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Chapter 2

Introduction to Control

Theory

In this chapter we review various control theory concepts that are used in
the control of robots. We first review the state-space formulation for both
linear and nonlinear systems and present the stability concepts needed in the
sequel. The chapter is intended to introduce modern control concepts, but
even readers with a background in control theory may wish to consult it for
notation and convenience.

2.1 Introduction

The control of robotic manipulators is a mature yet fruitful area for research,
development, and manufacturing. Industrial robots are basically positioning
and handling devices. Therefore, a useful robot is one that is able to control
its movement and the interactive forces and torques between the robot and
its environment. This book is concerned with the control aspect of robotic
manipulators. To control usually requires the availability of a mathematical
model and of some sort of intelligence to act on the model. The mathematical
model of a robot is obtained from the basic physical laws governing its
movement. Intelligence, on the other hand, requires sensory capabilities and
means for acting and reacting to the sensed variables. These actions and
reactions of the robot are the result of controller design.
In this chapter we review the concepts of control theory that are needed
in this book. All proofs are omitted, but references are made to more
specialized books and papers where proofs are provided. Once a satisfactory

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Copyright © 2004 by Marcel Dekker, Inc.