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210 Computed-Torque Control

Figure 4.4.9: (Cont.) (c)w n=50 rad/s.

Then there results

(4.4.51)

By selecting u i to depend only on joint variable i, this describes n decoupled
individual joint controllers and is called independent joint control.
Implementation on an actual robot arm is easy since the control input for
joint i only depends on locally measured variables, not on the variables of the
other joints. Moreover, the computations are easy and do not involve solving
the complicated nonlinear robot inverse dynamics.
During the early days of robotics, independent joint control was popular
[Paul 1981] since it allows a decoupled analysis of the closed-loop system
using single-input/single-output (SISO) classical techniques. It is also called
classical joint control. There are strong arguments even today by several
researchers that this control scheme is always suitable in practical
implementations, and that modern nonlinear control schemes are too
complicated for industrial robotic applications.
A traditional analysis of independent joint control control now follows. It
provides a connection with classical control notions and is important for the

Copyright © 2004 by Marcel Dekker, Inc.