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An approach to planning time-optimal collision-free motions of robotic
manipulators is presented. It is based on using a negative
formulation of the Pontryagin Maximum Principle which handles efficiently various
control and/or state constraints imposed on the manipulator motions, which
arise naturally out of manipulator joint limits and obstacle avoidance.
This approach becomes similar to that described by Weinreb and
Bryson, as well as by Bryson and Ho if no
state inequality constraints are imposed. In contrast to the penalty
function method, the proposed algorithm does not require an initial
admissible solution (i.e. an initial admissible trajectory) and finds manipulator
trajectories with a smaller cost value than the penalty function
approach. A computer example involving a planar redundant manipulator of
three revolute kinematic pairs is included. The numerical results are
compared with those obtained using an exterior penalty function method.
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