Kinematics of complex joint angles in robotics

A method for using complex numbers in the kinematic solution of robotic manipulators is presented. The inverse kinematics algorithm of a manipulator produces complex joint angles if it is given an end effector location outside its workspace. Although complex joint angles cannot be implemented physically, they can be converted to real numbers through a suitable mapping, and the robot approximates the configuration required to produce the desired location within the limits of its workspace. It is shown that for certain manipulators, the real-part mapping produces a minimization of the end effector location error. Examples of the technique using 2R and 3R manipulators are presented