Page 287 -

272 Robust Control of Robotic Manipulators

EXAMPLE 5.2–1: Static Controller (Lyapunov Design)

In all our examples in this chapter we use the two-link revolute-joint robot
first described in Chapter 3, Example 3.2.2, whose dynamics are repeated
here:

(1)

where

(2)

2
The parameters m 1 =1kg, m 2 =1kg, a 1 =1m, a 2 =1m, and g=9.8 m/s are given.
Let the desired trajectory used in all examples throughout this chapter be
described by

Then . It may then be shown that

Let =0 then

or that

Then use =6I and a=172 to satisfy (6). In fact, these values will lead to a
larger controller gains than are actually needed. Suppose instead that we let
^
6I, =0, and that

Copyright © 2004 by Marcel Dekker, Inc.