无需建图，用双KD树加速MPC实现高精度避障飞行。

Collision-free flight in cluttered environments is a critical capability for autonomous quadrotors. Traditional methods often rely on detailed 3D map construction, trajectory generation, and tracking. However, this cascade pipeline can introduce accumulated errors and computational delays, limiting flight agility and safety. In this paper, we propose a novel method for enabling collision-free flight in cluttered environments without explicitly constructing 3D maps or generating and tracking collision-free trajectories. Instead, we leverage Model Predictive Control (MPC) to directly produce safe actions from sparse waypoints and point clouds from a depth camera. These sparse waypoints are dynamically adjusted online based on nearby obstacles detected from point clouds. To achieve this, we introduce a dual KD-Tree mechanism: the Obstacle KD-Tree quickly identifies the nearest obstacle for avoidance, while the Edge KD-Tree provides a robust initial guess for the MPC solver, preventing it from getting stuck in local minima during obstacle avoidance. We validate our approach through extensive simulations and real-world experiments. The results show that our approach significantly outperforms the mapping-based methods and is also superior to imitation learning-based methods, demonstrating reliable obstacle avoidance at up to 12 m/s in simulations and 6 m/s in real-world tests. Our method provides a simple and robust alternative to existing methods. The code is publicly available at https://github.com/SJTU-ViSYS-team/avoid-mpc.