Patent US 5,159,249

This invention relates to the field of computer controlled robotics. More specifically, it relates to a novel method and algorithm to symbolically decompose the robot jacobian matrix, in such a way that the robot jacobian Moore-Penrose pseudo-inverse is obtained symbolically even when the robot jacobian is ill conditioned or rank deficient, and to a general purpose computer and method to perform the symbolic steps. The resulting symbolic pseudo-inverse, after symbolic reduction techniques, is not only efficient from the point of view of number of floating point operations, but is also accurate (exact) and stable. It removes the restrictions imposed by the computational complexity of the jacobian pseudo-inverse, especially when the robot jacobian is ill conditioned (robot near/at singularities). This method is sufficiently fast to allow real time control of the robot and is sufficiently stable to allow good robot performance near singularities. In addition, the method presented in this invention is of special importance for the future design of prototypes of robot manipulators, as well as for robot trajectory planning.