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Numerical Algebra, Control and Optimization (NACO)
 

Path planning and collision avoidance for robots

Pages: 437 - 463, Volume 2, Issue 3, September 2012      doi:10.3934/naco.2012.2.437

 
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Matthias Gerdts - Institute of Mathematics and Applied Computing (LRT), University of the Federal Armed Forces at Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany (email)
René Henrion - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany (email)
Dietmar Hömberg - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany (email)
Chantal Landry - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany (email)

Abstract: 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.

Keywords:  Optimal control, collision avoidance, cooperative robots, backface culling, active set strategy.
Mathematics Subject Classification:  Primary: 49J15, 49M25, 49N90; Secondary: 90C30.

Received: October 2011;      Revised: December 2011;      Available Online: August 2012.

 References