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180 Computed-Torque Control

Figure 4.2.5: (Cont.)(c) position.

whence (4.2.10) yields

(4.2.11)

A closed-loop formulation of minimum-time control appears in [Lewis 1986a].
Unfortunately, minimum-time trajectories computed using a constant
maximum acceleration are not directly relevant in robotics. This is due to the
fact that an actual manipulator has a torque limit of τ m . Since the robot
equation (see Table 3.3.1) is nonlinear, this does not correlate to a constant
upper bound on the acceleration. For instance, a robot arm has different
maximum accelerations in its fully extended and fully retracted positions. For
more discussion see [Kahn and Roth 1971], [Chen 1989], [Geering 1986],
[Gourdeau and Schwartz 1989], [Jayasuriya and Suh 1985], [Kahn and Roth
1971], [Kim and Shin 1985], [Shin and McKay 1985].

Copyright © 2004 by Marcel Dekker, Inc.