Modeling and Control of a Unicycle Robot on Manifolds

Adeel Akhtar; Mohamed Al Lawati

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arXiv · 2609.23878

Modeling and Control of a Unicycle Robot on Manifolds

Adeel Akhtar·Mohamed Al Lawati

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Abstract

This paper studies path-following control for a kinematic unicycle evolving on a smooth manifold embedded in $\mathbb{R}^3$. The objective is to stabilize a one-dimensional path on the manifold without imposing a temporal parameterization, thereby distinguishing the problem from trajectory tracking. Working in a geometric framework, we propose two feedback laws: a static controller for prescribed nonzero translational speed and a dynamic controller based on a dynamic extension of the translational speed. By lifting the path to the unit tangent bundle of the surface, we characterize the corresponding path-following manifold and establish its control invariance. We then show that the proposed controllers render the path-following manifold locally exponentially stable under suitable regularity conditions. A numerical simulation illustrates the proposed controller. Code and animations are publicly available at https://gradslab.github.io/UnicycleOnManifolds/.

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BibTeX RIS

Adeel Akhtar, Mohamed Al Lawati. 2026-09-20. Modeling and Control of a Unicycle Robot on Manifolds. https://arxiv.org/abs/2609.23878

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