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5.2 Feedback-Linearization Controllers 265

robustify the controllers by modifying the robot dynamics either explicitly
or implicitly.

5.2 Feedback-Linearization Controllers

The controllers designed in this section may be obtained as modification of
the feedback-linearization (or computed-torque) controllers of Chapter 3.
They are basically the computed-torque-like controllers of Section 4.4. We
study both static and dynamic feedback designs and compare different
controllers found in the literature. Note that such a study was started
in Section 4.4 and some of the controllers introduced there will reappear in
this chapter. The emphasis will be here on relating many of the controllers
scattered through the literature and to give them a common theoretical
justification.
We assume for simplicity that d = 0 in (5.1.1) and that w i=0 in (5.1.3),
although the effects of bounded d and w i can be easily accounted for and
will be considered in most examples. In a fashion similar to Chapter 4, the
dynamics of the robot are transformed into the linear system

and

(5.2.1)
leading to the nonlinear computed-torque controller

(5.2.2)

which, due to the invertibility of M(q), gives the following closed-loop system:

ë=u (5.2.3)

which is described by the transfer function

(5.2.4)

The problem is then reduced to finding a linear control u that will achieve
a desired closed-loop performance; that is, find F, G, H, and J in

Copyright © 2004 by Marcel Dekker, Inc.