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

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 taskspace to the joint space. This ill-posedness was originally found by Bernstein, who tried to unveil the secret of thecentral nervous system and how nicely it coordinates a skeletomotor system with many DOFs interacting in complex ways. Inthe history of robotics research, such ill-posedness has not yet been resolved directly but circumvented by introducingan artificial performance index and determining uniquely an inverse kinematics solution by minimization. This paper tacklessuch Bernstein's problem and proposes a new method for resolving the ill-posedness in a natural way without invokingany artificial index. First, given a curve on a horizontal plane for a redundant robot arm whose endpoint is imposed to tracethe curve, the existence of a unique ideal joint trajectory is proved. Second, such a uniquely determined motion can beacquired eventually as a joint control signal through iterative learning without reinforcement or reward