Formation Control of Multi-Agent Systems E-Book

Marcio de Queiroz

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Dynamics and Control of Electromechanical Systems
• Sprache: Englisch

Seitenzahl: 222

Veröffentlichungsjahr: 2018

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Preface

About the Companion Website

1 Introduction

1.1 Motivation

1.2 Notation

1.3 Graph Theory

1.4 Formation Control Problems

1.5 Book Overview and Organization

1.6 Notes and References

2 Single‐Integrator Model

2.1 Formation Acquisition

2.2 Formation Maneuvering

2.3 Flocking

2.4 Target Interception with Unknown Target Velocity

2.5 Dynamic Formation Acquisition

2.6 Simulation Results

2.7 Notes and References

3 Double‐Integrator Model

3.1 Cross‐Edge Energy

3.2 Formation Acquisition

3.3 Formation Maneuvering

3.4 Target Interception with Unknown Target Acceleration

3.5 Dynamic Formation Acquisition

3.6 Simulation Results

3.7 Notes and References

4 Robotic Vehicle Model

4.1 Model Description

4.2 Nonholonomic Kinematics

4.3 Holonomic Dynamics

4.4 Notes and References

5 Experimentation

5.1 Experimental Platform

5.2 Vehicle Equations of Motion

5.3 Low‐Level Control Design

5.4 Experimental Results

Appendix A: Matrix Theory and Linear Algebra

Appendix B: Functions and Signals

Appendix C: Systems Theory

C.1 Linear Systems

C.2 Nonlinear Systems

C.3 Lyapunov Stability

C.4 Input‐to‐State Stability

C.5 Nonsmooth Systems

C.6 Integrator Backstepping

Appendix D: Dynamic Model Terms

References

Index

End User License Agreement

List of Illustrations

Chapter 1

Figure 1.1 Examples of collective behavior in nature: a flock of birds (top lef...

Figure 1.2 Examples of engineering multi‐agent systems.

Figure 1.3 Centralized (left) and decentralized (right) formation control.

Figure 1.4 The complete graph

.

Figure 1.5 Examples of bar‐and‐joint frameworks, although the joints here are no...

Figure 1.6 Example of (a) a graph and (b) a corresponding framework.

Figure 1.7 Rigid body kinematics.

Figure 1.8 Isomorphic frameworks.

Figure 1.9 Examples of (a) flexible and (b) rigid bar‐and‐joint frameworks.

Figure 1.10 Example of a rigid framework that is not infinitesimally rigid.

Figure 1.11 A nongeneric framework in

.

Figure 1.12 A tetrahedron framework.

Figure 1.13 (a) Minimally and (b) nonminimally rigid graphs.

Figure 1.14 Examples of nonunique realizations for infinitesimally rigid framew...

Figure 1.15 (a) Rigidity versus (b) global rigidity.

Figure 1.16 Example of the construction of

: a tetrahedron formation where

st...

Figure 1.17 Overview of the book organization.

Chapter 2

Figure 2.1 Energy landscape showing the two equilibrium points, Iso

and Amb

, ...

Figure 2.2 (a) The collinearity of agents 1, 2, 3, and 4 is invariant. (b) The c...

Figure 2.3 Fixed and local coordinate frames.

Figure 2.4 Formation acquisition: desired formation

.

Figure 2.5 Formation acquisition: agent trajectories

,

.

Figure 2.6 Formation acquisition: distance errors

,

.

Figure 2.7 Formation acquisition: control inputs

,

.

Figure 2.8 Formation acquisition: agents converging to an ambiguous framework.

Figure 2.9 Formation acquisition: (a) distance errors

,

and (b) distance erro...

Figure 2.10 Desired formation

with modified edge set.

Figure 2.11 Formation acquisition: agents converging to correct formation after ...

Figure 2.12 Formation maneuvering (Simulation 1): desired formation

.

Figure 2.13 Formation maneuvering (Simulation 1): snapshots of

at different in...

Figure 2.14 Formation maneuvering (Simulation 1): distance errors

,

.

Figure 2.15 Formation maneuvering (Simulation 1): control inputs

,

.

Figure 2.16 Formation maneuvering (Simulation 2): desired formation

.

Figure 2.17 Formation maneuvering (Simulation 2): snapshots in time of the forma...

Figure 2.18 Formation maneuvering (Simulation 2): distance errors

,

.

Figure 2.19 Formation maneuvering (Simulation 2): control inputs

,

in the

,

Figure 2.20 Flocking (continuous controller–observer;

): snapshots of

at diff...

Figure 2.21 Flocking (continuous controller–observer;

): distance errors

,

.

Figure 2.22 Flocking (continuous controller–observer;

): velocity estimation er...

Figure 2.23 Flocking (continuous controller–observer;

): control inputs

,

in...

Figure 2.24 Flocking (continuous controller–observer;

): distance errors

,

.

Figure 2.25 Flocking (continuous controller–observer;

): velocity estimation er...

Figure 2.26 Flocking (continuous controller–observer;

): control inputs

,

in...

Figure 2.27 Flocking (continuous controller–observer;

): velocity estimation er...

Figure 2.28 Flocking (continuous controller–observer;

): distance errors with t...

Figure 2.29 Flocking (discontinuous controller–observer;

): distance errors wit...

Figure 2.30Figure 2.30 Flocking (discontinuous controller–observer;

): velocity...

Figure 2.31 Flocking (discontinuous controller–observer;

): control inputs.

Figure 2.32 Target interception: snapshots of

at different instants of time al...

Figure 2.33 Target interception: distance errors

,

.

Figure 2.34 Target interception: control inputs

,

.

Figure 2.35 Dynamic formation: snapshots of

at different instants of time alon...

Figure 2.36 Dynamic formation: distance errors

,

.

Figure 2.37 Dynamic formation: control inputs

.

Chapter 3

Figure 3.1 Relationship between the (a) single‐ and (b) double‐integrator contr...

Figure 3.2 Energy landscape where the formation is at position

with velocity

Figure 3.3 Desired formation (solid line) and a flip ambiguity (dashed line).

Figure 3.4 Triangulated hexagon framework.

Figure 3.5 Formation acquisition: desired formation

.

Figure 3.6 Formation acquisition: agent trajectories

,

.

Figure 3.7 Formation acquisition: distance errors

,

.

Figure 3.8 Formation acquisition: velocity errors

,

.

Figure 3.9 Formation acquisition: control inputs

,

.

Figure 3.10 Dynamic formation acquisition with maneuvering: snapshots of

at di...

Figure 3.11 Dynamic formation acquisition with maneuvering: distance errors

,

Figure 3.12 Dynamic formation acquisition with maneuvering: velocity errors

,

Figure 3.13 Dynamic formation acquisition with maneuvering: control inputs

,

.

Figure 3.14 Target interception: snapshots of

at different instants of time al...

Figure 3.15 Target interception: distance errors

,

.

Figure 3.16 Target interception: velocity errors

,

.

Figure 3.17Figure 3.17 Target interception: control inputs

,

.

Chapter 4

Figure 4.1 The

th robotic vehicle.

Figure 4.2 Desired formation

.

Figure 4.3 Trajectory of the poses

,

.

Figure 4.4 Distance errors

,

(top) and orientation errors

,

(bottom).

Figure 4.5 Control inputs

,

(top) and

,

(bottom).

Figure 4.6 Trajectory of the hand positions

,

.

Figure 4.7 Distance errors

,

.

Figure 4.8 Control inputs

,

.

Figure 4.9 Parameter estimates for vehicle 1,

.

Chapter 5

Figure 5.1 Top view of the experimental UGV platform.

Figure 5.2 Side view of the UGV.

Figure 5.3 Experimental control and communication scheme.

Figure 5.4 Schematic of the experimental UGV.

Figure 5.5 Friction force on the UGV.

Figure 5.6 Initial configuration of the UGVs during the experimental runs.

Figure 5.7 Single integrator: formation acquisition. UGV position trajectories

Figure 5.8 Single integrator: formation acquisition. UGV distance errors

,

.

Figure 5.9 Single integrator: formation acquisition. Drive‐wheel DC motor voltag...

Figure 5.10 Single integrator: formation acquisition. Steering angle commands

,...

Figure 5.11 Single integrator: formation acquisition. Velocity error

for each ...

Figure 5.12 Single integrator: formation translation. UGV position trajectories

Figure 5.13 Single integrator: formation translation. UGV distance errors

,

.

Figure 5.14 Single integrator: formation translation. UGV speeds and heading ang...

Figure 5.15 Single integrator: formation translation. Drive‐wheel DC motor volta...

Figure 5.16 Single integrator: formation translation. Steering angle commands

,...

Figure 5.17 Single integrator: formation translation/rotation. UGV position traj...

Figure 5.18 Single integrator: formation translation/rotation. UGV distance erro...

Figure 5.19 Single integrator: formation translation/rotation. UGV bearing rate

Figure 5.20 Single integrator: formation translation/rotation. Velocity error

...

Figure 5.21 Single integrator: formation translation/rotation. Drive‐wheel DC mo...

Figure 5.22 Single integrator: formation translation/rotation. Steering angle co...

Figure 5.23 Single integrator: target interception. UGV position trajectories

,...

Figure 5.24 Single integrator: target interception. UGV distance errors

,

.

Figure 5.25 Single integrator: target interception. Target interception error

.

Figure 5.26 Single integrator: target interception. Drive‐wheel DC motor voltage...

Figure 5.27 Single integrator: target interception. Steering angle commands

,

Figure 5.28 Single integrator: dynamic formation. UGV position trajectories

,

Figure 5.29 Single integrator: dynamic formation. UGV distance errors

,

.

Figure 5.30 Single integrator: dynamic formation. Drive‐wheel DC motor voltages

Figure 5.31 Single integrator: dynamic formation. Steering angle commands

,

.

Figure 5.32 Double integrator: formation acquisition. UGV position trajectories

Figure 5.33 Comparison of UGV position trajectories.

Figure 5.34 Double integrator: formation acquisition. UGV distance errors

,

.

Figure 5.35 Comparison of distance errors.

Figure 5.36 Double integrator: formation acquisition. Drive‐wheel DC motor volta...

Figure 5.37 Double integrator: formation acquisition. Steering angle commands

,...

Figure 5.38 Double integrator: formation maneuvering. UGV position trajectories

Figure 5.39 Comparison of UGV position trajectories.

Figure 5.40 Double integrator: formation maneuvering. UGV distance errors

,

.

Figure 5.41 Comparison of distance errors.

Figure 5.42 Double integrator: formation maneuvering. Velocity error

of each U...

Figure 5.43 Double integrator: formation maneuvering. Drive‐wheel DC motor volta...

Figure 5.44 Double integrator: formation maneuvering. Steering angle commands

,...

Figure 5.45 Double integrator: target interception. UGV position trajectories

,...

Figure 5.46 Double integrator: target interception. UGV distance errors

,

.

Figure 5.47 Double integrator: target interception. Target interception error

.

Figure 5.48 Double integrator: target interception. Velocity error

of each UGV...

Figure 5.49 Double integrator: target interception. Drive‐wheel DC motor voltage...

Figure 5.50 Double integrator: target interception. Steering angle commands

,

Figure 5.51 Double integrator: dynamic formation. UGV position trajectories

,

Figure 5.52Figure 5.52 Comparison of UGV position trajectories.

Figure 5.53 Double integrator: dynamic formation. UGV distance errors

,

.

Figure 5.54Figure 5.54 Comparison of distance errors.

Figure 5.55 Double integrator: dynamic formation. Drive‐wheel DC motor voltages

Figure 5.56 Double integrator: dynamic formation. Steering angle commands

,

.

Figure 5.57 Holonomic dynamics: formation acquisition. UGV position trajectories...

Figure 5.58 Holonomic dynamics: formation acquisition. UGV distance errors

,

.

Figure 5.59 Comparison of distance errors.

Figure 5.60 Holonomic dynamics: formation acquisition. Parameter estimates for U...

Figure 5.61 Holonomic dynamics: formation acquisition. Velocity error

of each ...

Figure 5.62 Holonomic dynamics: formation acquisition. Drive‐wheel DC motor volt...

Figure 5.63 Holonomic dynamics: formation acquisition. Steering angle commands

Guide

Cover

Table of Contents

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Wiley Series in Dynamics and Control of Electromechanical Systems

Formation Control of Multi‐Agent Systems De Queiroz, Cai and Feemster February 2019 A Graph Rigidity Approach

Finite‐Time Stability

Amato, Tommasi and Pironti

August 2018

An Input‐Output Approach

Process Control System Fault Diagnosis

Gonzalez, Qi and Huang

September 2016

A Bayesian Approach

Variance‐Constrained Multi‐Objective

Ma, Wang and Bo

April 2015

Stochastic Control and Filtering

Sliding Mode Control of Uncertain

Wu, Shi and Su

July 2014

Parameter‐Switching Hybrid Systems

Algebraic Identification and Estimation

Sira‐Ramírez, García Rodríguez,

May 2014

Methods in Feedback Control Systems Cortes

Romero and Luviano Juárez

Formation Control of Multi-Agent Systems: A Graph Rigidity Approach

Marcio de Queiroz

Louisiana State University USA

Xiaoyu Cai

Louisiana State University USA

Matthew Feemster

United States Naval Academy USA

Copyright

This edition first published 2019

© 2019 John Wiley & Sons Ltd

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Marcio de Queiroz, Xiaoyu Cai and Matthew Feemster to be identified as the authors of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication Data

Names: Queiroz, Marcio S. de, author. | Cai, Xiaoyu, 1987‐ author. |

 Feemster, Matthew, author.

Title: Formation control of multi‐agent systems : a graph rigidity approach /

 Professor Marcio de Queiroz (Louisiana State University), Dr. Xiaoyu Cai

 (Louisiana State University), Dr. Matthew Feemster (United States Naval

 Academy).

Description: Hoboken, NJ : John Wiley & Sons, Inc., [2019] | Includes

 bibliographical references and index. |

Identifiers: LCCN 2018040373 (print) | LCCN 2018050691 (ebook) | ISBN

 9781118887479 (Adobe PDF) | ISBN 9781118887462 (ePub) | ISBN 9781118887448

 (hardcover)

Subjects: LCSH: Multiagent systems. | Formation control (Machine theory) |

 Graph theory. | Rigidity (Geometry) | Automatic control–Mathematical

 models. | Robotics–Mathematical models.

Classification: LCC QA76.76.I58 (ebook) | LCC QA76.76.I58 Q84 2019 (print) |

 DDC 006.3/0285436–dc23

LC record available at https://lccn.loc.gov/2018040373

Cover Design: Wiley

Cover Image: © Kypros/Getty Images, © aapsky/Shutterstock, © Andrei Trentea/Shutterstock

Dedication

To my late father, José

M. de Q.

To my parents, Zhenjie and Chunmei,

and my wife, Bingqing

X.C.

To my parents, Sam and Gay and my family,

Agnes Ann, Sam, Ryn, and Meg

M.F.

Preface

As the initial hurdles of unmanned robotic platform development have been passed, focus is now being placed on advancing the behavior of these platforms so they perform coordinated operations in groups with and without human supervision. Over the past several years, a considerable amount of work has been conducted in this area under various names: multi‐agent systems, networked systems, cooperative control, and swarming. Research has evolved from fundamental studies of biological swarms in nature to the development and application of systems theoretical tools for modeling such behaviors to, more recently, the synthesis and experimental validation of engineered multi‐agent systems.

The premise behind engineering multi‐agent systems is that cooperation among group members can lead to the execution of complex functions that are otherwise not possible. Engineering multi‐agent systems have the potential to impact a variety of military, civilian, and commercial applications that involve some of form situational awareness. Examples include patrolling, monitoring, surveying, scouting, and element tracking over large geographical areas with unmanned robotic vehicles or mobile sensor networks.

Decentralization is a key characteristic of biological and engineered multi‐agent systems since it provides adaptability and robustness to the system operation. Several coordination‐type problems have been studied within the robotics, systems, and control research communities that involve some level of distributed operation. Graph theory plays an important role in modeling the decentralization and interaction among the multiple agents needed to achieve the common goal. Our interest in this book is in the class of coordination problems known as formation control and in the use of rigid graph theory as a solution tool. Specifically, the goal of the book is to provide the first comprehensive and unified treatment of the subject of graph rigidity‐based formation control of multi‐agent systems. The presentation is mostly based on the authors' own work and perspectives.

The book begins with an introduction to rigid graph theory for readers not familiar with the subject. The heart of the book is divided into three parts according to the model of the agents' equations of motion: the single‐integrator model, the double‐integrator model, and the robotic vehicle model. For each model, three types of formation problems are studied: formation acquisition, formation maneuvering, and target interception. All formation control results in the book are supported by computer simulations, while most are demonstrated experimentally using unmanned ground vehicles. The book is organized such that the material is presented in ascending level of difficulty, building upon previous sections and chapters.

The book is intended for researchers and graduate students in the areas of robotics, systems, and control who are interested in the topic of multi‐agent systems. We assume readers have a graduate‐level knowledge of linear algebra, matrix theory, control systems, and nonlinear systems, especially Lyapunov stability theory.

We would like to acknowledge and express our gratitude to Pengpeng Zhang and Milad Khaledyan for their assistance with some of the theoretical results and computer simulations presented in the book, and to Dr. Bingqing Wu for her assistance with the creation of Figures 1.3 and 1.5. We would also like to thank Eric Willner and Jemima Kingsly at Wiley for giving us the opportunity to publish this work and for their patience while we completed it.

Finally, we acknowledge the following entities for allowing us to reproduce their pictures:

Weaver ants making an emergency bridge between two plants by Rose Thumboor (see Figure 1.1). Retrieved from commons.wikimedia.org/ wiki/File:Weaver_Ants_‐_Oecophylla_smaragdina.jpg. Used under Creative Commons Attribution‐Share Alike 4.0 International license (creative commons.org/licenses/by‐sa/4.0/deed.en).

School of convict surgeonfish (

Acanthurus triostegus

) by Thomas Shahan (see Figure 1.1). Retrieved from

www.flickr.com/photos/49580580 @N02/14280168344/

. Used under Creative Commons Attribution 2.0 Generic license (creativecommons.org/licenses/by/2.0/).

xBee module (see Figure 5.3). Retrieved from

www.sparkfun.com/products/8665?

. Used under Creative Commons Attribution 2.0 Generic license (

creativecommons.org/licenses/by/2.0/

).

March 2018

Baton Rouge, LA, USA

Marcio de Queiroz

Exton, PA, USA

Xiaoyu Cai

Annapolis, MD, USA

Matthew Feemster

About the Companion Website

This book is accompanied by a companion website:

www.wiley.com/go/dequeiroz/formation_control

The website material consists of MATLAB files for most of the computer simulations

Scan this QR code to visit the companion website.

1Introduction

“The whole is more than the sum of its parts.”

Aristotle

1.1 Motivation

This book is devoted to multi‐agent systems. Since this term has different meanings within different research communities, we deem it necessary to precisely define the meaning used here. In this book, a multi‐agent system refers to a network of interacting, mobile, physical entities that collectively perform a complex task beyond their individual capabilities.

Nature is replete with biological systems that fit this definition: a flock of birds, a school of fish, and a colony of insects (see Figure 1.1), to name a few. The behavior of such biological swarms is decentralized since each biological agent does not have access to global knowledge or supervision, but uses its own local sensing, decision, and control mechanisms.

Ants are a model example of a biological multi‐agent system. Ant colonies share the common goals of surviving, growing, and reproducing. Their sense of community is so strong that they behave like a single “superorganism” that can solve difficult problems by processing information as a collection 1. This collective behavior facilitates food gathering, defending nests against enemies, and building intricate structures with tunnels, chambers, and ventilation systems. Ants accomplish such feats without a supervisor telling them what to do. Rather, ant workers perform tasks based on personal aptitudes, communications with colony mates, and cues from the environment. Interactions with other ants and the environment occur via chemicals, which they sense with their antennae 1.

Nature is inspiring humans to engineer multi‐agent systems that mimic this distributed, coordinated behavior. The agents in such engineering systems are not living beings, but machines such as robots, vehicles, and/or mobile sensors (see Figure 1.2). Recent advances in sensor technology, embedded systems, communication systems, and power storage now make it feasible to deploy such swarms of cooperating agents for various civilian and military applications. For instance, a group of autonomous (ground, underwater, water surface, or air) vehicles could be deployed in large disaster areas to perform search, mapping, surveillance, or environmental monitoring and clean up without putting first responders in harm's way. Some recent examples of such situations are Hurricane Katrina in 2005, the BP oil spill in the Gulf of Mexico in 2010, and the Fukushima nuclear disaster in 2011. Another application is a military mission where a group of unmanned air vehicles surround and intercept an intruding or evading aircraft or enemy combatants. Yet another potential application is a team of vehicles cooperatively transporting an object too large and/or heavy for a single vehicle to transport.

Figure 1.1Examples of collective behavior in nature: a flock of birds (top left), a school of fish (top right), and a swarm of ants building a bridge (bottom).

Figure 1.2Examples of engineering multi‐agent systems.

One may wonder why a multi‐agent system should be used instead of a single “large agent”. There are several advantages to doing so: more efficient and complex task execution, robustness when one or more agents fail, scalability, versatility, adaptability, and lower cost 2. For example, multiple agents could position themselves relative to each other to create a virtual, large‐scale antenna with higher sensitivity to acoustic signals than would be possible with a single antenna. If one of the agents malfunctions, the remaining ones would reconfigure to keep the antenna operational, whereas the stand‐alone antenna would be a single point of failure. Malfunctions of an agent are also less likely than in a single system because they are usually much simpler hardware‐ and software‐wise. This simplicity, along with larger quantities, also leads to mass production at a low cost.

On the other hand, multi‐agent systems introduce a host of unique challenges, including coordination and cooperation schemes, distribution of information and subtasks, negotiation between team and individual goals, communication protocols, sensing, and collision avoidance. These challenges are exacerbated by the fact that often the task is to be completed with limited computational, communication, and sensing resources. A key design decision is between a centralized coordination scheme and a decentralized/distributed one. In a centralized scheme, each agent has access to measurement and/or control information from a master entity, such as a central processing unit or a global positioning system (GPS). Therefore, centralized schemes have a single point of failure like a single “large agent”. They also do not scale well with the number of agents because the processing overhead and number of communication links become prohibitive.