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Control-Based Solution to Inverse Kinematics for Mobile Manipulators Using Penalty Functions

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Abstract

This study offers the solution at the control feedback level to the inverse kinematics problem subject to state equality and inequality constraints for mobile manipulators. Based on the Lyapunov stability theory, a class of controllers generating the mobile manipulator trajectory whose attractor attained in a finite time, fulfills the above state constraints. The problem of both holonomic manipulability enforcement and collision avoidance is solved here based on an exterior penalty function approach which results in continuous mobile manipulator velocities near obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both a constraint-free task space and task space including obstacles, illustrate the performance of the proposed controllers.

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References

  1. Barbehenn, M., Chen, P., and Hutchinson, S.: An efficient hybrid planner in changing environments, in: Proc. of ICRA 1994, 1994, pp. 2755–2760.

  2. Barraquand, J. and Latombe, J. C.: Robot motion planning: A distributed representation approach, Internat. J. Robotics Res. 10(6) (1991), 628–649.

    Google Scholar 

  3. Bayle, B., Fourquet, J.-Y., and Renaud, M.: A coordination strategy for mobile manipulation, in: IAS’2000, 2000, pp. 981–988.

  4. Bayle, B., Fourquet, J.-Y., and Renaud, M.: Manipulability analysis for mobile manipulators, in: Proc. of IEEE Internat. Conf. on Robotics and Automation, 2001, pp. 1251–1256.

  5. Bloch, A. M., Reyhanoglu, M., and McClamroch, N. H.: Control and stabilization of nonholonomic dynamic systems, IEEE Trans. Automat. Control 37(11) (1992), 1746–1757.

    Google Scholar 

  6. Brockett, R. W.: Asymptotic stability and feedback stabilization, in: Proc. of Conf. on Differential Geometric Control Theory, Progress in Mathematics, Vol. 27, Birkhäuser, Boston, MA, 1983, pp. 181–208.

    Google Scholar 

  7. Brooks R. A.: Solving the find-path problem by good representation of free space, in: Proc. AAAI 2nd Ann. National Conf. on Artifical Intelligence, 1982, pp. 381–386.

  8. Carriker, W. F., Khosla, P. K., and Krogh, B. H.: Path planning for mobile manipulators for multiple task execution, IEEE Trans. Robotics Automat. 7(3) (1991), 403–408.

    Google Scholar 

  9. Chuang, J.-H.: Potential-based modelling of three-dimensional workspace for obstacle avoidance, IEEE Trans. Robotics Automat. 14(5) (1998), 778–785.

    Google Scholar 

  10. Conn, R. A. and Kam, M.: Robot motion planning on N-dimensional star worlds among moving obstacles, IEEE Trans. Robotics Automat. 14(2) (1998), 320–325.

    Google Scholar 

  11. Desai, J. P. and Kumar, V.: Nonholonomic motion planning for multiple mobile manipulators, in: Proc. of IEEE Conf. on Robotics and Automation, 1997, pp. 3409–3414.

  12. Divelbiss, A. W. and Wen, J. T.: A path space approach to nonholonomic motion planning in the presence of obstacles, IEEE Trans. Robotics Automat. 13(3) (1997), 443–451.

    Google Scholar 

  13. Galicki, M.: Inverse kinematics solution to mobile manipulators, Internat. J. Robotics Res. 22(12) (2003).

  14. Galicki, M. and Morecki, A.: Finding collision-free trajectory for redundant manipulator by local information available, in: Proc. of the 9th CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, 1992, pp. 61–71.

  15. Gilbert, E. G. and Johnson, D. W.: Distance functions and their application to robot path planning, IEEE J. Robotics Automat. 1 (1985), 21–30.

    Google Scholar 

  16. Hootsmans, N. A. M. and Dubowsky, S.: Large motion control of mobile manipulators including vehicle suspension characteristics, in: Proc. of IEEE Conf. on Robotics and Automation, 1991, pp. 2336–2341.

  17. Huang, Q., Tanie, K., and Sugano, S.: Coordinated motion planning for a mobile manipulator considering stability and manipulation, Internat. J. Robotics Res. 19(8) (2000), 732–742.

    Google Scholar 

  18. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile manipulators, Internat. J. Robotics Res. 5(1) (1986), 90–98.

    Google Scholar 

  19. Khatib, O., Yokoi, K., Chang, K., Ruspini, D., Holberg, R., and Casai, A.: Coordination and decentralized cooperation of mobile manipulators, J. Robotic Systems 13(9) (1996), 755–764.

    Google Scholar 

  20. Kim, J.-O. and Khosla, P. K.: Real-time obstacle avoidance using harmonic potential functions, IEEE Trans. Robotics Automat. 8(3) (1992), 338–349.

    Google Scholar 

  21. Krstic, M., Kanellakopoulos, I., and Kokotovic, P.: Nonlinear and Adaptive Control Design, Wiley, New York, 1995.

    Google Scholar 

  22. Latombe, J. C.: Robot Motion Planning, Kluwer, Boston, MA, 1991.

    Google Scholar 

  23. Liu, K. and Lewis, F. L.: Control of mobile robot with onboard manipulator, in: Proc. Internat. Symp. on Robotics and Manufacturing, 1992, pp. 539–546.

  24. Lozano-Perez, T.: Spatial planning: A configuration space approach, IEEE Trans. Comput. C-32 (1983), 108–120.

    Google Scholar 

  25. Miksch, W. and Schroeder, D.: Performance-functional based controller design for a mobile manipulator, in: Proc. of IEEE Internat. Conf. on Robotics and Automation, 1992, pp. 227–232.

  26. Nagatani, K., Hirayama, T., Gofuku, A., and Tanaka, Y.: Motion planning for mobile manipulator with keeping manipulability, in: Proc. of IEEE/RSJ Internat. Conf. on Intelligent Robots and Systems, 2002, pp. 1663–1668.

  27. Nakamura, Y. and Mukherjee, R.: Nonholonomic path planning of space robots, in: Proc. of IEEE Conf. on Robotics and Automation, 1989, pp. 1050–1055.

  28. Papadopoulos, E. and Dubowsky, S.: Coordinated manipulator/spacecraft motion control for space robotics, in: Proc. of IEEE Conf. on Robotics and Automation, 1991, pp. 1696–1701.

  29. Perrier, C., Dauchez, P., and Pierrot, F.: A global approach for motion generation of non-holonomic mobile manipulators, in: Proc. of IEEE Conf. on Robotics and Automation, 1998, pp. 2971–2976.

  30. Pin, F. G. and Culioli, J. C.: Multi-criteria position and configuration optimization for redundant platform/manipulator systems, in: Proc. of IEEE Workshop on Intelligent Robots and Systems, 1990, pp. 103–107.

  31. Pin, F. G. and Culioli, J. C.: Optimal positioning of redundant manipulator-platform systems for maximum task efficiency, in: Proc. of Internat. Symp. on Robotics and Manufacturing, 1990, pp. 489–495.

  32. Pin, F. G., Hacker, C. J., Gower, K. B., and Morgansen, K. A.: Including a non-holonomic constraint in the FSP (Full Space Parameterization) method for mobile manipulators’ motion planning, in: Proc. of IEEE Conf. on Robotics Automation, 1997, pp. 2914–2919.

  33. Rimon, E. and Koditschek, D. E.: Exact robot navigation using artificial potential functions, IEEE Trans. Robotics Automat. 8(5) (1992), 501–518.

    Google Scholar 

  34. Schwartz, J. T. and Sharir, M.: On the “piano movers” problem II. General techniques for computing topological properties of real algebraic manifolds, Adv. Appl. Math. 4(1) (1983), 298–351.

    Google Scholar 

  35. Seraji, H.: An on-line approach to coordinated mobility and manipulation, in: Proc. of IEEE Conf. on Robotics and Automation, 1993, pp. 28–35.

  36. Seraji, H.: A unified approach to motion control of mobile manipulators, Internat. J. Robotics Res. 17(2) (1998), 107–118.

    Google Scholar 

  37. Shevitz, D. and Paden, B.: Lyapunov stability theory of nonsmooth systems, IEEE Trans. Automat. Control 30(9) (1994), 1910–1914.

    Google Scholar 

  38. Singh, S. K. and Leu, M. C.: Manipulator motion planning in the presence of obstacles and dynamic constraints, Internat. J. Robotics Res. 10(2) (1991), 177–187.

    Google Scholar 

  39. Singh, L., Wen, J., and Stephanou, H.: Motion planning and dynamic control of a linked manipulator using modified magnetic fields, in: Proc. of IEEE Conf. on Robotics and Automation, 1997, pp. 1142–1147.

  40. Tanner, H. G. and Kyriakopoulos, K. J.: Nonholonomic motion planning for mobile manipulators, in: Proc. of Internat. Conf. on Robotics and Automation, 2000, pp. 1233–1238.

  41. Tchon, K.: On inverse kinematics of stationary and mobile manipulators, in: Proc. of the 2nd Workshop on Robot Motion and Control, 2001, pp. 39–44.

  42. Yamamoto, Y. and Yun, X.: Coordinating locomotion and manipulation of a mobile manipulator, IEEE Trans. Automat. Control 39(6) (1994), 1326–1332.

    Google Scholar 

  43. Yamamoto, Y. and Yun, X.: Unified analysis on mobility and manipulability of mobile manipulators, in: Proc. of IEEE Internat. Conf. on Robotics and Automation, 1999, pp. 1200–1206.

  44. Yoshikawa, T.: Manipulability of robotic mechanisms, Internat. J. Robotics Res. 4(2) (1985), 3–9.

    Google Scholar 

  45. Yun, X. and Sarkar, N.: Unified formulation of robotic systems with holonomic and nonholonomic constraints, IEEE Trans. Robotics Automat. 14(4) (1998), 640–649.

    Google Scholar 

  46. Zak, M.: Terminal attractors for addressable memory in neural networks, Phys. Lett. A. 133 (1988), 218–222.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Medical Statistics, Computer Science and Documentation, Friedrich Schiller University Jena, Jahnstrasse 3, D-07740, Jena, Germany

    MirosŁaw Galicki

  2. Department of Mechanical Engineering, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland

    MirosŁaw Galicki

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  1. MirosŁaw Galicki
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Correspondence to MirosŁaw Galicki.

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Galicki, M. Control-Based Solution to Inverse Kinematics for Mobile Manipulators Using Penalty Functions. J Intell Robot Syst 42, 213–238 (2005). https://doi.org/10.1007/s10846-004-7196-9

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  • DOI: https://doi.org/10.1007/s10846-004-7196-9

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