多智能体编队控制的新图论方法
发布时间：2021-09-07 10:18
多智能体系统的分布式协同控制在现实中具有非常多的潜在应用。与单个智能体执行任务相比,成群智能体的协作具有更高的效率以及可调控性。近年来,分布式编队控制,作为分布式协同控制中非常重要的一类问题,已经被广泛的讨论和研究,并取得了一系列突破性的成果,但仍有一些关键的问题没有被解决。在这篇博士论文中,我们提出两种新的图论工.具,并将它们应用于分布式编队控制中。与已有的文献相比,我们提出的编队控制策略具有一些明显的优势,为提升编队性能提供了新的视角。我们的工作可以总结为以下几点。1.我们提出“弱刚性理论”来研究一个几何图形的形状是否可以由图中一些成对相对位移的内积来唯一确定。与已有的距离刚性和方位刚性相比,弱刚性在确定一个任意维空间中几何图形的形状时,需要边的数量更少。在已有文献中,一个图形是否刚性一般是通过计算刚性矩阵的秩来检测。因此,对于具有很多节点的大型编队,计算复杂度会很高。在我们的工作中,我们推导出了平面上图形是无穷小弱刚性图的充要图条件,利用这个条件,我们可以很容易检测任意一个平面图形是否是无穷小弱刚性的。之后我们将弱刚性理论应用在了多智能体编队中,针对一群单积分器智能体,我们提出了...
【文章来源】：西安电子科技大学陕西省 211工程院校 教育部直属院校
【文章页数】：130 页
【学位级别】：博士
【文章目录】：
ABSTRACT
摘要
List of Symbols
List of Abbreviations
Chapter 1 Introduction
1.1 Background of Multi-Agent Systems
1.2 Formation Control
1.2.1 Background and Motivation
1.2.2 Literature Review
1.2.3 Unsolved Problems
1.3 Organization and Contribution of the Thesis
Chapter 2 Preliminaries
2.1 Graph Theory
2.2 Graph Rigidity Theory
2.2.1 Distance Rigidity Theory
2.2.2 Bearing Rigidity Theory
2.3 Center Manifold Theory
2.4 Formation Shape Stabilization
2.4.1 Displacement-based Formation Control
2.4.2 Bearing-based Formation Control
2.4.3 Distance-based Formation Control
2.5 Practicality of Gradient Systems
2.5.1 Connection to Double-Integrator Systems
2.5.2 Connection to Non-Holonomic Systems
Chapter 3 Weak Rigidity Theory
3.1 Weak Rigidity
3.1.1 Definitions Associated with Weak Rigidity
3.1.2 Construction of a Minimal Constraint Set
3.1.3 Comparisons Between Rigidity and Weak Rigidity
3.1.4 A Matrix Completion Perspective
3.1.5 Generic Property
3.2 Application to Formation Control
3.2.1 Control Objective
3.2.2 A Steepest Descent Formation Controller
3.2.3 Stability Analysis
3.2.4 Formation Control Under Non-Rigid Graphs
3.3 Simulation Examples
3.4 Summary
Chapter 4 Angle Rigidity Theory
4.1 Angle Rigidity
4.1.1 The Relation to Bearing Rigidity
4.1.2 Construction of Angle Constraint Set for Rigidity
4.1.3 Frameworks Uniquely Determined by Angles
4.2 Application to Formation Control
4.2.1 The Formation Stabilization Problem
4.2.2 A Steepest Descent Formation Controller
4.2.3 Stability Analysis
4.2.4 Orientation and Scale Control
4.2.5 Simulation Examples
4.3 Summary
Chapter 5 Angle-based Formation Control with Almost Global Convergence
5.1 Stationary Angle-based Formation Stabilization
5.1.1 An Artificial Potential Function
5.1.2 A Steepest Descent Formation Controller
5.1.3 Stability Analysis
5.1.4 Sign of Triangulated Frameworks
5.1.5 Analysis for Collision Avoidance
5.1.6 A Simulation Example
5.2 Dynamic Angle-based Formation Stabilization
5.2.1 Agent Dynamics and Sensing Capability
5.2.2 Flocking with a Desired Formation Shape
5.2.3 A Distributed Formation Stabilization Controller
5.2.4 Stability Analysis
5.2.5 A Simulation Example
5.3 Dynamic Angle-based Formation with a Leader
5.3.1 The Formation Law and Its Properties
5.3.2 Stability Analysis
5.3.3 A Simulation Example
5.4 Summary
Chapter 6 Conclusion and Future Work
6.1 Summary of Contributions
6.2 Future Works
References
Acknowledgement
Biography
本文编号：3389368
【文章来源】：西安电子科技大学陕西省 211工程院校 教育部直属院校
【文章页数】：130 页
【学位级别】：博士
【文章目录】：
ABSTRACT
摘要
List of Symbols
List of Abbreviations
Chapter 1 Introduction
1.1 Background of Multi-Agent Systems
1.2 Formation Control
1.2.1 Background and Motivation
1.2.2 Literature Review
1.2.3 Unsolved Problems
1.3 Organization and Contribution of the Thesis
Chapter 2 Preliminaries
2.1 Graph Theory
2.2 Graph Rigidity Theory
2.2.1 Distance Rigidity Theory
2.2.2 Bearing Rigidity Theory
2.3 Center Manifold Theory
2.4 Formation Shape Stabilization
2.4.1 Displacement-based Formation Control
2.4.2 Bearing-based Formation Control
2.4.3 Distance-based Formation Control
2.5 Practicality of Gradient Systems
2.5.1 Connection to Double-Integrator Systems
2.5.2 Connection to Non-Holonomic Systems
Chapter 3 Weak Rigidity Theory
3.1 Weak Rigidity
3.1.1 Definitions Associated with Weak Rigidity
3.1.2 Construction of a Minimal Constraint Set
3.1.3 Comparisons Between Rigidity and Weak Rigidity
3.1.4 A Matrix Completion Perspective
3.1.5 Generic Property
3.2 Application to Formation Control
3.2.1 Control Objective
3.2.2 A Steepest Descent Formation Controller
3.2.3 Stability Analysis
3.2.4 Formation Control Under Non-Rigid Graphs
3.3 Simulation Examples
3.4 Summary
Chapter 4 Angle Rigidity Theory
4.1 Angle Rigidity
4.1.1 The Relation to Bearing Rigidity
4.1.2 Construction of Angle Constraint Set for Rigidity
4.1.3 Frameworks Uniquely Determined by Angles
4.2 Application to Formation Control
4.2.1 The Formation Stabilization Problem
4.2.2 A Steepest Descent Formation Controller
4.2.3 Stability Analysis
4.2.4 Orientation and Scale Control
4.2.5 Simulation Examples
4.3 Summary
Chapter 5 Angle-based Formation Control with Almost Global Convergence
5.1 Stationary Angle-based Formation Stabilization
5.1.1 An Artificial Potential Function
5.1.2 A Steepest Descent Formation Controller
5.1.3 Stability Analysis
5.1.4 Sign of Triangulated Frameworks
5.1.5 Analysis for Collision Avoidance
5.1.6 A Simulation Example
5.2 Dynamic Angle-based Formation Stabilization
5.2.1 Agent Dynamics and Sensing Capability
5.2.2 Flocking with a Desired Formation Shape
5.2.3 A Distributed Formation Stabilization Controller
5.2.4 Stability Analysis
5.2.5 A Simulation Example
5.3 Dynamic Angle-based Formation with a Leader
5.3.1 The Formation Law and Its Properties
5.3.2 Stability Analysis
5.3.3 A Simulation Example
5.4 Summary
Chapter 6 Conclusion and Future Work
6.1 Summary of Contributions
6.2 Future Works
References
Acknowledgement
Biography
本文编号：3389368
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