A Natural Resolution of Bernstein’s Degrees-of-Freedom Problem in Case of Multi-Joint Reaching

This paper aims at challenging Bernstein's problem called the "degrees of freedom problem", which is known to remain unsolved from both the physiological and the 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 multijoint movements with 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 illposedness of inverse kinematics from task description space to joint space. In the history of robotics research such illposedness 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 multijoint 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 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 choices 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

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