# Efficient and Safe Strategies for Intersection Management: A Review
## 3 Efficiency
### Trajectory Planning  
#### 3.3.1 Algorithms  
After obtaining the permission of the green wave, using methods of trajectory planning for local planning which is shown in Figure 7, the vehicles pass the intersection. For automated road vehicles, the trajectory planner should meet the requirements of different time scales. First, in just a few seconds, it must guarantee a collision-free trajectory for all road participants and a reasonable safety margin and comfort [47]. The fundamental goal of the trajectory planning work is to manage the driverless vehicle without collision to pass through the intersection, to keep the vehicle running continuously, and to reduce the waiting time of passing the intersection [48]. The trajectory planning methods are mainly divided into two categories: Traditional algorithms and methods based on reinforcement learning. Traditional algorithms of trajectory planning can be divided into technologies based on graph search and on sampling. The methods of graph search extend the path planning technique to ensure the vehicle state over time. Among the autonomous vehicles, the most commonly used graph search techniques based on trajectory planning techniques are state lattice, elastic-band (EB), and A-star [49]. The state lattice is a search graph in which the vertices represent states, and the edges represent paths that connect states that satisfy the kinematic constraints of the robot. The vertices are placed in the usual way so that the same path can be used to connect all the vertices. This state grid must accommodate road planning by indicating only the states that may be in the solution. In addition, the state lattice must be extended to a dynamic environment by increasing the time and speed dimensions. State grids can handle multiple dimensions, such as position, velocity, and acceleration, and are suitable for local planning and dynamic environments. However, they have high computational costs because it evaluates every possible solution in the diagram. The path planning method based on the elastic band optimization technique [50] uses a graph with elastic nodes and edges to represent the state space. Elastic nodes are  
Figure 7: The scene of trajectory planning. defined by adding an inner edge and an outer edge to the spatial node to connect adjacent spatial nodes. A predictive control method [51] based on the model is used to generate the optimal trajectory to avoid collision. In many cases, emergency braking cannot be performed. The safety factor of collision avoidance is implemented in each movement stage of the vehicle, and the nonlinear constraints between the brake and the steering angle are established for emergency motion planning of the vehicle. The efficiency of solution is evaluated through a simulation of different scenarios, which points out the direction for the application research of practical autonomous vehicle problems. The issue of optimal collision planning for vehicle collision avoidance based on the time elastic band (TEB) [52] framework has been studied. The collision avoidance trajectory is given by optimizing the TEB of multiple local optimization targets. The resulting trajectory constitutes the best compromise between simple braking and lane changing, avoiding collisions with the smoothest possible path. Since TEB considers vehicle dynamics, road boundaries, static obstacles, and constraints imposed by moving vehicles, this method is suitable for general critical trajectory situations. An obstacle avoidance trajectory planning method [53] for vehicle sin process can be used to plan the trajectory with continuous curvature and approximately zero longitudinal acceleration in the fixed frame system of a vehicle's body. Then, according to the characteristics of each subsystem, the trajectory tracking algorithms of the full-drive steering subsystem and the under-drive longitudinal subsystem of the work-in-process vehicle are constructed respectively by using the non-singular terminal sliding mode control and nested saturation method.