A practical exact motion planning algorithm for polygonal objects amidst polygonal obstacles

  • Francis Avnaim
  • Jean Daniel Boissonnat
  • Bernard Faverjon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 391)


Let I be a 2-dimensional polygonal rigid object (with m edges) moving amidst polygonal obstacles E (with n edges) and let P init and P end be two free placements of I, where the interior of I does not intersect E. We investigate here the problem of finding a continuous motion of I from P init to P end , such that during this motion the interior of I does not intersect E, or to establish that no such motion exists. This problem is an instance of the well known ”Piano Movers' Problem”. We have shown in [2] that it is possible to compute an exact description of free space in time O(m3n3log(mn)). We show in this paper that, using this description, a motion can be found in time O(m3n3). The actual complexity of our algorithm inmany practical situations is much smaller. In particular, for the so called situation of local bounded complexity often encontered in robotics, the complexity of computing free space is O(nlogn) and the complexity of planning a motion is O(n). The method has been implemented and experimental results are discussed.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Francis Avnaim
    • 1
  • Jean Daniel Boissonnat
    • 1
  • Bernard Faverjon
    • 1
  1. 1.Centre de Sophia-AntipolisINRIAValbonne

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