The car with N Trailers : characterization of the singular configurations

Frédéric Jean

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 1, page 241-266
  • ISSN: 1292-8119

Abstract

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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 is Fn+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 holonomy in 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.

How to cite

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Jean, Frédéric. "The car with N Trailers : characterization of the singular configurations." ESAIM: Control, Optimisation and Calculus of Variations 1 (2010): 241-266. <http://eudml.org/doc/116550>.

@article{Jean2010,
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 is Fn+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 holonomy in 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. },
author = {Jean, Frédéric},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Control Lie Algebra / Multibody mobile robot / Nonholonomic systems.; Control Lie Algebra; Multibody mobile robot; Nonholonomic systems; car pulling trailers; degree of nonholonomy; vector fields; Lie algebra},
language = {eng},
month = {3},
pages = {241-266},
publisher = {EDP Sciences},
title = {The car with N Trailers : characterization of the singular configurations},
url = {http://eudml.org/doc/116550},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Jean, Frédéric
TI - The car with N Trailers : characterization of the singular configurations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 241
EP - 266
AB - 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 is Fn+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 holonomy in 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.
LA - eng
KW - Control Lie Algebra / Multibody mobile robot / Nonholonomic systems.; Control Lie Algebra; Multibody mobile robot; Nonholonomic systems; car pulling trailers; degree of nonholonomy; vector fields; Lie algebra
UR - http://eudml.org/doc/116550
ER -

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