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arXiv · 2606.07449

On orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model

Artem Angelchev-Shiryaev·Pavel E. Aleshin·Anton S. Shiriaev·Pavel A. Shamanaev·Leonid B. Freidovich
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Abstract

This paper addresses orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model within a transverse-linearization framework. We show that the corresponding transverse linearization is unstable and not stabilizable by linear state feedback. Therefore, the standard linearization-based approach to orbital stabilization cannot be applied directly. The main contribution is a set of explicit and verifiable conditions that characterize when a controller design based on transverse linearization remains applicable. These conditions rely on the specific structure of the dynamics in a neighborhood of the motion and on the use of non-standard transverse coordinates for controller design and analysis. Numerical simulations illustrate the proposed design procedure.

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Artem Angelchev-Shiryaev, Pavel E. Aleshin, Anton S. Shiriaev, Pavel A. Shamanaev, Leonid B. Freidovich. 2026-06-05. On orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model. https://arxiv.org/abs/2606.07449

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