Non-smooth Approach for Contact Dynamics and Impulse-based Control of Frictional Furuta Pendulum

TL;DR

This paper introduces a non-smooth numerical approach for contact dynamics and impulse-based control, successfully stabilizing a frictional Furuta pendulum affected by stiction effects using innovative estimation and control techniques.

Contribution

It proposes a novel non-smooth numerical method combined with impulse-based control for frictional systems, applied to stabilize an under-actuated Furuta pendulum.

Findings

Successfully stabilized the frictional Furuta pendulum.

Validated the approach on a controlled frictional oscillator.

Improved impulse estimation with shooting method.

Abstract

In this thesis, a non-penetrated and physically consistent non-smooth numerical approach has been proposed, by employing the Prox formulation and Moreau's mid-point time-stepping rule, for the contact dynamics with coupled and decoupled constraints. Under this circumstance, the robust impulse-based control has been successfully implemented and validated on the motion system of controlled frictional oscillator. Further improvement has been achieved by utilizing shooting method in the impulse estimating process instead of robust estimation. This non-smooth numerical technique has been applied to the under-actuated friction-coupled mulit-body system, by means of an implementation on the controlled frictional Furuta pendulum. The specifically designed impulse-based controller has successfully solved the problem of stabilization of the inverted frictional Furuta pendulum, which is suffered from the stiction effect of friction.