Is a local linear PD feedback control law effective for trajectory tracking of robot motion?

A theorem is proposed and used to prove that a robot can track a desired trajectory described by time functions with required arbitrary accuracy, if a linear PD (proportional-derivative) feedback loop is provided at each joint of the robot and the velocity feedback gain can be set sufficiently large. It is shown how to apply the theorem to real robots in order to realize efficient, high-performance trajectory tracking. The relationship of the control to a linear PID feedback controller previously proposed for positioning is investigated, and a linear PID feedback controller which is capable of not only positioning but also trajectory tracking is obtained.>