Random probing to approximate medial axes and plan safe motion

We propose a novel approach to planning the safe motion of a robot - the motion is considered safe if the robot stays as distant as possible from the nearest obstacle. The approach is based on approximating the medial axis of the free configuration space through randomized probes of the full configuration space. Experiments with 2- and 3-DOF manipulators show that the approach generates longer but significantly safer motion when compared with naive planning to simply finds a shortest motion. In addition, once preprocessing is complete our approach spends much less time planning motion than the naive one. As it is based on probing randomly, rather than at points on a grid, our approach promises to extend effectively to robots with many DOF.