Study of solving for manipulator joint rates near singular configurations

This paper develops a new technique for manipulator inverse kinematics at kinematic singularities. The method is based on dropping rank of Jacobian matrix of the transformation between the joints rate and end effector Cartesian velocity in the vicinity of singular configurations. The method can find the solution more easily compared with conventional methods. The kinematic singularities can be included rather than avoided in manipulator motion planning and control. Examples are given to demonstrate implementation of the proposed approach.