Singular trajectories of driftless and control-affine systems

We establish generic properties for singular trajectories, first for driftless, and then for control-affine systems, extending results of [17], [16]. We show that, generically - for the Whitney topology - nontrivial singular trajectories are of minimal order and of corank one. As a consequence, if the number of vector fields of the system is greater than or equal to 3, then there exists generically no singular minimizing trajectory.