Modified Jacobian method of transversal passing through singularities of nonredundant manipulators

Abstract

This paper proposes a method which is able to pass transversally through singularities of co-rank 1 of nonredundant robotic manipulators. The method modifies Jacobian matrix of manipulator's forward kinematics to retrieve its full rank at singularities. As a natural candidate for the Jacobian matrix, the modification is derivative of the determinant of the Jacobian matrix. The method is illustrated with examples including the PUMA manipulator. Some restrictions on applicability of the method are also provided.