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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- 2026-06-05
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- 6/8/2026, 11:42:59 PM
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- papers/pdf/2026/2606_07449v1.pdf
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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