Geodesic
Abnormal extremals in the sub-Riemannian problem for a~general model of a~robot with a~trailer
Sbornik. Mathematics, Tome 214 (2023) no. 10, pp. 1351-1372

Voir la notice de l'article provenant de la source Math-Net.Ru

A symmetric mathematical model of a wheeled robot with a trailer is considered for various types of coupling between the robot and the trailer. It is shown that for fixed coupling parameters and fixed initial position of the robot with trailer there are two symmetric abnormal extremals. In motion along these trajectories the robot and the trailer traverse normal extremal trajectories for the sub-Riemannian problem on the group of motions of the plane; the coupling point always draws an inflectional elastica or a straight line. Bibliography: 33 titles.
Keywords: robot with trailer, kinematic model, Pontryagin maximum principle, abnormal trajectories, sub-Riemannian geometry. 
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     title = {Abnormal extremals in the {sub-Riemannian} problem for a~general model of a~robot with a~trailer},
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A. A. Ardentov; E. M. Artemova. Abnormal extremals in the sub-Riemannian problem for a~general model of a~robot with a~trailer. Sbornik. Mathematics, Tome 214 (2023) no. 10, pp. 1351-1372. http://geodesic.mathdoc.fr/item/SM_2023_214_10_a0/