High-Gain Natural Tracking Control in Cartesian Space of Redundant Robots

The natural trackability concept is extended to redundant robots controlled in Cartesian space. The necessary condition for finite-time natural trackability is presented for multi degree-of-freedom robots with unknown internal dynamics. A PID high-gain natural tracking control is synthesized to force a naturally trackable robot system to exhibit a prespecified elementwise exponential tracking. The tracking error is exponentially reduced from some unknown non-zero initial condition to zero in finite-time while the robot is subjected to internal non-linear, unknown, unmeasured, disturbances. The control is synthesized using the Cartesian tracking error, the pseudo-inverse of a product of the output Jacobian matrix, inertia matrix, and the control matrix, and the positive sum of the just realized control. A simulation is shown for a redundant multi degree-of-freedom robot that demonstrates elementwise exponential natural tracking control in Cartesian space.