Quadrotor motion planning in complex environments leverage the concept of safe flight corridor (SFC) to facilitate static obstacle avoidance. Typically, SFCs are constructed through convex decomposition of the environment's free space into cuboids, convex polyhedra, or spheres. However, when dealing with a quadrotor swarm, such SFCs can be overly conservative, substantially limiting the available free space for quadrotors to coordinate. This paper presents an Alternating Minimization-based approach that does not require building a conservative free-space approximation. Instead, both static and dynamic collision constraints are treated in a unified manner. Dynamic collisions are handled based on shared position trajectories of the quadrotors. Static obstacle avoidance is coupled with distance queries from the Octomap, providing an implicit non-convex decomposition of free space. As a result, our approach is scalable to arbitrary complex environments. Through extensive comparisons in simulation, we demonstrate a $60\%$ improvement in success rate, an average $1.8\times$ reduction in mission completion time, and an average $23\times$ reduction in per-agent computation time compared to SFC-based approaches. We also experimentally validated our approach using a Crazyflie quadrotor swarm of up to 12 quadrotors in obstacle-rich environments. The code, supplementary materials, and videos are released for reference.

翻译：在复杂环境中的四旋翼运动规划利用安全飞行走廊（SFC）概念以促进静态障碍物规避。通常，SFC通过将环境自由空间凸分解为长方体、凸多面体或球体来构建。然而，在处理四旋翼集群时，此类SFC可能过于保守，严重限制了四旋翼进行协同的可用自由空间。本文提出一种基于交替最小化的方法，无需构建保守的自由空间近似。相反，静态和动态碰撞约束均以统一方式处理。动态碰撞基于四旋翼共享位置轨迹进行管理，而静态障碍物规避则通过Octomap的距离查询耦合实现，从而提供自由空间的隐式非凸分解。因此，我们的方法可扩展至任意复杂环境。通过仿真中的广泛比较，我们证明相较于基于SFC的方法，成功率提升60%，任务完成时间平均减少1.8倍，每智能体计算时间平均减少23倍。我们还使用多达12架Crazyflie四旋翼集群在障碍物密集环境中实验验证了该方法。代码、补充材料及视频已公开发布以供参考。