# The car with N Trailers : characterization of the singular configurations

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

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

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topJean, 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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