Dynamic Gravity Cancellation and Regulation Control in Robots with Flexible Transmissions: Constant, Nonlinear, and Variable Stiffness

We consider the problem of perfect cancellation of gravity effects in the dynamics of robot manipulators having flexible transmissions at the joints. Based on the feedback equivalence principle, we aim at designing feedback control laws that let the system outputs behave as those of the same robot device when gravity is absent. The cases of constant stiffness (elastic joints), nonlinear flexible, and variable nonlinear flexible transmissions with antagonistic actuation are analyzed. As a particular case, antagonistic actuation with transmissions having constant but different stiffness is also considered. In all these situations, viable solutions are obtained either in closed algebraic form or by a simple numerical technique. The compensated system can then be controlled without taking into account the gravity bias, which is particularly relevant for safe physical human-robot interaction tasks where such compliant manipulators are commonly used. Moreover, dynamic gravity cancellation allows to design new PD-type regulation controllers and to show their global asymptotic stability without the need of any positive lower bound neither on the stiffness nor on the proportional control gain. A Lyapunov-based proof is provided for the case of robots with elastic joints. Simulation results are reported to illustrate the obtained performance in the various robotic systems with flexible transmissions.