Combined Analytical- Pseudoinverse Inverse Kinematic Solution for Simple Redundant Manipulators and Singularity Avoidance

Abstract

One of the problems in real-time control of redundant manip ulators is considerably increased computational complexity compared with nonredundant robots. This is due to the rela tively high dimensions of the Jacobian matrix (6 x n, n ≥ 7) and the fact that its pseudoinverse is to be computed. On the other side, analytical solutions for nonredundant robots offer minimal numerical complexity (if such exist). The main idea in this article is to reduce computational complexity by com bining the analytical and the pseudoinverse solution. Namely, some of the joint angles that do not actively participate in the redundancy are evaluated analytically, while the group of joint angles that are actually redundant are solved using the pseu doinverse of the Jacobian matrix. In this way the dimensions of Jacobian are considerably reduced yielding several times less computational complexity. Further reduction of computational time is achieved by applying the gradient projection method (Dubey et al. 1991) to the actually redundant subrobot. In this article the solution is derived for a 7-DOF manipulator, and the possibility of application to other robots is discussed. At the end, simple performance criteria for avoiding wrist singularity that take into account the knowledge of robot geometry are proposed.