Nonlinear Dynamics

, Volume 60, Issue 1–2, pp 115–129 | Cite as

An evolutionary approach for the motion planning of redundant and hyper-redundant manipulators

  • Maria da Graça Marcos
  • J. A. Tenreiro Machado
  • T.-P. Azevedo-Perdicoúlis
Review Paper

Abstract

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. The pseudoinverse control is not repeatable, causing drift in joint space which is undesirable for physical control. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms, leading to an optimization criterion for repeatable control of redundant manipulators, and avoiding the joint angle drift problem. Computer simulations performed based on redundant and hyper-redundant planar manipulators show that, when the end-effector traces a closed path in the workspace, the robot returns to its initial configuration. The solution is repeatable for a workspace with and without obstacles in the sense that, after executing several cycles, the initial and final states of the manipulator are very close.

Redundant manipulators Hyper-redundant manipulators Robots Kinematics Genetic algorithms Trajectory planning 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nenchev, D.N., Tsumaki, Y.: Motion analysis of a kinematically redundant seven-DOF manipulator under the singularity-consistent method. In: Proc. of the 2003 IEEE Int. Conf. on Robotics and Automation, pp. 2760–2765 (2003) Google Scholar
  2. 2.
    Doty, K.L., Melchiorri, C., Bonivento, C.: A theory of generalized inverses applied to robotics. Int. J. Robotics Res. 12, 1–19 (1993) CrossRefGoogle Scholar
  3. 3.
    Baillieul, J., Hollerbach, J., Brockett, R.: Programming and control of kinematically redundant manipulators. In: Proc. of the 23rd IEEE Conf. on Decision and Control, pp. 768–774 (1984) Google Scholar
  4. 4.
    Klein, C.A., Huang, C.-H.: Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern. 13(3), 245–250 (1983) Google Scholar
  5. 5.
    Roberts, R.G., Maciejewski, A.: Repeatable generalized inverse control strategies for kinematically redundant manipulators. IEEE Trans. Autom. Control 38(5), 689–699 (1993) CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    Klein, C.A., Ahmed, S.: Repeatable pseudoinverse control for planar kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern. 25(12), 1657–1662 (1995) CrossRefGoogle Scholar
  7. 7.
    Zhang, Y., Zhu, H., Lv, X., Li, K.: Joint angle drift problem of PUMA560 robot arm solved by a simplified LVI-based primal-dual neural network. In: Proc. of the IEEE Int. Conf. on Industrial Technology, pp. 1–26 (2008) Google Scholar
  8. 8.
    Zhang, Y., Lv, X., Li, Z., Yang, Z., Zhu, H.: Effective neural remedy for drift phenomenon of planar three-link robot arm using quadratic performance index. Electron. Lett. 44(6), 436–437 (2008). doi:10.1049/el:20080455 Google Scholar
  9. 9.
    Zhang, Y., Tan, Z., Yang, Z., Lv, X.: A dual neural network applied to drift-free resolution of five-link planar robot arm. In: Proc. of the 2008 IEEE International Conference on Information and Automation, pp. 1274–1279 (2008) Google Scholar
  10. 10.
    Baillieul, J.: Kinematic programming alternatives for redundant manipulators. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, pp. 722–728 (1985) Google Scholar
  11. 11.
    Baker, D.R., Wampler II, C.W.: On the inverse kinematics of redundant manipulators. Int. J. Robotics Res. 7(211), 3–21 (1988) Google Scholar
  12. 12.
    Park, K.-C., Chang, P.-H., Lee, S.: A new kind of singularity in redundant manipulation: semi-algorithmic singularity. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, vol. 2, pp. 1979–1984 (2002) Google Scholar
  13. 13.
    Park, J., Chung, W.-K., Youm, Y.: Characteristics of optimal solutions in kinematics resolutions of redundancy. IEEE Trans. Robotics Autom. 12(3), 471–478 (1996) CrossRefGoogle Scholar
  14. 14.
    Goldenberg, D.E.: Genetic Algorithms in Search Optimization, and Machine Learning. Addison-Wesley, Reading (1989) Google Scholar
  15. 15.
    Parker, J.K., Khoogar, A.R., Goldberg, D.E.: Inverse kinematics of redundant robots using genetic algorithms. In: Proc. of the 1989 IEEE Int. Conf. on Robotics and Automation, pp. 271–276 (1989) Google Scholar
  16. 16.
    Arakawa, T., Kubota, N., Fukuda, T.: Virus-evolutionary genetic algorithm with subpopulations: application to trajectory generation of redundant manipulator through energy optimization. In: Proc. of the 1996 IEEE Int. Conf. on Systems, Man, and Cybernetics, pp. 14–17 (1996) Google Scholar
  17. 17.
    Kubota, N., Arakawa, T., Fukuda, T., Shimojima, K.: Trajectory generation for redundant manipulator using virus evolutionary genetic algorithm. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, pp. 205–210 (1997) Google Scholar
  18. 18.
    de la Cueva, V., Ramos, F.: Cooperative genetic algorithms: a new approach to solve the path planning problem for cooperative robotic manipulators sharing the same work space. In: Proc. of the IEEE/RSJ Int. Conference on Intelligent Robots and Systems, pp. 267–272 (1998) Google Scholar
  19. 19.
    Nishimura, T., Sugawara, K., Yoshihara, I., Abe, K.: A motion planning method for a hyper multi-joint manipulator using genetic algorithm. In: Proc. of the IEEE Int. Conf. on Systems, Man, and Cybernetics, pp. 645–650 (1999) Google Scholar
  20. 20.
    McAvoy, B., Sangolola, B.: Optimal trajectory generation for redundant planar manipulators. In: Proc. of the IEEE Int. Conf. on Systems, Man, and Cybernetics, pp. 3241–3246 (2000) Google Scholar
  21. 21.
    Peng, Y., Wei, W.: A new trajectory planning method of redundant manipulator based on adaptive simulated annealing genetic algorithm (ASAGA). In: Proc. of the IEEE Int. Conf. on Computational Intelligence and Security, pp. 262–265 (2006) Google Scholar
  22. 22.
    Zhang, Y., Sun, Z., Yang, T.: Optimal motion generation of a flexible macro–micro manipulator system using genetic algorithm and neural network. In: Proc. of the 2006 IEEE Conf. on Robotics, Automation and Mechatronics, pp. 1–6 (2006) Google Scholar
  23. 23.
    Pires, E.J.S., Machado, J.A.T., Oliveira, P.B.M.: Manipulator trajectory planning using a MOEA. Appl. Soft Comput. J. 7(3), 659–667 (2007) CrossRefGoogle Scholar
  24. 24.
    Whitney, D.E.: Resolved motion rate control of manipulators and human prostheses. IEEE Trans. Man Mach. Syst. 10(2), 47–53 (1969) CrossRefMathSciNetGoogle Scholar
  25. 25.
    Siciliano, B.: Kinematic control of redundant robot manipulators: a tutorial. J. Intell. Robotic Syst. 3, 201–212 (1990) CrossRefGoogle Scholar
  26. 26.
    Marcos, M.G., Duarte, F.B., Machado, J.A.T.: Complex dynamics in the trajectory control of redundant manipulators. Trans. Nonlinear Sci. Complex. (World Scientific) 1, 134–143 (2007) CrossRefGoogle Scholar
  27. 27.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1992) (2nd edn.: MIT Press, Cambridge) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Maria da Graça Marcos
    • 1
  • J. A. Tenreiro Machado
    • 2
  • T.-P. Azevedo-Perdicoúlis
    • 3
  1. 1.Dept. of Mathematics, Institute of EngineeringPolytechnic Institute of PortoPortoPortugal
  2. 2.Dept. of Electrotechnical Engineering, Institute of EngineeringPolytechnic Institute of PortoPortoPortugal
  3. 3.Dept. of MathematicsUniversity of Trás-os-Montes and Alto DouroVila RealPortugal

Personalised recommendations