A Cyclic Differentiable Manifold Representation of Redundant Manipulator Kinematics

An inverse kinematic mapping for redundant serial manipulators is presented at the configuration level, for which periodic manipulator operational trajectories map into periodic input trajectories; i.e., for which all serial manipulators are cyclic. The inverse mapping defines a differentiable manifold on which output and self-motion coordinates comprise operational coordinates that represent manipulator redundant degrees of freedom. The inverse mapping and differentiable manifold are defined in analytical form and a computational method for their evaluation is presented. Numerical examples are presented to illustrate validity of the formulation.