Formation Control of Multi-Agent Systems

A comprehensive guide to formation control of multi-agent systems using rigid graph theory This book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems. Such systems are relevant to a variety of emerging engineering applications, including unmanned robotic vehicles and mobile sensor networks. Graph theory, and rigid graphs in particular, provides a natural tool for describing the multi-agent formation shape as well as the inter-agent sensing, communication, and control topology. Beginning with an introduction to rigid graph theory, the contents of the book are organized by the agent dynamic model (single integrator, double integrator, and mechanical dynamics) and by the type of formation problem (formation acquisition, formation manoeuvring, and target interception). The book presents the material in ascending level of difficulty and in a self-contained manner; thus, facilitating reader understanding. Key features: Uses the concept of graph rigidity as the basis for describing the multi-agent formation geometry and solving formation control problems. Considers different agent models and formation control problems. Control designs throughout the book progressively build upon each other. Provides a primer on rigid graph theory. Combines theory, computer simulations, and experimental results. Formation Control of Multi-Agent Systems: A Graph Rigidity Approach is targeted at researchers and graduate students in the areas of control systems and robotics. Prerequisite knowledge includes linear algebra, matrix theory, control systems, and nonlinear systems.

A comprehensive guide to formation control of multi-agent systems using rigid graph theoryThis book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems. Such systems are relevant to a variety of emerging engineering applications, including unmanned robotic vehicles and mobile sensor networks. Graph theory, and rigid graphs in particular, provides a natural tool for describing the multi-agent formation shape as well as the inter-agent sensing, communication, and control topology.Beginning with an introduction to rigid graph theory, the contents of the book are organized by the agent dynamic model (single integrator, double integrator, and mechanical dynamics) and by the type of formation problem (formation acquisition, formation manoeuvring, and target interception). The book presents the material in ascending level of difficulty and in a self-contained manner; thus, facilitating reader understanding.Key features:* Uses the concept of graph rigidity as the basis for describing the multi-agent formation geometry and solving formation control problems.* Considers different agent models and formation control problems.* Control designs throughout the book progressively build upon each other.* Provides a primer on rigid graph theory.* Combines theory, computer simulations, and experimental results.Formation Control of Multi-Agent Systems: A Graph Rigidity Approach is targeted at researchers and graduate students in the areas of control systems and robotics. Prerequisite knowledge includes linear algebra, matrix theory, control systems, and nonlinear systems.

Preface xiAbout the Companion Website xiii1 Introduction 11.1 Motivation 11.2 Notation 61.3 Graph Theory 71.3.1 Graph 71.3.2 Framework 91.3.3 Rigid Graphs 111.3.4 Infinitesimal Rigidity 141.3.5 Minimal Rigidity 191.3.6 Framework Ambiguities 201.3.7 Global Rigidity 221.4 Formation Control Problems 231.5 Book Overview and Organization 261.6 Notes and References 282 Single-Integrator Model 292.1 Formation Acquisition 292.2 Formation Maneuvering 352.3 Flocking 362.3.1 Constant Flocking Velocity 372.3.2 Time-Varying Flocking Velocity 382.4 Target Interception with Unknown Target Velocity 402.5 Dynamic Formation Acquisition 432.6 Simulation Results 452.6.1 Formation Acquisition 452.6.2 Formation Maneuvering 512.6.3 Flocking 562.6.4 Target Interception 582.6.5 Dynamic Formation 632.7 Notes and References 663 Double-Integrator Model 713.1 Cross-Edge Energy 733.2 Formation Acquisition 753.3 Formation Maneuvering 763.4 Target Interception with Unknown Target Acceleration 773.5 Dynamic Formation Acquisition 793.6 Simulation Results 803.6.1 Formation Acquisition 803.6.2 Dynamic Formation Acquisition with Maneuvering 813.6.3 Target Interception 843.7 Notes and References 874 Robotic Vehicle Model 914.1 Model Description 914.2 Nonholonomic Kinematics 934.2.1 Control Design 934.2.2 Simulation Results 944.3 Holonomic Dynamics 974.3.1 Model-Based Control 984.3.2 Adaptive Control 1004.3.3 Simulation Results 1024.4 Notes and References 1025 Experimentation 1075.1 Experimental Platform 1075.2 Vehicle Equations of Motion 1105.3 Low-Level Control Design 1135.4 Experimental Results 1145.4.1 Single Integrator: Formation Acquisition 1175.4.2 Single Integrator: Formation Maneuvering 1185.4.3 Single Integrator: Target Interception 1265.4.4 Single Integrator: Dynamic Formation 1285.4.5 Double Integrator: Formation Acquisition 1325.4.6 Double Integrator: Formation Maneuvering 1365.4.7 Double Integrator: Target Interception 1385.4.8 Double Integrator: Dynamic Formation 1485.4.9 Holonomic Dynamics: Formation Acquisition 1495.4.10 Summary 153A Matrix Theory and Linear Algebra 159B Functions and Signals 163C Systems Theory 165C.1 Linear Systems 165C.2 Nonlinear Systems 166C.3 Lyapunov Stability 168C.4 Input-to-State Stability 170C.5 Nonsmooth Systems 171C.6 Integrator Backstepping 172D Dynamic Model Terms 175References 177Index 187