The car with N trailers: characterisation of the singular configurations

Abstract In this paper we study the problem of the car with n trailers It was proved in previous works that when each trailer is perpendicular with the previous one the degree of nonholonomy is F n the n th term of the Fibonaccis sequence and that when no two consecutive trailers are perpendicular this degree is n 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 nonholonomy We give also for each area a set of vector elds in the Lie Algebra of the control system wich makes a basis of the tangent spac