitude dynamics on SO(3) using an infinite-dimensional linear system. With the assumption of low angular velocities, a finite-dimensional linear system is obtained by removing the high-order terms. An attitude control synthesis method is developed on the basis of the linear optimal control algorithm for the reduced linear system. The proposed controller design method is compared with some classical nonlinear optimal controllers to show its advantages. Also, the leaderless attitude synchronization problem is solved with the help of the reduced linear system and the well-studied linear multi-agent system theory. Furthermore, a possible solution to the case with a high angular velocity is provided. Simulations and experiments are conducted to verify the effectiveness of the theory.
Ti Chen, Jinjun Shan, Hao Wen
Metadata
Title
Distributed Attitude Consensus of Multiple Flexible Spacecraft
Authors
Ti Chen
Jinjun Shan
Hao Wen
Copyright Year
2023
Publisher
Springer Nature Singapore
Electronic ISBN
978-981-19-4258-7
Print ISBN
978-981-19-4257-0
DOI
https://doi.org/10.1007/978-981-19-4258-7

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