Singularity consistency and the natural motion of robot manipulators

This paper presents a new formulation of the inverse kinematics and dynamics of robot manipulators. A robot manipulator's motion is expressed as the motion of a point in Riemannian space. We show that the end-effector-motion constraint defines a specific metric over this space, in terms of pure kinematic motion. An inverse kinematic solution is obtained which guarantees the stability of the system in the neighborhood of kinematic singularities. Motion through singularities becomes also possible. Further on, we show that in the presence of forces, the metric has to be changed in an appropriate way. Then, taking advantage of full integrability of the equation of motion, we obtain another nonlinear solution of the inverse kinematics which gives rise to an internal potential energy.