Planning constrained motion

We consider the motion planning problem for a point constrained to move along a path with radius of curvature at least one. The point moves in a two-dimensional universe with polygonal obstacles. We show the decidability of the reachability question: “Given a source placement (position and direction pair) and a target placement, is there a curvature-constrained path from source to target avoiding obstacles?” The decision procedure has time and space complexity 2o(poly(n, m)) wheren is the number of corners andm is the number of bits required to specify the position of corners.

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