Neural network output feedback control of robot formations.

Abstract

In this paper, a combined kinematic/torque output feedback control law is developed for leader-follower-based formation control using backstepping to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers. A neural network (NN) is introduced to approximate the dynamics of the follower and its leader using online weight tuning. Furthermore, a novel NN observer is designed to estimate the linear and angular velocities of both the follower robot and its leader. It is shown, by using the Lyapunov theory, that the errors for the entire formation are uniformly ultimately bounded while relaxing the separation principle. In addition, the stability of the formation in the presence of obstacles, is examined using Lyapunov methods, and by treating other robots in the formation as obstacles, collisions within the formation are prevented. Numerical results are provided to verify the theoretical conjectures.

Full text

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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

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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.

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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.