A controller retrieves from memory a series of discrete end effector positions consisting of location and orientation of the end effector. Joint angle values are computed in real time corresponding to intermediate points along the path in a manner which provides smooth end effector motion, avoids the problems of singularities and efficiently accommodates kinematic redundancy. In particular, end effector reorientation between successive goal points is smoothly accomplished by rotating the end effector about the eigenvector of the two successive end effector orientations.