Closed-Form Trajectories of the Unicycle

TL;DR

This paper introduces a novel control methodology for unicycle robots using pseudo-kinetic energy, enabling closed-form solutions for trajectories and providing insights into stabilizing driftless nonlinear systems.

Contribution

It proposes a new control approach based on pseudo-kinetic energy that guarantees stability and allows explicit closed-form trajectory solutions for unicycle robots.

Findings

Closed-form solutions for unicycle trajectories achieved.

Stability guaranteed without requiring asymptotic stability.

Method provides a pathway for solving general unicycle control problems.

Abstract

This paper presents a methodology to stabilize some kind of Nonlinear Control system known as Driftless, utilizing the concept of \textit{Pseudo-Kinetic Energy} introduced in this work. Once this controller is applied to the Unicycle-type robot, stability is guaranteed with the salient property that the structure of the controller allows to solve in closed-form the trajectories of the vehicle. While the proposed controller only ensures stability (not asymptotic stability) the obtained closed-form solutions will show a path to obtain in closed form the solutions for the general control problem of the unicycle. Some conclusions and future directions for research are also depicted.