Robot global tracking with finite vector reachability time

A robot and its dynamical actuators are mathematically modelled in a general form of a 3D system without any particular information either about system parameters and nonlinearities or about external disturbances. A demanded system tracking quality is global elementwise q-tracking without oscillations and with a requested finite reachability time. It is described by a vector differential equation in terms of the q-error vector. In order for a q-tracking control to exist for such a system and under such uncertainty, and which will guarantee the demanded tracking quality, the robot should obey a qualitative dynamical property called its global natural elementwise q-trackability. The necessary and sufficient condition for global natural elementwise q-trackability is presented. It composes a part of the whole set of the necessary and sufficient conditions for a control to be global natural q-tracking control for the robot, which guarantees the requested tracking quality. The results are based on new issues in the framework of the robotic systems such as a novel physical principle called the Physical Continuity and Uniqueness Principle, the concept of global natural elementwise q-trackability and the concept of the natural q-tracking control.