A Global Optimal Approach for Robot Kinematics Design using the Grid Method

  • Park Joon-Young (Korea Electric Power Research Institute) ;
  • Chang Pyung-Hun (Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology) ;
  • Kim Jin-Oh (Department of Information and Control Engineering, Kwangwoon University)
  • Published : 2006.10.01

Abstract

In a previous research, we presented the Grid Method and confirmed it as a systematic and efficient problem formulation method for the task-oriented design of robot kinematics. However, our previous research was limited in two ways. First, it gave only a local optimum due to its use of a local optimization technique. Second, it used constant weights for a cost function chosen by the manual weights tuning algorithm, thereby showing low efficiency in finding an optimal solution. To overcome these two limitations, therefore, this paper presents a global optimization technique and an adaptive weights tuning algorithm to solve a formulated problem using the Grid Method. The efficiencies of the proposed algorithms have been confirmed through the kinematic design examples of various robot manipulators.

Keywords

References

  1. P.-H. Chang, J.-Y. Park, and J.-Y. Yang, 'Task oriented design of robot kinematics using grid method and its applications to nuclear power plant,' Proc. of Int. Symp. on Artificial Intelligence, Robotics and Human Centered Technology for Nuclear Applications, pp. 114- 123, 2002
  2. J.-Y. Park, P.-H. Chang, and J.-Y. Yang, 'Task oriented design of robot kinematics using the Grid Method,' Advanced Robotics, vol. 17, no. 9, pp. 879-907, 2003 https://doi.org/10.1163/156855303770558679
  3. C. J. J. Paredis and P. K. Khosla, 'Kinematic design of serial link manipulators from task specifications,' International Journal of Robotics Research, vol. 12, no. 3, pp. 274-287, 1993 https://doi.org/10.1177/027836499301200306
  4. I.-M. Chen and J. W. Burdick, 'Determining task optimal modular robot assembly configurations,' Proc. of the IEEE Int. Conf. on Robotics and Automation, vol. 1, pp. 132-137, 1995
  5. G. Yang and I.-M. Chen, 'Task-based optimization of modular robot configurations: Minimized degree-of-freedom approach,' Mechanism and Machine Theory, vol. 35, no. 4, pp. 517-540, 2000 https://doi.org/10.1016/S0094-114X(99)00021-X
  6. O. Chocron and P. Bidaud, 'Evolutionary algorithms in kinematic design of robotic systems,' Proc. of the IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, vol. 2, pp. 1111- 1117, 1997
  7. J.-O. Kim and P. K. Khosla, 'A formulation for task based design of robot manipulators,' Proc. of the IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, vol. 3, pp. 2310-2317, 1993
  8. J.-O. Kim, Task Based Kinematic Design of Robot Manipulators, Ph.D. thesis, Carnegie- Mellon University, 1992
  9. C. Leger, Automated Synthesis and Optimization of Robot Configurations: An Evolutionary Approach, Ph.D. thesis, Carnegie-Mellon University, 1999
  10. C. J. J. Paredis and P. K. Khosla, 'An approach for mapping kinematic task specifications into a manipulator design,' Proc. of the Fifth Int. Conf. on Advanced Robotics 'Robots in Unstructured Environments, vol. 1, pp. 556-561, 1991
  11. J. Wunderlich and C. Boncelet, 'Local optimization of redundant manipulator kinematics within constrained workspaces,' Proc. of the IEEE Int. Conf. on Robotics and Automation, vol. 1, pp. 127-132, 1996
  12. L. Ingber, 'Very fast simulated re-annealing,' Mathematical and Computer Modelling, vol. 12, no. 8, pp. 967-973, 1989 https://doi.org/10.1016/0895-7177(89)90202-1
  13. B. Rosen, 'Function optimization based on advanced simulated annealing,' Proc. of Workshop on Physics and Computation, pp. 289- 293, 1992
  14. W. S. Jung and N. Z. Cho, 'Determination of design alternatives and performance criteria for safety systems in a nuclear power plant via simulated annealing,' Reliability Engineering and System Safety, vol. 41, no. 1, pp. 71-94, 1993 https://doi.org/10.1016/0951-8320(93)90019-U
  15. R. P. Paul, B. Shimano, and G. E. Mayer, 'Kinematic control equations for simple manipulators,' IEEE Trans. on Systems, Man and Cybernetics, vol. SMC-11, no. 6, pp. 449- 455, 1981
  16. A. Mohri, X. D. Yang, and M. Yamamoto, 'Collision free trajectory planning for manipulator using potential function,' Proc. of the IEEE Int. Conf. on Robotics and Automation, vol. 3, pp. 3069-3074, 1995
  17. F. Ranjbaran, J. Angeles, and A. Kecskemethy, 'On the kinematic conditioning of robotic manipulators,' Proc. of the IEEE Int. Conf. on Robotics and Automation, vol. 4, pp. 3167-3172, 1996
  18. J. S. Arora, Introduction to Optimum Design, McGraw-Hill, New York, 1989
  19. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, and A. H. Teller, 'Equations of state calculations by fast computing machines,' Journal of Chemical Physics, vol. 21, pp. 1087- 1092, 1953 https://doi.org/10.1063/1.1699114
  20. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, 'Optimization by simulated annealing,' Science, vol. 220, no. 4598, pp. 671-680, 1983 https://doi.org/10.1126/science.220.4598.671
  21. D. Vanderbilt and S. G. Louie, 'A Monte Carlo simulated annealing approach to optimization over continuous variables,' Journal of Computational Physics, vol. 56, pp. 259-271, 1984 https://doi.org/10.1016/0021-9991(84)90095-0
  22. M. Lundy and A. Mees, 'Convergence of annealing algorithm,' Mathematical Programming, vol. 34, pp. 111-124, 1986 https://doi.org/10.1007/BF01582166
  23. H. H. Szu and R. L. Hartley, 'Fast simulated annealing,' Physics Letters A, vol. 122, pp. 157- 162, 1987 https://doi.org/10.1016/0375-9601(87)90796-1
  24. A. D. Belegundu and T. R. Chandrupatla, Optimization Concepts and Applications in Engineering, Prentice-Hall, Inc., 1999