Skip to main content
SpringerLink
Log in

Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots

  • Published:
Journal of Intelligent and Robotic Systems Aims and scope Submit manuscript

Abstract

A new control method for kinematically redundant manipulators having the properties of torque-optimality and singularity-robustness is developed. A dynamic control equation, an equation of joint torques that should be satisfied to get the desired dynamic behavior of the end-effector, is formulated using the feedback linearization theory. The optimal control law is determined by locally optimizing an appropriate norm of joint torques using the weighted generalized inverses of the manipulator Jacobian-inertia product. In addition, the optimal control law is augmented with fictitious joint damping forces to stabilize the uncontrolled dynamics acting in the null-space of the Jacobian-inertia product. This paper also presents a new method for the robust handling of robot kinematic singularities in the context of joint torque optimization. Control of the end-effector motions in the neighborhood of a singular configuration is based on the use of the damped least-squares inverse of the Jacobian-inertia product. A damping factor as a function of the generalized dynamic manipulability measure is introduced to reduce the end-effector acceleration error caused by the damping. The proposed control method is applied to the numerical model of SNU-ERC 3-DOF planar direct-drive manipulator.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baíllieul, J.: Kinematic programming alternatives for redundant manipulators, in: IEEE Internat. Conf. on Robotics and Automation, 1985, pp. 722-728.

  2. Ben-Israel, A. and Greville, T. N. E.: Generalized Inverse: Theory and Applications, Wiley, New York, 1974.

    Google Scholar 

  3. Chan, T. F. and Dubey, R. V.: A weighted least-norm solution based scheme for avoiding joint limits for redundant joint manipulators, IEEE Trans. Robotics Automat. 11(2) (1995), 286-292.

    Google Scholar 

  4. Doty, K. L., Melchiorri, C., and Bonivento, C.: A theory of generalized inverse applied to robotics, Internat. J. Robotics Res. 12(1) (1993), 1-19.

    Google Scholar 

  5. Gao, F., Guy, F., and Gruver, W. A.: Criteria-based analysis and design of three-degree of freedom planar robotic manipulators, in: IEEE Internat. Conf. on Robotics and Automation, 1997, pp. 468-473.

  6. Glass, K., Colbaugh, R., Lim, D., and Seragji, H.: Real-time collision avoidance for redundant mnipulators, IEEE Trans. Robotics Automat. 11(3) (1995), 448-457.

    Google Scholar 

  7. Gosselin, C. M. and Angeles, J.: A global performance index for the kinematic optimization of robotic manipulators, ASME J. Mech. Design 113 (1991), 220-226.

    Google Scholar 

  8. Hogan, N.: Impedance control: An approach to manipulation: Part 1-theory, part 2-implementation and part 3-applications, ASME J. Dyn. Systems Meas. Control (1985), 1-24.

  9. Hogan, N.: Stable execution of contact tasks using impedance control, in: IEEE Internat. Conf. on Robotics and Automation, 1987, pp. 1047-1054.

  10. Hollerbach, J. M. and Suh, K. C.: Redundancy resolution of manipulators through torque optimization, IEEE Trans. Robotics Automat. 3(4) (1987), 308-316.

    Google Scholar 

  11. Hsu, P., Hauser, J., and Sastry, S.: Dynamic control of redundant manipulators, J. Robotic Systems (1988), 133-148.

  12. Kang, H. J. and Freeman, R. A.: Joint torque optimization of redundant manipulators via the null space damping method, in: IEEE Internat. Conf. on Robotics and Automation, 1992, pp. 520-525.

  13. Kazerooni, H., Sheridan, T. B., and Haupt, P. K.: Robust compliant motion control for manipulators, part 1: The fundamental concepts of compliant motion, part 2: Design method, IEEE J. Robotics Automat. 2 (1986), 83-105.

    Google Scholar 

  14. Kazerounian, K. and Nedungadi, A.: An alternative method for minimization of the driving forces in redundant manipulators, in: IEEE Internat. Conf. on Robotics and Automation, 1987, pp. 1701-1706.

  15. Kazerounian, K. and Wang, Z.: Global versus local optimization in redundancy resolution of robotic manipulators, Internat. J. Robotics Res. 7(5) (1988), 3-12.

    Google Scholar 

  16. Khatib, O.: Dynamic control of manipulators in operational space, in: Proc. of the 6th IFToMM Congress Theory on Machines and Mechanisms, 1983, pp. 1123-1131

  17. Khatib, O.: A unified approach for motion and force control of robot manipulators: The operational space formulation, IEEE J. Robotics Automat. 3(1) (1987), 43-53.

    Google Scholar 

  18. Khatib, O.: Motion/force redundancy of manipulators, in: Proc. of Japan-USA Symp. on Flexible Automat, Vol. 1, 1990, pp. 337-342.

    Google Scholar 

  19. Kircanski, M., Kircanski, N., Lekovic, D., and Vukobratovic, M.: An experimental study of resolved acceleration control in singularities: Damped least-squares approach, in: IEEE Internat. Conf. on Robotics and Automation, San Diego, CA, May 1994.

  20. Klein, C. A. and Chirco, A. I.: Dynamic simulation of a kinematically redundant manipulator system, J. Robotic Systems 4(1) (1987), 5-23.

    Google Scholar 

  21. Klein, C. A. and Huang, C. H.: Review of pseudoinverse control for use with kinematically redundant manipulators, IEEE Trans. Systems Man Cybernet. 13(3) (1983).

  22. Liegeois, A.: Automatic supervisory control of the configuration and behavior of multibody mechanisms, IEEE Trans. Systems Man Cybernet. 7(12) (1977), 868-871.

    Google Scholar 

  23. Luh, J. Y. S., Walker, M. W., and Paul, R. P.: Resolved-acceleration control of mechanical manipulators, IEEE Trans. Automat. Control 25(3) (1980), 468-474.

    Google Scholar 

  24. Ma, S., Hirose, S., and Nenchev, D.: Improving local torque optimization techniques for redundant robotic mechanisms, J. Robotic Systems (1991), 75-91.

  25. Maciejewski, A. A. and Klein, C. A.: Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments, Internat. J. Robotics Res. 4 (1985), 109-117.

    Google Scholar 

  26. Maciejewski, A. A. and Klein, C. A.: Numerical filtering for the operation of robotic manipulators through kinematically singular configurations, J. Robotic Systems 5(6) (1988), 527-552.

    Google Scholar 

  27. Nakamura, Y. and Hanafusa, H.: Inverse kinematic solution with singularity robustness for robot manipulator control, ASME J. Dyn. Systems Meas. Control 108(3) (1987), 163-171.

    Google Scholar 

  28. Nakamura, Y., Hanafusa, H., and Yoshikawa, T.: Task priority based redundancy control of robot manipulators, Internat. J. Robotics Res. 6 (1987) 3-15

    Google Scholar 

  29. Nedungadi, A. and Kazerounian, K.: A local solution with global characteristics for the joint torque optimization of a redundant manipulator, J. Robotic Systems 6(5) (1989), 631-654.

    Google Scholar 

  30. Sciavicco, L. and Sciliano, B.: A dynamic solution to the inverse kinematic problem for redundant manipulators,” in: IEEE Internat. Conf. on Robotics and Automation, Los Alamitos, CA, 1987, pp. 1081-1087.

  31. Spong, M. W. and Vidyasagar, M.: Robust linear compensator design for nonlinear robotic control, in: IEEE Internat. Conf. on Robotics and Automation, 1985, pp. 954-959.

  32. Spong, M. and Vidyasagar, M.: Robot Dynamics and Control, Wiley, New York, 1989.

    Google Scholar 

  33. Suh, K. and Kazerounian, K.: Local versus global torque optimization of redundant manipulators, in: IEEE Internat. Conf. on Robotics and Automation, 1987.

  34. Tsuji, T., Akanatsu, H., and Kaneko, M.: Non-contact impedance control for redundant manipulators using visual information, in: IEEE Internat. Conf. on Robotics and Automation, 1997, pp. 2571-2576.

  35. Vukobratovic, M. and Kircanski, M.: A dynamic approach to nominal trajectory synthesis for redundant manipulators, IEEE Trans. Systems Man Cybernet. 14 (1984), 580-586.

    Google Scholar 

  36. Walker, I. D.: Impact configuration and measures for kinematically redundant and multiple armed robot systems, IEEE Trans. Robotics Automat. 10(5) (1994), 670-683.

    Google Scholar 

  37. Wampler, C. W.: Manipulator inverse kinematic solution based on vector formulation and damped least-squares methods, IEEE Trans. Systems Man Cybernet. 16(1) (1986), 93-101.

    Google Scholar 

  38. Wampler, C. W. and Leifer, L. J.: Applications of damped least-squares methods to resolvedrate and resolved acceleration control of manipulators, ASME J. Dyn. Systems Meas. Control 110 (1988), 31-38.

    Google Scholar 

  39. Whitney, D.E.: The mathematics of coordinated control of prostheses and manipulators, ASME J. Dynamic Systems Meas. Control (1972), 303-309.

  40. Williams, R. L.: Local performance optimization for a class of redundant eight-degree of freedom manipulators, in: IEEE Internat. Conf. on Robotics and Automation, Los Alamitos, CA, 1994, pp. 992-997.

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

    Google Scholar 

  42. Yoshikawa, T.: Manipulability and redundancy control of robotic mechanisms, in: IEEE Internat. Conf. on Robotics and Automation, 1985, pp. 1004-1009.

  43. Yoshikawa, T.: Dynamic manipulability of robot manipulators, in: IEEE Internat. Conf. on Robotics and Automation, 1985, pp. 1033-1038.

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Seoul National University, Shillim-dong, Kwanak-ku, Seoul, 151-742, Korea

    C. Y. Chung

  2. School of Electrical Engineering, Seoul National University, Shillim-dong, Kwanak-ku, Seoul, 151-742, Korea

    B. H. Lee

  3. Human Robot Research Center, Korea Institute of Science and Technology, Seoul, 135-081, Korea

    M. S. Kim & C. W. Lee

Authors
  1. C. Y. Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. H. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. S. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. W. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chung, C.Y., Lee, B.H., Kim, M.S. et al. Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots. Journal of Intelligent and Robotic Systems 28, 231–258 (2000). https://doi.org/10.1023/A:1008152705719

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008152705719

Search

Navigation