Redundant robotic chains on Riemannian manifolds

A geometric framework for the study of redundant robotic chains is proposed. Once a suitable metric for the workspace of the end-effector is chosen, the forward kinematic map from joint space to workspace can be described in terms of Riemannian submersions. Consequently, the inverse kinematics admits an interpretation in terms of horizontal lift of the Riemannian submersion. It is shown that for the most common class of robotic manipulators, those composed of one degree of freedom lower-pair joints, the commonly used Moore-Penrose pseudoinversion corresponds exactly to the horizontal lift of vector fields from workspace to joint space.