We propose a novel two-phase approach for planning the safe motion of a robot. First, in a preprocessing phase, an approximation of the medial axis of the free configuration space is constructed through: 1) a probing of the full configuration space along a grid, and 2) a careful selection of a subset of grid configurations that are likely to lie near the actual medial axis. Though the selection process is akin to skeletonization in digital image processing our implementation differs owing to the particular requirements of motion planning. In a subsequent planning phase, a given start-goal configuration pair is first connected to the medial axis by an inexpensive local planner, and then a motion is planned as a path within the medial axis. Experiments with 2- and 3-DOF manipulators show that the approach generates longer but significantly safer motion compared to a naive planning approach that always finds a shortest motion. In addition, once preprocessing is completed our approach spends much less time for planning than the naive approach. Variations of this approach hold possibilities for extension to robots with many DOF.
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