Barriers and Potentially Safe Sets in Hybrid Systems: Pendulum with Non-Rigid Cable

TL;DR

This paper develops a method to compute safe control boundaries for a hybrid pendulum system with a non-rigid cable, ensuring the cable remains taut despite switching dynamics.

Contribution

It introduces a direct construction of the safe set boundary in hybrid nonlinear systems with switching dynamics, applied to a pendulum with a non-rigid cable.

Findings

Safe set boundary can be explicitly constructed for the system.

The safe set depends on the masses of the pendulum and cart.

Control strategies can keep the cable from going slack.

Abstract

This paper deals with an application of the notion of barrier in mixed constrained nonlinear systems to an example of a pendulum mounted on a cart with non-rigid cable, whose dynamics may switch to free-fall when the tension of the cable vanishes. We present a direct construction of the boundary of the potentially safe set in which there always exists a control such that the cable never goes slack. A discussion on the dependence of this set with respect to the pendulum and cart masses is then sketched.