Combined analytical-gradient-projection inverse kinematic solutions for simple redundant manipulators

One of the problem in real-time control of redundant manipulators is considerably increased computational complexity as compared with nonredundant robots. The paper attempts to reduce the computational complexity by combining the analytical and the gradient projection methods proposed by Dubey et al. (1988). 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 either the pseudoinverse of the Jacobian matrix, or the gradient projection scheme. In this way the dimensions of Jacobian are considerably reduced yielding about 10 times less computational complexity. The solution is derived for a 7-DOF manipulator and the possibility of its application to other robot geometries is discussed.