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Optimization and Engineering

, Volume 17, Issue 3, pp 533–556 | Cite as

Combining discrete and continuous optimization to solve kinodynamic motion planning problems

  • Chantal Landry
  • Wolfgang Welz
  • Matthias Gerdts
Article

Abstract

A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamic constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of intermediate points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the intermediate points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost.

Keywords

Trajectory planning Optimal control problem Collision avoidance Graph search algorithm Initialization Robotics 

Mathematics Subject Classification

49J15 49M25 49N90 70E60 90C30 90C35 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Chantal Landry
    • 1
  • Wolfgang Welz
    • 2
  • Matthias Gerdts
    • 3
  1. 1.Zurich University of Applied SciencesWinterthurSwitzerland
  2. 2.Technische Universität BerlinBerlinGermany
  3. 3.University of the Federal Armed Forces at MunichNeubibergGermany

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