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The car with N Trailers : characterization of the singular configurations

Published online by Cambridge University Press:  15 August 2002

Frédéric Jean
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Abstract

In this paper we study the problem of the car with N trailers. It was proved in previous works ([9], [12]) that when each trailer is perpendicular with the previous one the degree of nonholonomy isFn+3 (the (n+3)-th term of the Fibonacci's sequence) and that when no two consecutive trailers are perpendicular this degree is n+2. We compute here by induction the degree of non holonomyin every state and obtain a partition of the singular set by this degree of non-holonomy. We give also for each area a set of vector fields in the Lie Algebra of the control system wich makes a basis of the tangent space.

Keywords

Control Lie Algebra / Multibody mobile robot / Nonholonomic systems.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 1 , 1996 , pp. 241 - 266
Copyright
© EDP Sciences, SMAI, 1996

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