The problem of a planning collision-free motion of a planar 3R-manipulator among point obstacles is studied using techniques from topology and homology. By completely characterizing the set of singular configurations (the points in configuration space corresponding to an intersection of the chain with itself or a point obstacle), the complementary space, the free space, is also completely characterized. This characterization dictates an exact, complete, motion planning algorithm that builds on the authors’ algorithm developed for 2R-manipulators [9]. Results obtained with a preliminary version of the algorithm are given.
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