Regularization of the differential inverse positioning problem of an elbow manipulator

Solution of the differential inverse positioning sub-task is an important problem in robotics, that is burdened with kinematic singularities. This problem can be handled by regularizing the task Jacobian, however this requires the knowledge of the regularization vector. A candidate for the regularization vector for an elbow manipulator is given, and it is proved that this candidate can be used in almost every configuration. The candidate is the linear velocity generator of the last joint, so the calculation of the regularization vector does not require high computational capacity. The smallest singular value of the regularized task Jacobian is further analyzed in different singular configurations.