Natural control of robots for fine tracking

Global natural elementwise q-trackability is indispensable qualitative dynamic property for the natural tracking control of a robot. A simple criterion for global natural elementwise q-trackability of a robot is presented in a form of the necessary and sufficient condition. The designed controller guarantees global both global desired motion stability and global q-tracking with a pre-specified finite vector reachability time, dependent only on the initial error vector. The controller is very simple for a technical implementation. The natural q-tracking control is completely robust relative to unpredictable and unknown variations of external disturbance vector function and of system internal dynamics