Inverse kinematic functions for approach and catching operations

The paper proposes an approach to obtain inverse kinematic functions whose domain is not limited to the manipulator´s workspace. As a result, these functions can be used to map points of the Cartesian space that do not belong to the manipulator´s workspace. The positioning problem is formulated as a minimization of the distance between the prescribed Cartesian point and the end-effector. Hence, points outside of the workspace of the manipulator are mapped by the inverse kinematic function into joint coordinates that bring the manipulator as close as possible to the prescribed Cartesian location. The formulation is derived for both planar and spatial motion and an extension to problems where the orientation has to be considered is also given. Examples pertaining to 2-DOF and 3-DOF manipulators are solved and both analytical and numerical results are given. The proposed inverse kinematic functions are of great interest for tracking approach and catching operations where the object to be reached or tracked by the manipulator can be outside of the workspace,