Computing global configuration-space maps using multidimensional set-theoretic modelling

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Efficient motion planning for an L-shaped object

We present an algorithm that solves the following motion-planning problem. Given an L-shaped body L and a 2-dimensional region with n point obstacles, decide whether there is a continuous motion connecting two given positions and orientations of L during which L avoids collision with the obstacles. The algorithm requires O(n 2 log 2 n) time and O(n 2 ) storage. The algorithm is a variant of the cell-decomposition technique of the configuration space ([SS, LS]) but it employs a new and efficient technique for obtaining a compact representation of the free space, which results in a saving of nearly an order of magnitude. The approach used in our algorithm is also applicable to motion-planning of certain robotic arms whose spaces of free placements have a structure similar to that of the L-shaped body. 1 Introduction Let B be a robot system having k degrees of freedom and free to move within a two- or three-dimensional domain V which is bounded by various obstacles whose 0 Work o..