Modeling and Control of a Unicycle Robot on Manifolds
Abstract
This paper studies path-following control for a kinematic unicycle evolving on a smooth manifold embedded in ℝ3. 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
@misc{akhtar2026modeling,
title = {{Modeling and Control of a Unicycle Robot on Manifolds}},
author = {Adeel Akhtar and Mohamed Al Lawati},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23878},
eprint = {2609.23878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23878},
}
RIS
TY - UNPB
TI - Modeling and Control of a Unicycle Robot on Manifolds
AU - Adeel Akhtar
AU - Mohamed Al Lawati
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23878
UR - https://arxiv.org/abs/2609.23878
AB - This paper studies path-following control for a kinematic unicycle evolving on a smooth manifold embedded in 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/.
ER -