The recent development of a new kind of public transportation system relies on a particular double-steering kinematic structure enhancing maneuverability in cluttered environments such as downtown areas. We call bi-steerable car a vehicle showing this kind of kinematics. Endowed with autonomy capacities, the bi-steerable car ought to combine suitably and safely a set of abilities: simultaneous localization and environment modeling, motion planning and motion execution amidst dynamic obstacles. In this paper we address the integration of these four essential autonomy abilities into a single application. Specifically, we aim at reactive execution of planned motion. We address the fusion of controls issued from the control law and the obstacle avoidance module using probabilistic techniques.