# Optimal Vehicle Lane Change Trajectory Planning in Multi-Vehicle Traffic Environments
## 4 Discussion  
University and corporate research methods are mostly end-to-end for intelligent driving, whereby vehicles are directly controlled by training driving behavior data. However, this research method requires a large amount of experimental data, and as a result, it poses a challenge in terms of computational requirements. When a vehicle changes lanes, lateral stability is a key point. Because vehicle dynamics are considered in the trajectory planning module, it is unnecessary to design a vehicle lateral stability controller, which simplifies the research. In a multi-vehicle traffic environment, it is inevitable that other vehicles will change lanes. In this case, it is necessary to propose a safe collision avoidance algorithm so that even if two vehicles change lanes at the same time, there will be no collision. However, in this paper, it was assumed that the speed of the vehicle was constant. Real-time changes of vehicle speed need to be tested in an experimental environment. This will be done in future research.  
Many trajectories result from the application of vehicle lateral stability constraints and safe collision avoidance algorithms. These processes seek to determine the optimal lane change trajectory. Most previous research has tended to establish the optimization objective function and constraints; subsequently, the optimization variables are calculated by the algorithm. The four indexes and simulation test data can be used for quantitative analyses of lane change performance. In other words, the four optimization indexes corresponding to each lane-changing trajectory can be obtained with specific values. Multi-objective optimization belongs to the multi-attribute decision making problem, and the best way to solve this kind of problem is by using the TOPSIS algorithm.  
Figure 12: (**a**) Lane change trajectory cluster and Lag trajectory of Subject and Separate vehicle; (**b**) Results of the safe collision avoidance algorithm; (**c**) Results based on Topsis algorithm scores; (**d**) Optimal lane change trajectory for the subject vehicle.  
For traditional auxiliary lane changing system, decisions made by engineers regarding lane change times are based on driver habits; generally, the minimum lane change time is 3 s, which lacks flexibility. In contrast, our simulation results show that a lane-changing time of 2.8 s would be acceptable, improving lane-changing efficiency by 6.67% in overtaking scenarios. In addition, in lane-exchanging and cut-in scenarios, the general auxiliary lane-changing system is unable to plan the trajectory. The traditional RRT algorithm (Rapidly Exploring Random Tree) and APF algorithm (Artificial Potential Field) can be used to perform simulations in overtaking scenarios, but they cannot handle the latter two complex scenarios; for example, the APF algorithm is generally unable to build an attractive area in a random environment, while the RRT algorithm will report an error. The absence of collisions, as well as efficiency and comfort, are the advantages of the optimized reference trajectory. The above proposed planning strategies provide ideas and methods for intelligent driving research. However, our planning strategy is a non-game system, which does not take the psychological factors of the driver into account. The typical scenarios cannot represent all the scenarios, more complex lane changing scenarios need to be researched in the future.