Natural Resolution of Ill-posedness of Inverse Kinematics for Redundant Robots under Constraints∗

In order to enhance dexterity in execution of robot tasks, a redundant number of degrees-of-freedom (DOF) is adopted for design of robotic mechanisms like robot arms and multifingered robot hands. Associated with such redundancy in DOFs relative to the number of physical variables necessary and sufficient for description of a given task, an extra performance index is introduced for controlling such a redundant robot in order to avoid arising of ill-posedness of inverse kinematics from the task space to the joint space. This paper shows that such an ill-posedness problem of DOF redundancy can be resolved in a natural way on the basis of construction of sensory feedback signals from the task space and a novel concept named “stability on a manifold”. To show this, two illustrative robot tasks are analyzed in details, which are 1) posture control of an object via rolling contact by a redundant multi-DOF finger and 2) stable pinching and object manipulation by a pair of multi-DOF robot fingers.