INVERSE KINEMATIC FUNCTIONS FOR APPROACH AND CATCHING OPERATIONS

The paper proposes an approach to obtain inverse kinematic functions w hose domain is not limited to the manipulator's workspace. As a result , these functions can be used to map points of the Cartesian space tha t do not belong to the manipulator's workspace. The positioning proble m is formulated as a minimization of the distance between the prescrib ed Cartesian point and the end-effector. Hence, points outside of the workspace of the manipulator are mapped by the inverse kinematic funct ion into joint coordinates that bring the manipulator as close as poss ible 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 pertainin g to 2-DOF and 3-DOF manipulators are solved and both analytical and n umerical results are given. The proposed inverse kinematic functions a re of great interest for tracking, approach and catching operations wh ere the object to be reached or tracked by the manipulator can be outs ide of the workspace.