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4.5 Digital Robot Control 223

sorts of digital controllers for robot arms can be considered as members of the
computer-torque-like class (see Table 4.4.1).
One approach to digital robot control is shown in Figure 4.5.1. There, a
.
sampler is placed on q(t) and q(t) to define

Figure 4.5.1: Digital robot control scheme.

(4.5.1)

with T the sample period. Sample periods in robotic applications vary from
about 1 to 20 ms. A zero-order hold is used to reconstruct the continuous-time
control input (t)needed for the actuators from the samples k. In this section
we use superscripts “d” for the desired trajectory for notational ease.
This digital control law amounts to selecting

(4.5.2)

in the approximate computed-torque controller in Table 4.4.1 and a digital
outer loop control signal u k. Then, with PD outer-loop control, the arm control
input is

(4.5.3)

where the tracking error is e(t)=q d (t)-q(t). There are many variations of this
control scheme. For instance, it is very reasonable to use multirate sampling
and update and less frequently than the sampling frequency. That is, the

Copyright © 2004 by Marcel Dekker, Inc.