106
Real-time computations would have to be performed very quickly and would
most likely require techniques such as those described by Wander [30]
where array processors have been employed.
Compensation for Flexibilities in the Manipulator's Links
The desire for greater accuracy and reduced weight in robotic
manipulators has spurred interest in control algorithms capable of
compensating for structural flexibilities. Here we develop a control
strategy for the manipulator which provides compensation for end-
effector deviations resulting from link flexibilities. This control
strategy is based on the assumption that the external disturbance forces
which cause link flexing can be measured by force sensing equipment. In
addition, it is assumed that the external disturbances are of a very low
frequency content and that the manipulator is not undergoing rapid
motion. This means that the manipulator dynamics can still be modeled
as though it were rigid as opposed to more complex models [31-32],
devised for flexible manipulators.
The proposed control strategy involves little more than providing a
suitable corrective reference signal ^(t) for the scheme shown in
Figure 6-1. Previously it was indicated that if tracking of a nominal
trajectory is desired, then e^t) should be taken as zero since a
nonzero e (t) gives a deviation from the nominal trajectory. Here,
however, this deviation is used to adjust the joint angles in such a way
that the end-effector remains on a specified path, even when bending
occurs in the links.
We now give a brief description of the method used to calculate the
corrective reference signal ^(t). By considering the stress-strain