Numerically Stable Dynamic Bicycle Model for Discrete-time Control

Abstract

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 such driving scenarios. Inspired by the concept of backward Euler method, this paper presents a discrete dynamic bicycle model feasible at any low speed. 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 65% 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.