This paper introduces a method to maximize the speed of the motions of an autonomous vehicle on-line, while avoiding any predictable collision. This prediction is performed by the on-line computation of the envelope of possible paths, taking into account the instantaneous uncertainties of the localization of the vehicle in its environment map. A speed profile is thus computed so that the vehicle can stop immediately when reaching the first predicted collision risk. The motion envelope prediction is based upon an uncertainty evolution model of the dead reckoning localization and it is computed each time a new localization based on exteroceptive measurement is carried out. An observable result of the method is the self-adaptation of the motion speed to the displacement task difficulty.