Singularity Control for Simple Manipulators

A new method is presented for controlling the trajectories of straight-line Cartesian paths near the kinematic singularities of simple manipulators. Conventional approachs to this problem, which typically employ a pseudo-inverse of the manipulator Jacobian, result in path deviations and have diiculty controlling joint accelerations. The more global approach described here uses a \potential function" in the region of the singularity to reduce the path velocity in such a way that both the joint velocities and accelerations remain bounded without incurring any deviation from the desired path. For cases such as the elbow or shoulder singularities of the PUMA manipulator, the results are very good and the necessary computations are simple enough to be done on-line.