Robot Modeling and Control, 2nd Edition

CHAPTER 9NONLINEAR AND MULTIVARIABLE CONTROL

9.1 Introduction

In Chapter 8 we discussed techniques to derive control laws for each joint of a manipulator based on a single-input/single-output model. Coupling effects among the joints were regarded as disturbances to the individual systems. In reality, the dynamic equations of a robot manipulator form a complex, nonlinear, and multivariable system. In this chapter, therefore, we treat the robot control problem in the context of nonlinear, multivariable control. This approach allows us to provide more rigorous analysis of the performance of control systems, and also allows us to design robust and adaptive nonlinear control laws that guarantee stability and tracking of planned trajectories.

We first reformulate the manipulator dynamic equations in a form more suitable for the discussion to follow. We then treat the problem of inverse dynamics in both joint space and task space. The inverse dynamics control relies on exact cancellation of nonlinearities in the system, which is not possible in practical applications. For this reason, we discuss several methods for robust and adaptive control, which are aimed at providing good tracking performance despite uncertainty in knowledge of parameters or external disturbances. In distinguishing between robust control and adaptive control we follow the commonly accepted notion that a robust controller is a fixed controller designed to satisfy performance specifications over a given range of ...