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

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

2000-04-19

arxiv.org/abs/math/0004125v1

Mathematics

Optimization and Control

LaTeX2e, 23 pages, 4 figures, submitted to International journal of control

Scientific paper

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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