<title>Optimal damped least-squares methods for inverse kinematics of robot manipulators</title>

Abstract

Inverse kinematics of robotic manipulators poses a challenging problem, especially near singular configurations where the joint velocities tend to become extremely high, even if the minimum-norm pseudo-inverse solution is used. The singularity robust inverse (SRI), which arises from the damped least-squares technique, damps joint velocities using a damping factor but causes some deviation of the end-effector from its specified trajectory. The trade-off between obtaining an accurate solution and a feasible one is decided by the damping factor. In this work, we present a new optimal method of computing the damping factor which yields minimum end-effector deviation while ensuring feasible joint velocities. This method is computationally efficient with an added advantage in that it can be implemented even if the SVD of the Jacobian is not available. The method is effective for both planar and spatial manipulators, redundant or non-redundant. This is borne out by the simulations presented at the end of this paper.