Copyright © 2005 The Institute of Electronics, Information and Communication Engineers
Special Section on Nonlinear Theory and its Applications -- Papers |
A Challenge to Bernstein's Degrees-of-Freedom Problem in Both Cases of Human and Robotic Multi-Joint Movements
1 The authors are with the Department of Robotics, Ritsumeikan University, Kusatsu-shi, 525-8577 Japan. E-mail: arimoto{at}se.ritsumei.ac.jp, 2 The author is with the BMC Research Center, RIKEN, Nagoya-shi, 463-0003 Japan.
This paper aims at challenging Bernstein's problem called the "Degrees-of-Freedom problem," which remains unsolved from both the physiological and robotics viewpoints. More than a half century ago A.N. Bernstein observed that "dexterity" residing in human limb motion emerges from accumulated involvement of multi-joint movements in surplus DOF. It is also said in robotics that redundancy of DOFs in robot mechanisms may contribute to enhancement of dexterity and versatility. However, kinematic redundancy incurs a problem of ill-posedness of inverse kinematics from task-description space to joint space. In the history of robotics research such ill-posedness problem of inverse-kinematics has not yet been attacked directly but circumvented by introducing an artificial performance index and determining uniquely an inverse kinematics solution by minimizing it. Instead of it, this paper introduces two novel concepts named "stability on a manifold" and "transferability to a submanifold" in treating the case of human multi-joint movements of reaching and shows that a sensory feedback from task space to joint space together with a set of adequate dampings enables any solution to the 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, without considering any type of inverse kinematics, the reaching task can be accomplished by a sensory feedback with adequate choice of a stiffness parameter and damping coefficients. It is also shown that these novel concepts can cope with annoying characteristics called "variability" of redundant joint motions seen typically in human skilled reaching. Finally, it is pointed out that the proposed control signals can be generated in a feedforward manner in case of human limb movements by referring to mechano-chemical characteristics of activation of muscles. Based on this observation, generation of human skilled movements of reaching can be interpreted in terms of the proposed "Virtual-Spring" hypothesis instead of the traditional "Equilibrium-Point" hypothesis.
Key Words: Bernstein's problem, multi-joint reaching, redundant robots, inverse kinematics, ill-posedness of inverse
Manuscript received March 10, 2005. Final manuscript received June 16, 2005.