Non-commensurate Manipulator Jacobian

The Jacobian matrix of a robot manipulator is central to the analysis, kinematics, dynamics, and control of robot manipulators. In many instances, the Jacobian and its inverse or pseudo-inverse are needed and utilized in the control equations of robot manipulators. In robotics, translations and rotations, transforms whose variables of motion, distance for translations, angles for rotations, combine to generate motions in a given workspace. Object motion and speed also combine units of angle and distance or angular and translational velocities. The mathematical complexities of the control process often obscure the interaction of units and lead to results that may be misinterpreted, erroneous, or simply arbitrary. The research results presented in this article indicate that control equations based on the manipulator Jacobian, its generalized inverse, or its pseudo-inverse may be erroneously combining quantities of different physical units thereby reaching arbitrary results.