Abstract
We consider minimal time problems governed by control-affine-systems in the plane. We focus on the synthesis problem in presence of a singular locus that involves a saturation point for the singular control. We show that the minimum time synthesis can exhibit a prior-saturation point at the intersection of the singular locus and a switching curve. We also provide a set of non-linear equations to compute the prior-saturation point, and, at this point, we show a tangency property involving the switching curve.