Invariant feedback control for the kinematic car on the sphere

TL;DR

This paper develops an invariant feedback control law for a kinematic car on a sphere using Lie group theory, enabling geometric error tracking and observer design, extending planar control concepts to spherical surfaces.

Contribution

It introduces a Lie group framework for invariant control of a car on a sphere, generalizing planar control methods to curved surfaces.

Findings

Invariant tracking error is successfully defined on SO(3)

A feedback control law for the spherical car is designed

An invariant asymptotic observer is proposed

Abstract

The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO(3) is derived. Basic geometric considerations allow a direct comparison of the model with the usual planar case. Exploiting the Lie group structure an invariant tracking error is defined and a feedback is designed. Finally, one possible design of an invariant asymptotic observer is sketched.