_Article_  
**Motion Planning for Autonomous Vehicles**  
**Considering Longitudinal and Lateral**  
**Dynamics Coupling**  
**[PERSON]\({}^{\text{\textcircled{\textcircled{\textcircled{\textcircled{\textcircled{\textcircled{\textcircled{\textcircled{\textcircled{\text{\textcircledcled{\text{\text{\text{\text{\text{\text{\text{\text  
real-time performance and better search in the spatiotemporal domain. However, the inherent random mechanism makes it impossible to effectively deal with the constraints of vehicle dynamics. Limited by their theoretical fundamentals, neither of the methods above can consider the nonlinear dynamics and safety constraints of obstacles [16]. This causes the planning module to generate control commands that may exceed the vehicle's executable ability. Accordingly, the actual state trajectory will deviate from the desired one [17]. To solve the problems mentioned above, optimal control based schemes have been investigated widely in recent years. Among them, model predictive control (MPC) has received more attention because it puts the finite horizon optimal motion planning in continuous state space and can handle nonlinear dynamics, as well as environmental disturbances. Essentially, MPC is a model-based approach, and its performance is greatly affected by the accuracy and complexity of the model. [PERSON] et al. designed a nonlinear MPC (NMPC)-based planner for obstacle avoidance by considering the vehicle as a point-mass [18]. This model treats the vehicle as a particle, regardless of vehicle geometry and tire dynamics. This will produce a large predictive error in dynamical conditions and also increase the requirements of the path tracking module [19]. The point-mass model is replaced by a nonlinear kinematic model in [20] and an extended kinematic model over a three dimensional motion surface is presented in [21] for off-road navigation and control. But both point-mass and kinematic models only can describe vehicle behavior at low speed. At high speed, the cornering characteristics of tire are not negligible [22]. A data-driven statistical vehicle model is proposed in [23], which simultaneously describes the control constraints, actuator delay and vehicle dynamics. However, this model contains both continuous and discrete states. [PERSON] et al. proposed a one-level NMPC planner for high-speed obstacle avoidance using a four-wheel nonlinear dynamical model with the Fiala tire constraints [24]. However, such complex models greatly increase the consumption of computational resource. To increase the real-time performance, [PERSON] et al. reduced the high degree model to the single-track model and presented a field-based model predictive path-planning controller for high-speed conditions [25]. This single-track model is simplified with the small angle assumption and ignores the coupling effects between lateral and longitudinal dynamics. In essence, such coupling is not negligible when the steering angle becomes large enough, which easily happens at low speed. The point-mass model and kinematic model are simplified to facilitate the motion planning and they are not applicable to dynamical driving conditions, for example, driving on a curve at speed. Although the complex nonlinear dynamic model is accurate enough, it is too complicated to be used for the design of a motion planner. The simplified single-track model doesn't consider the coupling among longitudinal and lateral dynamics and is only applicable to the condition that the steering angle is small. The main contributions of this paper can be summarized as follows:  
1. Based on the statistical results of naturalistic driving data, a nonlinear vehicle model describing both longitudinal and lateral dynamics in the normal operating range was first established. It was simplified to a single-coupled dynamical model (SDM) with enough accuracy by analyzing the transfer characteristics and dynamical coupling effects at the equilibrium points numerically. This simplified model has a good balance between model accuracy and complexity. 2.