A Challenge to Bernstein's Degrees-of-Freedom Problem in Both Cases of Human and Robotic Multi-Joint Movements

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 robotics viewpoints. More than a half century ago A.N. Bernstein observed and claimed that “dexterity” resident 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 taskdescription 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 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. 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 a human skilled movement can be interpreted in terms of the proposed “Virtual-Spring”hypothes instead of the traditional “Equilibrium-point” hypothesis.