Year: 2026
Type: preprint
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/.
Source: arXiv (Cornell University)
Authors: Akhtar, Adeel, Lawati, Mohamed Al
Institution: New Jersey Institute of Technology
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Nanjing Institute of Technology
OpenAlex ID: W7214032682