From Gymnastics to Virtual Nonholonomic Constraints: Energy Injection, Dissipation, and Regulation for the Acrobot

In this article, we study virtual nonholonomic constraints (VNHCs), 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.