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4.4 Computed-Torque Control 185

subsequent examples. The use of such simulation software as SIMNON is
quite similar.
We discuss the implementation of digital robot arm controllers in Section
4.5. Some detailed discussion on digital control, simulation, and DSP
implementation of controllers is given in [Lewis 1992].

4.4 Computed-Torque Control

Through the years there have been proposed many sorts of robot control
schemes. As it happens, most of them can be considered as special cases of the
class of computed-torque controllers. Computed torque, at the same time, is a
special application of feedback linearization of nonlinear systems, which has
gained popularity in modern systems theory [Hunt et al. 1983], [Gilbert and
Ha 1984]. In fact, one way to classify robot control schemes is to divide them
as “computed-torque-like” or “noncomputed-torque-like.” Computed-torque-
like controls appear in robust control, adaptive control, learning control, and
so on.
In the remainder of this chapter we explore this class of robot controllers,
which includes such a broad range of designs. Computed-torque control allows
us to conveniently derive very effective robot controllers, while providing a
framework to bring together classical independent joint control and some
modern design techniques, as well as set the stage for the rest of the book. A
summary of the different computed-torque-like controllers is given at the end
of the section in Table 4.4.1. We shall see that many digital robot controllers
are also computed-torque-like controllers (Section 4.5).
Derivation of Inner Feedforward Loop

The robot arm dynamics are

(4.4.1)

or

(4.4.2)

with the joint variable the control torque, and d(t) a
disturbance. If this equation includes motor actuator dynamics (Section 3.6),
then (t) is an input voltage.
Suppose that a desired trajectory q d(t) has been selected for the arm motion,
according to the discussion in Section 4.2. To ensure trajectory tracking by
the joint variable, define an output or tracking error as

Copyright © 2004 by Marcel Dekker, Inc.