On the Control of Self-Balancing Unicycles

TL;DR

This paper models and analyzes the control problem of a self-balancing unicycle using hybrid automata, providing a framework for verification, validation, and simulation of controllers and user interactions.

Contribution

It introduces an abstract hybrid automata model for a self-balancing unicycle and discusses its verification and simulation, aiding controller design and testing.

Findings

Developed a hybrid automata model for the unicycle

Proposed a verification approach using SpaceEx

Created a simulation framework for controller testing

Abstract

This paper discusses the problem of designing a self-balancing unicycle where pedals are used for both power generation and speed control. After developing the principal physical aspects (in the longitudinal dimension), we describe an abstract model in the form of a collection of hybrid automata, together with design requirements to be met by an ideal controller. We discuss simplifications and assumptions that make this model amenable to verification and validation tools such as SpaceEx. To enable experimentation with different prototypical controllers and user behaviours in concrete scenarios, we also develop a simple simulation framework using digital time.