Complex Robotic Inverse Kinematic Solutions

A new method exploiting complex numbers in the inverse kinematic solution of serial robotic manipulators is presented. If a prescribed end effector location is outside of the manipulator workspace, complex joint values result. While they cannot be implemented physically, they may be mapped to real numbers. The result approximates the prescribed location. For many industrial manipulators, mapped solutions may be explained using spherical and planar dyads. An important criterion characterizes error minimization properties, and is illustrated for a 3R regional robot.