Formation control of mobile robots and unmanned aerial vehicles

344 Pages·2016·4.73 MB·English

by  Travis Alan Dierks

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Doctoral Dissertations Student Theses and Dissertations
Fall 2009
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Travis Alan Dierks
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Dierks, Travis Alan, "Formation control of mobile robots and unmanned aerial vehicles" (2009). Doctoral
Dissertations. 1936.
https://scholarsmine.mst.edu/doctoral_dissertations/1936
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FORMATION CONTROL OF MOBILE ROBOTS AND

UNMANNED AERIAL VEHICLES
by
TRAVIS DIERKS

A DISSERTATION
Presented to the Faculty of the Graduate School of the
MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY
In Partial Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY
in
ELECTRICAL ENGINEERING

2009
Approved by
Jagannathan Sarangapani, Advisor
Kelvin Erickson
Donald Wunsch
Cihan Dagli
S. N. Balakrishnan

iii
PUBLICATION DISSERTATION OPTION

This dissertation consists of the following six articles that have been submitted for
publication as follows:
Paper 1, T. Dierks and S. Jagannathan, “Neural Network Control of Mobile Robot
Formations using RISE Feedback,” has been published in IEEE Trans. on Systems, Man,
and Cybernetics—Part B, Vol. 39, no. 2, 2009.
Paper 2, T. Dierks and S. Jagannathan, “Neural Network Output Feedback
Control of Robot Formations,” will appear in IEEE Trans. on Systems, Man, and
Cybernetics— Part B.
Paper 3, T. Dierks and S. Jagannathan, “Output Feedback Control of a Quadrotor
UAV using Neural Networks,” is provisionally accepted to IEEE Trans. on Neural
Networks.
Paper 4, T. Dierks and S. Jagannathan, “Leader-Follower Formation Control of
Multiple Quadrotor Unmanned Aerial Vehicles using Neural Networks,” is under
revision with Automatica.
Paper 5, T. Dierks and S. Jagannathan, “Optimal Control of Affine Nonlinear
Discrete-time Systems with Unknown Internal Dynamics using Online Approximators,”
has been submitted to IEEE Trans. on Automatic Control.
Paper 6, T. Dierks and S. Jagannathan, “Optimal Control of Affine Nonlinear
Continuous-time Systems using an Online Approximator,” has been submitted to IEEE
Trans. on Automatic Control.
iv
ABSTRACT

In this dissertation, the nonlinear control of nonholonomic mobile robot
formations and unmanned aerial vehicle (UAV) formations is undertaken and presented
in six papers. In the first paper, an asymptotically stable combined kinematic/torque
control law is developed for leader-follower based formation control of mobile robots
using backstepping. A neural network (NN) is introduced along with robust integral of
the sign of the error (RISE) feedback to approximate the dynamics of the follower as well
as its leader using online weight tuning. Subsequently, in the second paper, a novel NN
observer is designed to estimate the linear and angular velocities of both the follower and
its leader robot and a NN output feedback control law is developed.
On the other hand, in the third paper, a NN-based output feedback control law is
presented for the control of an underactuated quad rotor UAV, and a NN virtual control
input scheme is proposed which allows all six degrees of freedom to be controlled using
only four control inputs. The results of this paper are extended to include the control of
quadrotor UAV formations, and a novel three-dimensional leader-follower framework is
proposed in the fourth paper. Next, in the fifth paper, the discrete-time nonlinear optimal
control is undertaken using two online approximators (OLA’s) to solve the infinite
horizon Hamilton-Jacobi-Bellman (HJB) equation forward-in-time to achieve nearly
optimal regulation and tracking control. In contrast, paper six utilizes a single OLA to
solve the infinite horizon HJB and Hamilton-Jacobi-Isaacs (HJI) equations forward-in-
time for the near optimal regulation and tracking control of continuous affine nonlinear
systems. The effectiveness of the optimal tracking controllers proposed in the fifth and
sixth papers are then demonstrated using nonholonomic mobile robot formation control.
v
ACKNOWLEDGMENTS

I would like to thank my advisor, Dr. Jagannathan Sarangapani, for his guidance,
support, and patience over the last several years. I also would like to thank Dr. Kelvin
Erickson, Dr. Donald Wunsch, Dr. Cihan Dagli, and Dr. S. N. Balakrishnan for serving
on my doctoral committee. I thank the Department of Education for providing financial
support through the GAANN Fellowship program. In addition, I would like to thank the
National Science Foundation for providing additional support.
I also thank my wife, Laura, my parents, Alan and Carrie, as well as the rest of
my family for their love and support. Their encouragement and understanding over the
course of my education has truly been a blessing. I would also like to thank God for the
opportunities I have been presented with and the courage to pursue them.
vi
TABLE OF CONTENTS

PAGE
PUBLICATION DISSERTATION OPTION..................................................................................iii
ABSTRACT...........................................................................................................................iv

ACKNOWLEDGMENTS ..........................................................................................................v

LIST OF ILLUSTRATIONS…………………………………………………………….……...x

LIST OF TABLES…………………………………………………………………….……xiv

SECTION
1. INTRODUCTION.......................................................................................................... 1
1.1 APPLICATIONS OF FORMATION CONTROL ……………………………………..3

1.2 OVERVIEW OF FORMATION CONTROL METHODOLOGIES……………………....6
1.3 ORGANIZATION OF THE DISSERTATION………………………………..………8

1.4 CONTRIBUTIONS OF THE DISSERTATION…………………………..………….12

1.5 REFERENCES ……………………….………………………………………...13
PAPER
1. NEURAL NETWORK CONTROL OF MOBILE ROBOT FORMATIONS USING
RISE FEEDBACK…………………………………………………………………...15

ABSTRACT ……………………………………………………………………………15
I. INTRODUCTION …...………………………………………………………………..16

II. LEADER-FOLLOWER FORMATION CONTROL …..………………………………….19
..
A. BACKSTEPPING CONTROLLER DESIGN ………………………………………..21

B. LEADER-FOLLOWER TRACKING CONTROL……………………………………22

C. DYNAMIC NN/RISE CONTROLLER DESIGN…...………………………………25

D. LEADER CONTROL STRUCTURE ……...……………………………………….30

E. FORMATION STABILITY……………………………………………………….33

III. LEADER-FOLLOWER OBSTACLE AVOIDANCE …………………………………....34

IV. SIMULATION RESULTS………………………………………………………...…41

A. SCENARIO I: OBSTACLE FREE ENVIRONMENT………………………………..43

B. SCENARIO II: OBSTACLE RIDDEN ENVIRONMENT…………………………….46

V. CONCLUSIONS.……………………………………………………………………47
vii
REFERENCES………………………………………………………………………….48

APPENDIX…………………………………………………………………………….50

2. NEURAL NETWORK OUTPUT FEEDBACK CONTROL OF ROBOT FORMATIONS……...62

ABSTRACT…………………………………………………………………………....62

I. INTRODUCTION…………………………………………………………………….63

II. LEADER-FOLLOWER FORMATION CONTROL……………………………………...66

A. BACKSTEPPING CONTROLLER DESIGN………………………………………..68

B. LEADER-FOLLOWER TRACKING CONTROL………………………………..…..70

C. LEADER-FOLLOWER NN OBSERVER DESIGN …………………………………72

D. DYNAMICAL NN TORQUE CONTROLLER …………………………………......76

E. LEADER CONTROL STRUCTURE………………………………………...……..81

F. FORMATION STABILITY …………………………………………..…………...85

III. LEADER-FOLLOWER OBSTACLE AVOIDANCE ……………………………..……..88

IV. SIMULATION RESULTS…………………………………………………………...91

A. SCENARIO I: OBSTACLE FREE ENVIRONMENT…….………………………….93

B. SCENARIO II: OBSTACLE RIDDEN ENVIRONMENT……………………………..96

V. CONCLUSIONS ……………………………………………………………………98

REFERENCES …………………………………………………………………………98

APPENDIX……………...……………………………………………………………100

3. OUTPUT FEEDBACK CONTROL OF A QUADROTOR UAV USING
NEURAL NETWORKS……………………………………………………………..111

ABSTRACT…………………………………………………………………………..111

I. INTRODUCTION…………………………………………………………………...112

II. BACKGROUND …………………………………………………………………..116

A. QUADROTOR UAV DYNAMICS ………..……………………………………116

B. CONSTRAINTS OF THE UNDERACTUATED SYSTEM …………………………..120

C. NEURAL NETWORKS …………………………………………...……………121

III. NEURAL NETWORK OUTPUT FEEDBACK TRACKING CONTROL……………..…..122

A. NN OBSERVER DESIGN……………………………………………….……..123

B. KINEMATIC CONTROL SYSTEM ………………………………………..…….127

C. NN VIRTUAL CONTROL DEVELOPMENT……………………………………..133
viii
D. NN OUTPUT FEEDBACK CONTROL LAW….…………………………………137

E. COMMENTS ON IMPLEMENTATION AND PRACTICAL CONSIDERATIONS………145

IV. SIMULATION RESULTS……………………………………………………...…..147

V. CONCLUSIONS………………………………………………….………………..156

VI. REFERENCES …………………………………………………………………...157

4. LEADER-FOLLOWER FORMATION CONTROL OF MULTIPLE QUADROTOR
UNMANNED AERIAL VEHICLES USING NEURAL NETWORKS ……………………..160

ABSTRACT…………………………………………………………………………..160

NOMENCLATURE ………………………………………………………...……….…161

I. INTRODUCTION…………………………………………………………………...163

II. BACKGROUND…………………………………………….……………………..167

A. QUADROTOR UAV DYNAMICS ………………………………...……………167

B. NEURAL NETWORKS ………………………………………………...………170

C. A NOVEL THREE DIMENSIONAL LEADER-FOLLOWER UAV FORMATION
CONTROL FRAMEWORK…………………………………………………..….171

III. LEADER-FOLLOWER FORMATION TRACKING CONTROL …….………………….174

A. FOLLOWER UAV CONTROL LAW …………………………………………...175

B. FORMATION LEADER CONTROL LAW………………………………………..191

C. QUADROTOR UAV FORMATION STABILITY……………………………...…..195

IV. SIMULATION RESULTS……………………………………………………….....203

V. CONCLUSIONS ……………………………………………..……………….…...213

REFERENCES…………………………………………………………….…………..214

5. OPTIMAL CONTROL OF AFFINE NONLINEAR DISCRETE-TIME SYSTEMS WITH
UNKNOWN INTERNAL DYNAMICS USING ONLINE APPROXIMATORS……………..216

ABSTRACT………………………………….……………………………………….216

I. INTRODUCTION…………………………………………………………………...217

II. BACKGROUND………………………….………………………………………..220

III. NEAR OPTIMAL REGULATION OF NONLINEAR SYSTEMS ………………….……222

A. COST FUNCTION APPROXIMATION FOR OPTIMAL REGULATOR DESIGN ……..223

B. ESTIMATION OF THE OPTIMAL FEEDBACK CONTROL SIGNAL ……………….229

C. CONVERGENCE PROOF ……………………………………………...……….233