  In unstructured environments, obstacles are diverse and lack lane markings,
making trajectory planning for intelligent vehicles a challenging task.
Traditional trajectory planning methods typically involve multiple stages,
including path planning, speed planning, and trajectory optimization. These
methods require the manual design of numerous parameters for each stage,
resulting in significant workload and computational burden. While end-to-end
trajectory planning methods are simple and efficient, they often fail to ensure
that the trajectory meets vehicle dynamics and obstacle avoidance constraints
in unstructured scenarios. Therefore, this paper proposes a novel trajectory
planning method based on Graph Neural Networks (GNN) and numerical
optimization. The proposed method consists of two stages: (1) initial
trajectory prediction using the GNN, (2) trajectory optimization using
numerical optimization. First, the graph neural network processes the
environment information and predicts a rough trajectory, replacing traditional
path and speed planning. This predicted trajectory serves as the initial
solution for the numerical optimization stage, which optimizes the trajectory
to ensure compliance with vehicle dynamics and obstacle avoidance constraints.
We conducted simulation experiments to validate the feasibility of the proposed
algorithm and compared it with other mainstream planning algorithms. The
results demonstrate that the proposed method simplifies the trajectory planning
process and significantly improves planning efficiency.
