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Nilpotentization of the kinematics of the n-trailer system at singular points and motion planning through the singular locus

William Pasillas-Lepine·Witold Respondek
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Abstract

We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equations), which we illustrate by steering the two-trailer system in a neighborhood of singular configurations. We show also that the n-trailer system is a universal local model for all Goursat structures and that all Goursat structures are locally nilpotentizable.

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William Pasillas-Lepine, Witold Respondek. 2000-04-19. Nilpotentization of the kinematics of the n-trailer system at singular points and motion planning through the singular locus. https://arxiv.org/abs/math/0004125

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