In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of F. Jean), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses, it turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C[infinite] case, we study some non-generic generalizations in the analytic case.