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Issues dealing with fast, 3-D, collision-free motion planning are discussed, and a fast path planning system under development at NBS is described. The components of a general motion planner are outlined, and some of their computational aspects are discussed. It is argued that an octree representation of the obstacles in the world leads to fast path planning algorithms. The system we are developing uses such an octree representation. The robot and its swept-volume paths are approximated by primitive shapes so as to result in fast collision detection algorithms. The search for a path is performed in the octree space, and combines hypothesize and test, hill climbing, and A.