Natural Resolution of Ill-Posedness of Inverse Kinematics for Redundant Robots Under Constraints

Abstract

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 multi- fingered 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 in- troduced 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 prob- lem 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