The method of orienting curves and its application to manipulator trajectory planning

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Abstract
The method of orienting curves was developed for solving some classes of optimal control problems with state constraints. In the present paper, this method is transferred to the problem of finding the upper bound of a class of functions with fixed end points and restrictions to their value and their derivative. The algorithm presented here delivers constructively the optimal solution as a path consisting of orienting curves, boundary arcs, and final curves. The result is applied to determining the time-optimal motion of a robot following a prescribed trajectory under some restrictions to its velocity and acceleration.