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Journal of Robotics
Volume 2010 (2010), Article ID 217867, 15 pages
Research Article

Iterative Learning without Reinforcement or Reward for Multijoint Movements: A Revisit of Bernstein's DOF Problem on Dexterity

1Research Organization of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
2RIKEN-TRI Collaboration Center for Human-Interactive Robot Research, Nagoya, Aichi 463-0003, Japan
3Organization for the Promotion of Advanced Research, Kyushu University, Fukuoka 819-0395, Japan

Received 5 November 2009; Accepted 17 May 2010

Academic Editor: Noriyasu Homma

Copyright © 2010 Suguru Arimoto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A robot designed to mimic a human becomes kinematically redundant and its total degrees of freedom becomes larger than the number of physical variables required for describing a given task. Kinematic redundancy may contribute to enhancement of dexterity and versatility but it incurs a problem of ill-posedness of inverse kinematics from the task space to the joint space. This ill-posedness was originally found by Bernstein, who tried to unveil the secret of the central nervous system and how nicely it coordinates a skeletomotor system with many DOFs interacting in complex ways. In the history of robotics research, such ill-posedness has not yet been resolved directly but circumvented by introducing an artificial performance index and determining uniquely an inverse kinematics solution by minimization. This paper tackles such Bernstein's problem and proposes a new method for resolving the ill-posedness in a natural way without invoking any artificial index. First, given a curve on a horizontal plane for a redundant robot arm whose endpoint is imposed to trace the curve, the existence of a unique ideal joint trajectory is proved. Second, such a uniquely determined motion can be acquired eventually as a joint control signal through iterative learning without reinforcement or reward.