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A trajectory planning of redundant manipulators based on bilevel optimization

Author

Listed:
  • Menasri, R.
  • Nakib, A.
  • Daachi, B.
  • Oulhadj, H.
  • Siarry, P.

Abstract

In this paper, a novel trajectory planning approach is proposed for redundant manipulators in the case of several obstacles. The trajectory is discretized and at each step, we search for a new position of the end effector in the Cartesian space to reach the final position. Because of the redundancy, this position can be achieved by an infinity of configurations in the joint space. Thus, we use this property to find the best configuration that allows to avoid obstacles and singularities of the robot. The proposed method is based on a bilevel optimization formulation of the problem and bi-genetic algorithm to solve it. In order to avoid obstacles, we also proposed to manage constraints of the problem dynamically. This technique adapts the number of constraints in the formulation of the problem with the position of the obstacles. Simulation results showed the effectiveness of the proposed method.

Suggested Citation

  • Menasri, R. & Nakib, A. & Daachi, B. & Oulhadj, H. & Siarry, P., 2015. "A trajectory planning of redundant manipulators based on bilevel optimization," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 934-947.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:934-947
    DOI: 10.1016/j.amc.2014.10.101
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    References listed on IDEAS

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    1. Konak, Abdullah & Coit, David W. & Smith, Alice E., 2006. "Multi-objective optimization using genetic algorithms: A tutorial," Reliability Engineering and System Safety, Elsevier, vol. 91(9), pages 992-1007.
    2. Yu, J.S. & Müller, P.C., 1996. "An on-line cartesian space obstacle avoidance scheme for robot arms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 41(5), pages 627-637.
    3. Calvete, Herminia I. & Gale, Carmen & Mateo, Pedro M., 2008. "A new approach for solving linear bilevel problems using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 188(1), pages 14-28, July.
    4. Le Boudec, Brice & Saad, Maarouf & Nerguizian, Vahé, 2006. "Modeling and adaptive control of redundant robots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(4), pages 395-403.
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