Studies the topology of the free configuration space (FCS) of any robot that consists of one or more connected rigid bodies and operates in an environment with obstacles. It is shown that if a certain unrestrictive robot-obstacle spatial relationship is satisfied, then FCS is uniformly locally connected (ULC). Conditions are derived under which the FCS boundary presents a manifold. Although the ULC property is not sufficient for the general case, it is shown that for the two-dimensional (2D) case the ULC property guarantees that FCS is bounded by simple curves. This result provides an effective tool for reducing the robot motion problem to the analysis of simple closed curves in the robot configuration space.
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