Abstract
The problem of robot motion planning in an environment with obstacles can often be reduced to the study of connectivity of the robot's free configuration space. In turn, space connectivity can be analyzed via the corresponding connectivity graph. For some two-and three-dimensioned (2D and 3D) robots, the free configuration space presents a compact subspace of a 2D orientable compact manifold. This paper addresses the following abstract problem: given a compact 2D surface bounded by simple closed curves and lying in an orientable 2D manifold (a sphere, a torus, etc) and given two points in the subspace, suggest a systematic way of defining the connectivity graph in the sub-space, based on its topological properties. The use of space topology results in powerful, from the robotics standpoint, provable algorithms which can be used for real-time sensor-based motion planning in an environment with unknown obstacles of arbitrary shapes.
Published Version
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