# Vehicle Lane Change Models--A Historical Review
## 2 Vehicle Lane Change Models
### Physical Models of Lane Change
#### 2.2.2 Dynamic Models  
Dynamic vehicle models mainly focus on the dynamic performance, such as the acceleration, steering, and braking abilities of the vehicle. They are constructed using Newtonian mechanics and dynamic equations to describe the acceleration, braking, and steering capabilities of the vehicle in the process of lane change. Dynamic models can represent the balance and change in forces and moments during lane changes, as well as the vehicle's interaction with the environment during lane changes. Vehicle following and lane changing are two important components of traffic behavior, which have been widely studied by scholars. As early as several decades ago, the car-following model, which evolved from the car-following theory, was successfully applied to the study of traffic \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Paper** & **Input Variables** & **Algorithm** & **Key Issues to Be Resolved** \\ \hline \multirow{3}{*}{[61]} & Driving environment, driver behavior, & & Anticipate driver maneuvers and \\  & event criticality, and driver response & Random forest & identify key behavioral and \\  & event criticality, and driver response & & environmental factors that lead to such \\  & & & evasive maneuvers \\ \hline \multirow{3}{*}{[62]} & State vector, control vector, system & Collaborative lane change & The motion planner can effectively \\  & dynamics, and cost function & motion planning & reduce vibration and has excellent \\ \hline \multirow{3}{*}{[39]} & Longitudinal distance, longitudinal & & real-time performance \\  & velocity, longitudinal acceleration, & & real-time performance \\ \cline{1-1}  & lateral distance, lateral velocity, and lateral acceleration & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Input parameters of different kinematic lane change models and key problems to be solved. dynamics [63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76]. Vehicle lane change behavior has also been extensively studied and modeled [77; 78; 79; 80]. The main research method of vehicle lane change behavior is to introduce specific lane change rules according to different needs and scenarios. [PERSON]'s [79] model expresses the driver's expectation, and it uses an asymmetric model to express that the processes of moving from fast lane to slow lane and from slow lane to fast lane are controlled by different forms. Heuristic lane-changing rules are generally used in the micro-modeling of multi-lane traffic, but the modeling results often cannot meet people's needs. [PERSON] et al. [80] summarized different lane change methods and results, and used a cellular automaton model for two-lane traffic to meet people's needs, creating density inversion when the density was slightly lower than the maximum flow density. Several different lane change rules are used to test the effectiveness of the scheme. Although there are some differences in the results, similar and real-world-applicable results are obtained. On the real road, drivers may show different lane change behaviors due to the different vehicles in front of them. If the acceleration and top speed of the front car are relatively low, the car with the strong acceleration will generally change lanes more. [PERSON] et al. [81] introduced this factor and proposed a symmetric two-lane cellular automata model to study the lane-changing behavior of fast vehicles. The experimental results show that the positive lane-changing behavior of fast vehicles inhibits the speed of slow vehicles and may cause road congestion. [PERSON] and [PERSON] [82] derived a basic diagram of the traffic flow of toll stations to represent the queuing and traffic status, representing multi-lane toll stations on expressways, where the traffic flow can be extended to the nearest toll station under the condition of high density. [PERSON] et al. [84] extracted vehicle track data from urban streets and modeled different lane change behaviors. The decision model, condition model, and maneuver model were mainly used.