Top > JRM > Natural Resolution of Ill-Posed Inverse Kinematics for Redunda ...

single-rb.php

JRM Vol.18 No.5 pp. 651-660
doi: 10.20965/jrm.2006.p0651
(2006)

Paper:

Views over last 60 days: 432

Natural Resolution of Ill-Posed Inverse Kinematics for Redundant Robots: A Challenge to Bernstein’s Degrees-of-Freedom Problem

Suguru Arimoto*,** and Masahiro Sekimoto*

*Department of Robotics, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan

**BMC Research Center, RIKEN, Nagoya, Aichi 463-0003, Japan

Received:
January 27, 2006
Accepted:
July 14, 2006
Published:
October 20, 2006
Creative Commons License
Keywords:
redundant robot, multijoint reaching, ill-posed inverse kinematics, Bernstein’s problem, surplus DOF
Abstract
Over half a century ago, A. N. Bernstein observed that “dexterity” in human limb movement emerges from the involvement of multijoint motion with surplus degrees of freedom (DOF). Robotics posits that DOF redundancy in robot may enhance dexterity and versatility. Kinematic redundancy involves the problem of ill-posed inverse kinematics from task-description space to joint space. This problem is conventionally avoided by introducing an artificial performance index and uniquely determining an inverse kinematics solution by minimizing it. Instead of taking this conventional avoidance solution, we propose challenging Bernstein’s DOF problem by introducing two direct novel concepts - stability on a manifold and transferability to a submanifold - in dealing with human multijoint movement in reaching and showing that sensory feedback from task space to joint space together with adequate damping (joint velocity feedback) enables any solution to overall closed-loop dynamics to converge naturally and coordinately to a lower-dimensional manifold describing a set of joint states fulfilling a given motion task. This means that a reaching task is accomplished by sensory feedback with the appropriate choice of a stiffness parameter and damping coefficients without having to consider inverse kinematics. We also show that these concepts cope with the annoying “variability” of redundant joint motion seen typically in skilled human reaching. In conclusion, we propose a virtual spring/damper hypothesis that leads to natural control of skilled movement in redundant multijoint reaching.
Cite this article as:
S. Arimoto and M. Sekimoto, “Natural Resolution of Ill-Posed Inverse Kinematics for Redundant Robots: A Challenge to Bernstein’s Degrees-of-Freedom Problem,” J. Robot. Mechatron., Vol.18 No.5, pp. 651-660, 2006.
Data files:
References
  1. [1] N. A. Bernstein (translated from the Russian by M. L. Latash), “On Dexterity and Its Development,” Lawrence Erlbaum Associates, Inc., 1996.
  2. [2] N. A. Bernstein, “The Coordination and Regulation of Movements,” Pergamon, London, 1967.
  3. [3] J. Lenarcic (ed.), “Special Issue on Redundant Robots. Laboratory Robotics and Automation,” 6-1, 1991.
  4. [4] Y. Nakamura, “Advanced Robotics: Redundancy and Optimization,” Addison-Wesley, Reading, MA, 1991.
  5. [5] O. Khatib, “A unified approach for motion and force control of robot manipulators: The operational space formulation,” IEEE J. Robotics and Automation, RA-3-1, pp. 43-53, 1987.
  6. [6] J. M. Hollerbach and K. C. Suh, “Redundancy resolution of manipulators through torque optimization,” IEEE J. of Robotics and Automation, RA-3-4, pp. 308-316, 1987.
  7. [7] T. Yoshikawa, “Manipulability of robotic mechanisms,” Intl. J. of Robotics Research, 4-2, pp. 3-9, 1985.
  8. [8] V. Potkonjak, S. Tzafestas, D. Kostic, G. Djoudjevic, and M. Rasic, “The handwriting problem,” IEEE Robotics & Automation Magazine, 10-1, pp. 35-46, 2003.
  9. [9] Y. Nakamura and H. Hanafusa, “Task priority based redundancy control of robot manipulators,” in H. Hanafusa and H. Inoue (eds.), Robotics Research: The Second Intl. Symp., MIT Press, Cambridge, MA, pp. 447-456, 1985.
  10. [10] J. Baillieul, “Avoiding obstacles and resolving kinematic redundancy,” Proc. of the IEEE Intl. Conf. on Robotics and Automation, San Francisco, CA, pp. 1698-1704, 1986.
  11. [11] D. E. Whitney, “Resolved motion rate control of manipulators and human prostheses,” IEEE Trans. on Man-Machine Systems, MMS-10-2, pp. 47-53, 1969.
  12. [12] A. Liegeois, “Automatic supervisory control of the configuration and behavior of multibody mechanisms,” IEEE Trans. on Systems, Man and Cybernetics, SMC-7-12, pp. 868-871, 1977.
  13. [13] A. G. Feldman, “Once more on the equilibrium-point hypothesis (λ model) for motor control,” J. of motor behavior, 18-1, pp. 17-54, 1986.
  14. [14] T. Flash, “The control of hand equilibrium trajectories in multijoint arm movements,” Biological Cybernetics, 57-4-5, pp. 257-274, 1987.
  15. [15] T. Flash and N. Hogan, “The coordination of arm movements: an experimentally confirmed mathematical model,” J. of Neuroscience, 5-7, pp. 1688-1703, 1985.
  16. [16] A. P. Georgopoulos, “On reaching,” Annual review of Neuroscience, 9, pp. 147-170, 1986.
  17. [17] E. Bizzi, N. Hogan, F. A. Mussa-Ivaldi, and S. Giszter, “Does the nervous system use equilibrium-point control to guide single and multiple joint movements?,” Behavioral and Brain Sciences, 15-4, pp. 603-613, 1992.
  18. [18] A. G. Feldman, “Functional turing of the nervous system with control of movement or maintenance of a steady posture. III. mechanographic analysis of the execution by man of the simplest motor tasks,” Biophysics, 11, pp. 766-775, 1966.
  19. [19] E. Bizzi, A. Polit, and P. Morasso, “Mechanisms underlying achievement of final head position,” J. of neurophysiology, 39-2, pp. 435-444, 1976.
  20. [20] E. Bizzi, N. Accornero, W. Chapple, and N. Hogan, “Posture control and trajectory formation during arm movement,” J. of Neuroscience, 4-11, pp. 2738-2744, 1984.
  21. [21] M. Takegaki and S. Arimoto, “A new feedback method for dynamic control of manipulators,” Trans. of the ASME, J. of Dynamic Systems, Measurement, and Control, 103-2, pp. 119-125, 1981.
  22. [22] S. Arimoto, “Control Theory of Nonlinear Mechanical Systems: A Passivity-based and Circuit-theoretic Approach,” Oxford Univ. Press, Oxford, UK, 1996.
  23. [23] N. Hogan, “An organizing principle for a class of voluntary movements, J. of neuroscience, 4-11, pp. 2745-2754, 1984.
  24. [24] W. L. Nelson, “Physical principles for economies of skilled movements,” Biological Cybernetics, 46-2, pp. 135-147, 1983.
  25. [25] Z. Hasan, “Optimized movement trajectories and joint stiffness in unperturbed, inertially loaded movements,” Biological cybernetics, 53-6, pp. 373-382, 1986.
  26. [26] Y. Uno, M. Kawato, and R. Suzuki, “Formation and control of optimal trajectory in human multijoint arm movement. Minimum torque-change model,” Biological Cybernetics, 61-2, pp. 89-101, 1989.
  27. [27] M. Kawato, Y. Maeda, Y. Uno, and R. Suzuki, “Trajectory formation of arm movement by cascade neural network model based on minimum torque-change criterion,” Biological Cybernetics, 62-4, pp. 275-288, 1990.
  28. [28] H. Cruse, E. Wischmeyer, M. Bruwer, P. Brockfield, and A. Dress, “On the cost functions for the control of the human arm movement,” Biological Cybernetics, 62-6, pp. 519-528, 1990.
  29. [29] S. Arimoto, “Intelligent control of multi-fingered hands,” Annual Review in Control, 28-1, pp. 75-85, 2004.
  30. [30] S. Arimoto, H. Hashiguchi, and R. Ozawa, “A simple control method coping with a kinematically ill-posed inverse problem of redundant robots: analysis in case of a handwriting robot,” Asian J. of Robotics, 7-2, pp. 112-123, 2005.
  31. [31] M. L. Latash, “Neurophysiological Basis of Movement,” Human Kinetics Pub., New York, 1998.
  32. [32] H. Seraji, “Configuration control of redundant manipulators: Theory and implementation,” IEEE Trans. on Robotics and Automation, 5-4, pp. 472-490, 1989.
  33. [33] J. M. Winters and L. Stark, “Muscle models: what is gained and what is lost by varying model complexity,” Biological Cybernetics, 55-6, pp. 403-420, 1987.
  34. [34] N. Hogan, “The mechanics of multi-joint posture and movement control,” Biological Cybernetics, 52-5, pp. 315-331, 1985.
  35. [35] S. Arimoto and M. Sekimoto, “Human-like movements of robotic arms with redundant DOFs virtual spring-damper hypothesis to tackle the Bernstein problem,” Proc. of the 2006 IEEE Intl. Conf. on Robotics and Automation, Orlando, FL, pp. 1860-1866, 2006.
  36. [36] P. L. Gribble, L. I. Mullin, N. Cothros, and A. Mattar, “Role of cocontraction in arm movement accuracy,” J. of Neurophysiology, 89-5, pp. 2396-2405, 2003.

Creative Commons License  This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

Copyright© 2006 by Fuji Technology Press Ltd. and Japan Society of Mechanical Engineers. All right reserved.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Oct. 01, 2024