A PD-type regulator with exact gravity cancellation for robots with flexible joints

We present a new control approach to regulation tasks for robots with elastic joints in the presence of gravity. The control law combines a term that cancels the gravity effects on the robot link dynamics with a PD-type error feedback on the motor variables. The first control component follows from the feedback equivalence principle when imposing to the link variables the same dynamic behavior as if gravity were absent. The PD component can then be designed in a rather straightforward way. Global asymptotic stability is shown via Lyapunov analysis, without the need of strictly positive lower bounds neither on the proportional control gain nor on the structural joint stiffness. The control approach is also extended to the case of robot joints with nonlinear stiffness