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

TL;DR

This paper introduces virtual nonholonomic constraints for acrobots, enabling energy injection or dissipation through feedback control, with proven effectiveness and robustness demonstrated via simulation and real-world experiments.

Contribution

It presents a novel feedback control-based virtual constraint that emulates gymnastics motion and regulates energy in an acrobot, validated through simulations and experiments.

Findings

Effective energy regulation demonstrated in simulations.

Robustness to disturbances confirmed experimentally.

Constraint can inject or dissipate energy based on design parameters.

Abstract

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.