Stabilization of self-motions in redundant robots

Kinematic redundancy endows a robotic manipulator with the possibility of executing self-motions, that is changing its configuration without moving the end-effector This ability may be used to assume the most convenient posture for a given task, to avoid singularities or workspace obstacles, as well as to obtain closed joint motion on cyclic end-effector paths. We investigate the self-motion stabilization problem: the objective is to design a feedback scheme which drives the robot joint variables to a reference value keeping the end-effector still. Two main approaches are presented. The first is based on the idea of projecting the error term in the null space of the Jacobian matrix. Pure proportional feedback yields simple stability in general, and asymptotic stability in special cases. More interestingly, by using time-varying feedback joint convergence to the desired configuration is achieved. The second approach exploits the concept of reduction in the space of redundant degrees of freedom to design stabilization schemes which take advantage of the mechanical structure of the manipulator. Both approaches are illustrated by application to planar robot arms