From gymnastics to virtual nonholonomic constraints: energy injection, dissipation, and regulation for the acrobot

In this article we study virtual nonholonomic constraints, which are relations between the generalized coordinates and momenta of a mechanical system that can be enforced via feedback control. We design a constraint which emulates gymnastics giant motion in an acrobot, and prove that this constraint can inject or dissipate energy based on the sign of a design parameter. The proposed constraint is tested both in simulation and experimentally on a real-world acrobot, demonstrating highly effective energy regulation properties and robustness to a variety of disturbances.