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 serial manipulators are cyclic. The inverse kinematic mapping defines a differentiable manifold on which output and self-motion coordinates comprise operational coordinates that represent manipulator redundant degrees-of-freedom. The inverse kinematic mapping and differentiable manifold are defined in analytical form and a computational method for their evaluation is presented. Numerical examples are presented to illustrate the validity of the formulation on subsets of manipulator regular configuration space, or on the entire space.