The car with n trailers: Characterisation of the singular configurations

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 F_{n + 3} (the (n + 3)-th term of the Fibonaccis 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.