On the theory of nonlinear systems tracking with guaranteed performance index bounds: application to robot control

A tracking concept called the kth-order tracking concept is explained and defined as kth-order tracking obeying prespecified performance index limits. It contains all other existing tracking concepts. The output negative feedback principle is used to prove an algebraic necessary and sufficient tracking condition which is a criterion for kth-order tracking. This criterion is utilized to establish a criterion for such tracking without output error oscillations, overshoot, and undershoot. Moreover, Liapunov-like tracking conditions are established using the output-feedback principle. They yield tracking control algorithms guaranteeing the bounds of the prespecified performance index in various forms. The general results are applied to robot and control synthesis for various types of performance index and limiting function. The advantages of this approach include the complete avoidance of nominal joint-space trajectory, nominal motion, nominal control, inverse dynamics, and inversion of Jacobian matrix, bounds on the prespecified performance index, and tracking over a given finite time interval