Motion Control of Manipulators with Closed-Form Inverse Solutions Near Wrist Singularities

Two algorithms, the degenerate axis and iterative methods, are developed for the motion control of manipulators with closed-form solutions in the neighborhood of singularities. These two methods theoretically guarantee a robot’s position accuracy. The degenerate axis method may not work well when a robot’s orientation and location increments become finite. If a robot is moving with slow speed or the interpolation time is in the order of microsecond, the location and orientation increments are small. In this case, the degenerate axis method is favored for it has less computation than that of the iterative method. Two examples are given to illustrate the concepts presented in this paper. Although it cannot be proved that the iterative scheme gives the required position accuracy and minimizes the orientation error, the results seem to show that this scheme converges to an acceptable solution. It is believed that the iterative method is the first of its kind to solve the singular motion control problem by using a robot’s closed-form inverse kinematics. Simple computation for the iterative scheme makes it possible to be implemented in many industrial robots.