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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.
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 -