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5.2 Feedback-Linearization Controllers 267

The quest for more performance is, however, leading researchers and
manufacturers to use direct-drive robots and to attempt moving them at
higher speeds with less powerful but more efficient motors [Asada and Youcef-
Toumi 1987]. This new direction is increasing the need for more robust
controllers such as the ones described next.
The approaches of this section revolve around the design of linear
controllers C(s) such that the complete closed-loop system in Figure 5.5.1 is
stable in some suitable sense (e.g., uniformly ultimately bounded, globally
asymptotically stable, p stable etc.) for a given class of nonlinear perturbation
. In other words choose C(s) in (5.2.5) such that the error e(t) in (5.2.8) is
stable in some desired sense.

Figure 5.2.1: Feedback-linearization; uncertain structure.

The reasonable assumptions (5.2.9)–(5.2.11) below are often made for
revolute-joint robots when using this approach [Spong and Vidyasagar 1987].
In the following, µ 1, µ 2, , 0, 1, and 2 are nonnegative finite constants
which depend on the size of the uncertainties.

(5.2.8)

(5.2.9)

(5.2.10)

(5.2.11)

Recall that inequality (5.2.8) was introduced in Section 3.3, and note that
the norms used in the inequalities above can be, depending on the application,
either ∞ or 2 norms. Also note that the bounds µ i and i are scalar functions

Copyright © 2004 by Marcel Dekker, Inc.