INVERSE DYNAMICS OF REDUNDANT MANIPULATORS USING A MINIMUM NUMBER OF CONTROL FORCES

The number of the control actuators used by the inverse kinematics and dynamics algorithms that have been developed in the literature for ge nerating redundant robot joint trajectories is equal to the number of the degrees of freedom of the manipulator. In this article, an inverse dynamics algorithm that performs the tasks using only a minimum numbe r of actuators is proposed. The number of actuators is equal to the di mension of the task space, and the control forces are solved simultane ously with the corresponding system motion. It is shown that because a ll degrees of freedom are not actuated, the control forces may lose th e ability to make an instantaneous effect on the end-effector accelera tion at certain configurations, yielding the dynamical equation set of the system to be singular. The dynamical equations are modified in th e neighborhood of the singular configurations by utilizing higher-orde r derivative information, so that the singularities in the numerical p rocedure are avoided. Asymptotically stable inverse dynamics closed-lo op control in the presence of perturbations is also discussed. The alg orithm is further generalized to dosed chain manipulators. Three-link and two-link redundant planar manipulators are analyzed to illustrate the validity of the approach. (C) 1995 John Wiley & Sons, Inc.