A computationally effective singularity avoidance method for redundant manipulators with non-spherical wrists

For redundant manipulators with non-spherical wrists, we propose a general and computation-effective method of singularity avoidance. Firstly, the dimension of the Jacobian of the redundant manipulator is reduced by the elementary transformation method to obtain the singular factors. Secondly, we use the damped reciprocal method to solve the inverse kinematics solutions of the redundant manipulator. Thirdly, the singularities of the redundant manipulator are divided into non-escapable and escapable singularities, and the singular conditions are determined with the singular factors. Then taking the singularity avoidance as the secondary task of the control system, we propose a singular factor optimization method to avoid both types of singularities of the redundant manipulator. The complexity analysis shows that no need to calculate the pseudo-inverses or partial derivatives of the Jacobian, the proposed method has lower computational complexity. Finally, simulations have been made on the non-escapable and escapable singularities to verify the proposed methods.