Singularity of nonlinear feedback control scheme for robots

The author investigates the singular problem of a robot-control scheme with u sin theta as the orientation error, where u and theta are, respectively, the unit vector of the rotational axis and the rotational angle from the current orientation of the end effector to the desired one. It is rigorously found that the singularity points of the control scheme are at theta =+or- pi /2 and +or- pi , and, for a step into theta , pi /2>