Trajectory related information in Experiment 1.

With the rapid deployment of autonomous micro-UAVs in dynamic environments, path planning must ensure both safety and real-time performance under stringent onboard computational constraints. This paper proposes a dynamic path planning method based on the reciprocal velocity obstacles algorithm, enabling micro-UAVs to safely and efficiently accomplish flight tasks in complex environments. In three-dimensional space, we introduce the Velocity-Obstacle Spherical Crown (VOSC) model to delineate safe and feasible velocity boundaries, thereby ensuring reliable avoidance of moving obstacles. Within this velocity domain, a minimum-deflection-angle replanning strategy generates smooth and dynamically feasible trajectories. For multi-obstacle scenarios, we design a critical-curve-based avoidance scheme that allows the UAV to flexibly select feasible maneuvers along the curve, improving efficiency and robustness. Simulation results demonstrate that, compared with traditional methods, the proposed approach significantly reduces planning time while enhancing trajectory smoothness. Moreover, the algorithm runs online on micro-UAV hardware, highlighting its potential for warehouse navigation, low-altitude urban transport, and other real-time missions.