WIAS Preprint No. 1658, (2011)

Path planning and collision avoidance for robots


  • Gerdts, Matthias
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Landry, Chantal

2010 Mathematics Subject Classification

  • 49J15 49M25 49N90 90C30


  • Optimal control, collision avoidance, cooperative robots, backface culling, active set strategy




An optimal control problem to find the fastest collision-free trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique.

Appeared in

  • Numer. Algebra Control Optim., 2 (2012) pp. 437--463.

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