An automatic motion planning system for a convex polygonal mobile robot in 2-dimensional polygonal space

We present an automatic system for planning the (translational and rotational) collision-free motion of a convex polygonal body <italic>B</italic> in two-dimensional space bounded by a collection of polygonal obstacles. The system consists of a (combinatorial, non-heuristic) motion planning algorithm, based on sophisticated algorithmic and combinatorial techniques in computational geometry, and is implemented on a Cartesian robot system equipped with a 2-D vision system. Our algorithm runs in the worst-case in time <italic>&Ogr;</italic>(<italic>kn</italic>λ<subscrpt>6</subscrpt>(<italic>kn</italic>) log <italic>kn</italic>), where <italic>k</italic> is the number of sides of <italic>B</italic>, <italic>n</italic> is the total number of obstacle edges, and λ<subscrpt>6</subscrpt>(<italic>r</italic>) is the (nearly-linear) maximum length of an (<italic>r</italic>, 6) Davenport Schinzel sequence. Our implemented system provides an “intelligent” robot that, using its attached vision system, can acquire a geometric description of the robot and its polygonal environment, and then, given a high-level motion command from the user, can plan a collision-free path (if one exists), and then go ahead and execute that motion.

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