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

  • Authors:

  • K. Kedem;M. Sharir

  • Affiliations:

  • School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel;Courant Institute of Mathematical Sciences, New York University, New York, NY and School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

  • Venue:
  • SCG '88 Proceedings of the fourth annual symposium on Computational geometry
  • Year:
  • 1988

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Abstract

We present an automatic system for planning the (translational and rotational) collision-free motion of a convex polygonal body B 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 &Ogr;(kn&lgr;6(kn) log kn), where k is the number of sides of B, n is the total number of obstacle edges, and &lgr;6(r) is the (nearly-linear) maximum length of an (r, 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.