Modified Jacobian method of transversal passing through the smallest deficiency singularities for robot manipulators

Abstract

This paper proposes a method for transversal passing through singularities of corank 1, both for nonredundant and redundant robotic manipulators. The method modifies the Jacobian matrix of manipulator's forward kinematics to retrieve its full rank at singularities. Natural candidates for the Jacobian matrix modification are derivatives of determinants of full size sub-matrices of the Jacobian matrix. The method is illustrated with examples, including a PUMA manipulator and 2-link and 3-link planar manipulators. Some restrictions on the applicability of the method for nonredundant manipulators are also discussed.