# Vehicle Lane Change Models--A Historical Review
## 2 Vehicle Lane Change Models
### Physical Models of Lane Change
#### 2.2.1 Kinematic Models  
A kinematic model mainly involves the position information, velocity, and acceleration information. This model adds certain motion constraints, such as constant acceleration or velocity, to describe the lane change time and lane change distance of the lane change behavior. Lane changing is one of the important functions to improve traffic safety, and it is also one of the avoidance behaviors of the driver under the critical condition of safety. Evasive behavior is mainly divided into three categories: the first type is avoidance by braking, which mainly increases the longitudinal deceleration of the vehicle. The second type is steering evasion, which mainly increases the lateral acceleration of the vehicle. The third type is co-avoidance by braking and steering, and the combination of the two may enable better avoidance [55; 56]. Models of avoidance behavior that combine braking and steering are complex and have only been used by a few researchers. Most researchers are more focused on using a categorical approach to predict the choice of evasive behavior [57; 58]. [PERSON] [59] proposed an evasive behavior model that includes braking and steering, to measure the effectiveness of collision-mitigation braking systems (CMBSs). Based on ideas from neuroscience, [PERSON] [60] proposed a method to model steering and pedal behavior as a series of individual control adjustments. [PERSON] et al. [58] used facial video and a kinematic response to reduce the occurrence of events, and used a random-forest-based classifier to verify the relationship between the driver's pre-accident behavior and the driver's perception of the event and the criticality of the event as measured by collision time. Since the unexpected lane change of motor vehicles affects the normal running of vehicles behind, if the lane change behavior of vehicles can be predicted in advance, the adverse impact of the lane change will be very low. [PERSON] et al. [61] proposed a collaborative lane change motion planning algorithm based on the influence of lane change on traffic flow in partially connected and automated environments. Collaborative lane change is realized through mutual communication between vehicles and mutual communication between vehicles and infrastructure. The algorithm reduces the vibration and shockwave caused by lane change through cooperative lane change, and it further improves the traffic maneuverability. Model predictive control follows a numerical algorithm based on dynamic programming, which mainly involves a state vector, control vector, system dynamics, and cost function. A dynamic programming method is adopted to solve the problem of cooperative lane change, the predicted visual boundary is discretized into N steps, and the maximum deceleration and acceleration of the vehicle are adjusted through the correlation matrix in the system dynamics. If the time lead is less than the safe time lead or the speed exceeds the maximum speed, the time headway and speed can be corrected to ensure that the given constraint conditions are met. The experimental results show that this optimization method improves the lane change technology compared to the traditional method. [PERSON] et al. [62] consider that a model with assumed constraints is relatively poor in terms of flexibility, and thus extreme driving behaviors occurring at critical moments may not be effectively avoided. Therefore, they proposed a prospective risk-detection method based on SSM, and they used the data-driven method to build the avoidance behavior model. [PERSON] et al. [62] adopted a model-free non-strategy reinforcement learning algorithm from DDPG [39], which is characterized by its ability to capture complex nonlinear relationships.