Arimoto, Suguru (Ritsumeikan Univ.), Sekimoto, Masahiro (Ritsumeikan Univ.)

Natural Redundancy Resolution for PTP Control of Multi-Joint Reaching Movements: A Virtual Spring/Damper Hypothesis

Scheduled for presentation during the Regular Session "Control of Mechanical Systems" (TuP07), Tuesday, July 25, 2006, 16:35−17:00, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 27, 2023

Abstract

This paper aims at challenging Bernstein's problem called the "Degrees-of-Freedom problem," which remains unsolved from not only the control theoretic viewpoint but also the physiological and robotics viewpoints. More than a half century ago A.N. Bernstein observed and claimed that "dexterity" resident in human limb motion emerges from involvement of multi-joint movements with surplus DOF. It is also said in robotics that redundancy of DOFs 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 multi-joint movements of reaching and shows that a sensory feedback from task space to joint space together with a set of adequate dampings (joint velocity feedbacks) enables any solution to the overall closed-loop dynamics to converge naturally and coordinately to a lower-dimensional manifold consisting of 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 choices of a stiffness parameter and damping coefficients. As a conclusion, "virtual spring/damper hypothesis" is proposed, that leads to a natural control scheme for skilled movements of redundant multi-joint reaching.