Three-dimensional multi-joint reaching under redundancy of DOFs

A simple control method for 3-dimensional multi-joint reaching movements under redundancy of Degrees-of-Freedom is proposed, which neither need to introduce any performance index to solve inverse kinematics uniquely nor need to calculate pseudo-inverse of the Jacobian matrix of task coordinates with respect to joint coordinates. The proposed control signal is composed of linear superposition of three terms: 1) angular-velocity feedback for damping shaping; 2) task-space position feedback with a single stiffness parameter; and 3) compensation for gravity force on the basis of estimates for uncertain parameters of the potential energy. Through a variety of computer simulations by using a whole arm model with five DOFs, the importance of synergistic adjustments of damping factors as well as its relation to selection of the stiffness parameter is pointed out. It is shown that if damping factors are chosen synergistically corresponding to the inertia matrix at the initial time and the stiffness parameter then the endpoint converges asymptotically to the target position and reaches it smoothly without incurring any self-motion.