## 1 Introduction
### Literature Review
[13] established the vehicle kinematics model with the constraints of drivable road area and vehicle geometry, designed the MPC controller, studied the trajectory tracking of autonomous vehicles by using the longitudinal and lateral coupling control method, and completed the effectiveness verification of the control algorithm. [PERSON] et al. [14] proposed a nonlinear MPC controller based on the genetic algorithm to control vehicle speed and steering, considering driving safety and comfort, and had a good track following effect. [PERSON] et al. [15] proposed the model discretisation method through the pseudospectral approach and presented the simplification method based on modularisation and constraint set compression to reduce the calculation amount of optimisation problems and improve the real-time performance of optimisation solutions. [PERSON] et al. [16] studied the trajectory tracking control method of the autonomous vehicle, based on the vehicle dynamics model with 6 degrees of freedom (DOF) and integrating the operational stability constraints of the vehicle. [PERSON] et al. [17] designed a predictive control algorithm based on the vehicle dynamics model and simulated annealing model based on the longitudinal and lateral coupling 2 DOF vehicle dynamics model. Equality constraints and inequality constraints are set according to the actual driving conditions, and the solution speed of MPC controller can be optimised. [PERSON] et al. [18], based on the vehicle 3 DOF monozuil dynamics model, proposed a linear time-varying model predictive path tracking coupling control method and simulated and analysed the real-time performance and robustness of the control algorithm through double line shifting conditions. According to the differences of vehicle models, the above research on trajectory tracking control of autonomous vehicles based on model predictive control can be divided into simplified vehicle kinematics model-based and vehicle dynamics model-based. The former does not consider the rigid body dynamic constraints such as vehicle tires and the suspension but carries out kinematic analysis and modelling of the vehicle in the plane. It mainly realises the real-time description of vehicle motion law under low model accuracy. It is only suitable for researching non-fully constrained tracking control of autonomous vehicles under low-speed conditions and low requirements for vehicle stability. The latter needs to consider the time-varying characteristics of vehicle tires and describe the vehicle's state more accurately combined with yaw and slide. Under the same conditions, the improvement of model accuracy improves the state tracking accuracy to a great extent, but this is at the cost of dissipating the calculation amount, so the real-time performance of the algorithm is insufficient. When the model is too complex, the real-time requirements of the algorithm will be hard to meet. To improve the measurement accuracy of the vehicle state and realise the online application of predictive control algorithm, an online active set-based longitudinal and lateral model predictive tracking control of autonomous driving is proposed in this paper. Based on ensuring the accuracy of the vehicle model, the complexity of model calculation is reduced. On the other hand, the optimisation set is established to reduce the time required for optimisation.