  Dynamic/kinematic model is of great significance in decision and control of
intelligent vehicles. However, due to the singularity of dynamic models at low
speed, kinematic models have been the only choice under many driving scenarios.
This paper presents a discrete dynamic bicycle model feasible at any low speed
utilizing the concept of backward Euler method. We further give a sufficient
condition, based on which the numerical stability is proved. Simulation
verifies that (1) the proposed model is numerically stable while the
forward-Euler discretized dynamic model diverges; (2) the model reduces
forecast error by up to 49% compared to the kinematic model. As far as we know,
it is the first time that a dynamic bicycle model is qualified for urban
driving scenarios involving stop-and-go tasks.
