Multi-criteria Manipulator Trajectory Optimization Based on Evolutionary Algorithms

  • E. J. Solteiro Pires
  • P. B. de Moura Oliveira
  • J. A. Tenreiro Machado
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 73)


This paper proposes a method, based on a genetic algorithm, to generate smoth manipulator trajectories in a multi-objective perspective. The method uses terms proportional to the integral of the squared displacements in order to eliminate the jerk movement. In this work, the algorithm, based on NSGA-II and maximin sorting schemes, considers manipulators of two, three and four rotational axis (2R, 3R, 4R). The efficiency of the algorithm is evaluated, namely the extension of the front and the dispersion along the front. The effectiveness and capacity of the proposed approach are shown through simulations tests.


Genetic Algorithm Pareto Front Trajectory Planning Pareto Optimal Front Extreme Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bäck, T., Hammel, U., Schwefel, H.P.: Evolutionary computation: Comments on the history and current state. IEEE Trans. on Evolutionary Computation 1(1), 3–17 (1997)CrossRefGoogle Scholar
  2. 2.
    Fonseca, C.M., Fleming, P.J.: An overview of evolutionary algorithms in multi-objective optimization. Evolutionary Computation Journal 3(1), 1–16 (1995)CrossRefGoogle Scholar
  3. 3.
    Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Ltd., Chichester (2001)zbMATHGoogle Scholar
  4. 4.
    Horn, J., Nafploitis, N., Goldberg, D.: A niched pareto genetic algorithm for multi-objective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 82–87 (1994)Google Scholar
  5. 5.
    Coello, C.A.C.: A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowledge and Information Systems 1(3), 269–308 (1998)Google Scholar
  6. 6.
    Coello Coello, C.: Evolutionary multi-objective optimization: a historical view of the field. IEEE Computational Intelligence Magazine 1(1), 28–36 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Davidor, Y.: Genetic Algorithms and Robotics, a Heuristic Strategy for Optimization. Robotics and Automated Systems, vol. 1. World Scientific Publishing Co. Pte Ltd., Singapore (1991)zbMATHGoogle Scholar
  8. 8.
    Kubota, N., Fukuda, T., Shimojima, K.: Trajectory planning of cellular manipulator system using virus-evolutionary genetic algorithm. Robotics and Autonomous systems 19, 85–94 (1996)CrossRefGoogle Scholar
  9. 9.
    Luo, X., Wei, W.: A new immune genetic algorithm and its application in redundant manipulator path planning. Journal of Robotic Systems 21(3), 141–151 (2004)CrossRefGoogle Scholar
  10. 10.
    Ridao, M.A., Camacho, E.F., Riquelme, J., Toro, M.: An evolutionary and local search algorithm for motion planning of two manipulators. Journal of Robotic Systems 18(8), 463–476 (2001)zbMATHCrossRefGoogle Scholar
  11. 11.
    Solteiro Pires, E.J., de Moura Oliveira, P.B., Tenreiro Machado, J.A.: Multi-objective genetic manipulator trajectory planner. In: Raidl, G.R., Cagnoni, S., Branke, J., Corne, D.W., Drechsler, R., Jin, Y., Johnson, C.G., Machado, P., Marchiori, E., Rothlauf, F., Smith, G.D., Squillero, G. (eds.) EvoWorkshops 2004. LNCS, vol. 3005, pp. 219–229. Springer, Heidelberg (2004)Google Scholar
  12. 12.
    Ramabalan, S., Saravanan, R., Balamurugan, C.: Multi-objective dynamic optimal trajectory planning of robot manipulators in the presence of obstacles. The International Journal of Advanced Manufacturing Technology 41(5-6), 580–594 (2009)CrossRefGoogle Scholar
  13. 13.
    Liu, Z., Huang, P., Yan, J., Liu, G.: Multi-objective genetic algorithms for trajectory optimization of space manipulator. In: 4th IEEE Conference on Industrial Electronics and Applications, ICIEA 2009, Xi’an, China, May 25-27, pp. 2810–2815 (2009)Google Scholar
  14. 14.
    Solteiro Pires, E.J., de Moura Oliveira, P.B., Tenreiro Machado, J.A.: Multi-objective MaxiMin Sorting Scheme. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 165–175. Springer, Heidelberg (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • E. J. Solteiro Pires
    • 1
  • P. B. de Moura Oliveira
    • 1
  • J. A. Tenreiro Machado
    • 2
  1. 1.Centro de Investigação e de Tecnologias Agro-Ambientais e BiológicasEscola de Ciências e Tecnologia da Universidade de Trás-os-Montes e Alto Douro, Quinta de PradosVila RealPortugal
  2. 2.Instituto Superior de Engenharia do Porto, Instituto Politécnico do PortoPortoPortugal

Personalised recommendations