Advertisement

Autonomous Robots

, Volume 25, Issue 1–2, pp 71–83 | Cite as

Reaching with multi-referential dynamical systems

  • Micha Hersch
  • Aude G. Billard
Article

Abstract

We study a reaching movement controller for a redundant serial arm manipulator, based on two principles believed to be central to biological motion control: multi-referential control and dynamical system control. The resulting controller is based on two concurrent dynamical systems acting on different, yet redundant variables. The first dynamical system acts on the end-effector location variables and the second one acts on the joint angle variables. Coherence constraints are enforced between those two redundant representations of the movement and can be used to modulate the relative influence of each dynamical system. We illustrate the advantages of such a redundant representation of the movement regarding singularities and joint angle avoidance.

Keywords

Bio-inspired reaching Dynamical system control Multi-referential control DLS inverse Redundant manipulator control Joint limit avoidance Singularity avoidance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abend, W., Bizzi, E., & Morasso, P. (1982). Human arm trajectory formation. Brain, 105, 331–348. CrossRefGoogle Scholar
  2. Ariff, G., Donchin, O., Nanayakkaran, T., & Shadmehr, R. (2002). A real-time state predictor in motor control: Study of saccadic eye movements during unseen reaching movements. The Journal of Neuroscience, 22, 7721–7729. Google Scholar
  3. Atkeson, C. G., & Hollerbach, J. M. (1985). Kinematic features of unrestrained vertical arm movements. The Journal of Neuroscience, 5(9), 2318–2330. Google Scholar
  4. Baillieul, J. (1985). Kinematic programming alternatives for redundant manipulators. In Proceedings of the IEEE international conference on robotics and automation (pp. 722–728). Google Scholar
  5. Billard, A., Calinon, S., & Guenter, F. (2006). Discriminative and adaptive imitation in uni-manual and bi-manual tasks. Robotics and Autonomous Systems, 54(5), 370–384. CrossRefGoogle Scholar
  6. Bizzi, E., Accornero, N., Chapple, W., & Hogan, N. (1984). Posture control and trajectory formation during arm movement. The Journal of Neuroscience, 4, 2738–2744. Google Scholar
  7. Bullock, D., & Grossberg, S. (1988). Neural dynamics of planned arm movements: Emergent invariants and speed-accuracy properties during trajectory formation. Psychological Review, 95(1), 49–90. CrossRefGoogle Scholar
  8. Burdick, J. W. (1989). On the inverse kinematics of redundant manipulators: Characterization of the self-motion manifolds. In: Proceedings of the IEEE international conference on robotics and automation (pp. 264–270). Google Scholar
  9. Carrozzo, M., & Lacquaniti, F. (1994). A hybrid frame of reference for visuo-manual coordination. Neuroreport, 5, 453–456. Google Scholar
  10. Chaumette, F., & Marchand, É. (2001). A redundancy-based iterative approach for avoiding joint limits: Application to visual servoing. IEEE Transactions on Robotics and Automation, 17(5), 719–730. CrossRefGoogle Scholar
  11. Chiaverini, S., Siciliano, B., & Egeland, O. (1994). Review of the damped leat-squares inverse kinematics with experiments on an industrial robot manipulator. IEEE Transactions on Control Systems Technology, 2(2), 123–134. CrossRefGoogle Scholar
  12. Cruse, H., & Brüwer, M. (1987). The human arm as a redundant manipulator: The control of path and joint angles. Biological Cybernetics, 57, 137–144. CrossRefGoogle Scholar
  13. Desmurget, M., Jordan, M., Prablanc, C., & Jeannerod, M. (1997). Constrained and unconstrained movements involve different control strategies. Journal of Neurophysiology, 77, 1644–1650. Google Scholar
  14. Desmurget, M., Gréa, H., & Prablanc, C. (1998a). Final posture of the upper limb depends on the initial position of the hand during prehension movements. Experimental Brain Research, 119, 411–516. CrossRefGoogle Scholar
  15. Desmurget, M., Pélisson, D., Rosseti, Y., & Prablanc, C. (1998b). From eye to hand: Planning goal-directed movements. Neuroscience and Biobehavioural Reviews, 22(6), 761–788. CrossRefGoogle Scholar
  16. Feldman, A. G., & Levin, M. F. (1995). The origin and use of positional frames of reference in motor control. Behavioral Brain Sciences, 18, 723–806. CrossRefGoogle Scholar
  17. Flash, T., & Hogan, N. (1985). The coordination of arm movements: An experimentally confirmed mathematical model. The Journal of Neuroscience, 5(7), 1688–1703. Google Scholar
  18. Fung Chan, T., & Dubey, R. V. (1995). A weighted least-norm solution based scheme for avoiding joint limits for redundant joint manipulator. IEEE Transactions on Robotics and Automation, 11(2), 286–292. CrossRefGoogle Scholar
  19. Giszter, S. F., Mussa-Ivaldi, F. A., & Bizzi, E. (1993). Convergent force fields organized in the frog’s spinal cord. The Journal of Neuroscience, 13(2), 467–491. Google Scholar
  20. Ijspeert, A. J., Nakanishi, J., & Schaal, S. (2002). Movement imitation with nonlinear dynamical systems in humanoid robots. In Proceedings of the IEEE international conference on robotics and automation (pp. 1398–1403). Google Scholar
  21. Iossifidis, I., & Schöner, G. (2004). Autonomous reaching and obstacle avoidance with the anthropomorphic arm of a robotic assistant using the attractor dynamics approach. In Proceedings of the IEEE international conference on robotics and automation (pp. 4295–4300). Google Scholar
  22. Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge: MIT Press. Google Scholar
  23. Khatib, O. (1985). Real-time obstacle avoidance for manipulators and mobile robots. In Proceedings of the IEEE international conference on robotics and automation (pp. 500–505). Google Scholar
  24. Lacquaniti, F., Soechting, J. F., & Terzuolo, S. A. (1986). Path constraints on point-to-point arm movements in three-dimensional space. Neuroscience, 17(2), 313–324. CrossRefGoogle Scholar
  25. Liégeois, A. (1977). Automatic supervisory control of the configuration and behavior of multibody mechanisms. IEEE Transactions on Systems, Man, and Cybernetics, 7(12), 868–871. zbMATHCrossRefGoogle Scholar
  26. Morasso, P. (1981). Spatial control of arm movements. Experimental Brain Research, 42, 223–227. CrossRefGoogle Scholar
  27. Nakamura, Y., & Hanafusa, H. (1986). Inverse kinematics solutions with singularity robustness for robot manipulator control. ASME Journal of Dynamic Systems, Measurement, and Control, 108, 163–171. zbMATHCrossRefGoogle Scholar
  28. Paillard, J. (Ed.). (1991). Brain and space. London: Oxford University Press. Chaps. from Arbib, Berthoz and Paillard. Google Scholar
  29. Righetti, L., & Ijspeert, A. J. (2006). Programmable central pattern generators: an application to biped locomotion control. In Proceedings of the 2006 IEEE international conference on robotics and automation (pp. 1585–1590). Google Scholar
  30. Schöner, G., Dose, M., & Engels, C. (1995). Dynamics of behavior: theory and applications for autonomous robot architectures. Robotics and Autonomous Systems, 16, 213–245. CrossRefGoogle Scholar
  31. Shadmehr, R., & Wise, S. P. (2005). The computational neurobiology of reaching and pointing. Cambridge: MIT Press. Google Scholar
  32. Soechting, J. F., Buneo, C.A., & Flanders, M. (1995). Moving effortlessly in three dimensions: Does Donder’s law apply to arm movement? Journal of Neuroscience, 15(9), 6271–6280. Google Scholar
  33. Todorov, E., & Jordan, M. I. (2002). Optimal feedback control as a theory of motor coordination. Nature Neuroscience, 5(11), 1226–1235. CrossRefGoogle Scholar
  34. Wampler, C. W. (1986). Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods. IEEE Transactions on Systems, Man, and Cybernetics, 16(1), 93–101. CrossRefzbMATHGoogle Scholar
  35. Whitney, D. E. (1969). Resolved motion rate control of manipulators and human prosteses. IEEE Transactions on Man-Machine Systems, 10(2), 47–52. CrossRefMathSciNetGoogle Scholar
  36. Wolpert, D., Ghahramani, Z., & Jordan, M. I. (1995). An internal model for sensorimotor integration. Science, 269(5232), 1880–1882. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.LASA Laboratory, School of EngineeringEPFLLausanneSwitzerland

Personalised recommendations