多様体上の安定性と冗長自由度の不良設定問題の解消

抄録

It is well known that, in order to control a multi-fingered hand to grasp an object and manipulate it toward a prescribed orientation and position, there arises an ill-posed problem of redundancy of DOF (degrees of freedom) because the total DOF of all fingers that constitute the hand is larger than the number of total DOFs that can enough describe motion of the object. The Russian psychologist Bernstein also raised a similar question how the brain could control a system with so many different degrees of freedom interacting in a complex fashion. This paper introduces a new concept of “Stability on a Manifold” in an illustrative problem how to realize secure grasp and orientation control of a 2D object by means of a pair of 3 DOF robot fingers and show that the ill-posedness can be resolved in a natural way without introducing any artificial extra performance index.