Time-Optimal Trajectory Planning for Multi-Vehicle Coordinated Left-Turn Condition at an Unsignalized Intersection

The left-turn condition is the most complicated one at the unsignalized intersection, which is one of the key factors that affect traffic safety and efficiency. To solve this problem, this study proposes a distributed trajectory optimization framework based on the Gauss pseudospectral method (GPM). First, a circular obstacle based on the road size is constructed to replace the actual path constraint. The movement of obstacle is used for iterative calculations, and the trajectory of the left-turn vehicle is approached to the theoretical path. Then, for the multi-vehicle coordinated condition, the collision free constraints between vehicles is added to the optimization framework several times. In addition, the previous calculation result is used as the initial guess solution for the next calculation until all constraints are set. The simulation results show that the circular obstacle is effective and convenient, and the trajectory of a single vehicle is close to the actual driving state due to the good restraint effect. The iterative method of gradually increasing constraints can effectively avoid calculation failures caused by complex conditions, and the real-time performance of the framework is improved. Finally, the order of addition of constraints is discussed to explain the universality of the proposed framework.