On duality of inverse Jacobian and transpose Jacobian in task-space regulation of robots

In this paper, we show that a duality property exists in task-space regulation of robots in the sense that the transformation from task space to joint space can be either defined as transpose Jacobian or inverse Jacobian. The two basic transformations, namely transpose Jacobian and inverse Jacobian, are said to be dual and any task-space setpoint controller can be obtained from the other by replacing the transpose Jacobian by the inverse Jacobian, and vice versa. Our result also provides a unified analysis for the transpose Jacobian setpoint control and inverse Jacobian setpoint control problems. Experiment results are also presented to verify the theory