Urban drone delivery, a rapidly evolving sector, holds the potential to enhance accessibility, address last-mile delivery issues, and alleviate ground traffic congestion in cities. Effective Unmanned Aircraft System Traffic Management (UTM) is essential to scale drone delivery. A critical aspect of UTM involves planning a city-wide network with spatially-separated air corridors (air routes). Most existing works have focused on routing problems or air traffic management. Compared to these problems, the air corridor planning problem requires much higher spatial and temporal resolutions and presents computational challenges due to the scale, complexity, and density of urban airspace, along with the coupling issues of multi-path planning. Therefore, we conducted this research to understand the complexity and computational resources required to optimally solve the air corridor planning problem. In this paper, we use a minimum-cost Multi-Commodity Network Flow (MCNF) model, a mathematical model, to model the problem and demonstrate the complexity of air corridor planning through the complexity of MCNF. We then apply Gurobi’s and GLPK’s integer programming (IP) solvers to find optimal solutions. Additionally, we present two existing multi-path graph search algorithms, the Sequential Route Network Planning (SRP) algorithm and the Distributed Route Network Planning (DRP) algorithm, to address this corridor planning problem. Numerical experiments conducted at various scales and settings using IP solvers and graph search algorithms indicate that finding an optimal solution requires significant computational resources and yields only a slight improvement in optimality compared to graph search algorithms. Thus, air corridor planning is complex both theoretically and numerically, and graph search algorithms can provide a feasible solution with good enough optimality for corridor planning in real-world scenarios. Moreover, the multi-path graph search algorithms can easily incorporate side constraints that are known to be impossible to solve with polynomial algorithms, making it more practical for real-world applications. Finally, we demonstrate the application of SRP and DRP in real-world 3D urban scenarios.

中文翻译：

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城市无人机配送的空中走廊规划：通过多商品网络流和图形搜索进行复杂性分析和比较


城市无人机送货是一个快速发展的行业，具有提高可达性、解决最后一英里交付问题和缓解城市地面交通拥堵的潜力。有效的无人机系统交通管理 （UTM） 对于扩大无人机交付规模至关重要。UTM 的一个关键方面涉及规划具有空间分离的空中走廊（航空路线）的城市范围网络。大多数现有工作都集中在路线问题或空中交通管理上。与这些问题相比，空中走廊规划问题需要更高的空间和时间分辨率，并且由于城市空域的规模、复杂性和密度以及多路径规划的耦合问题，带来了计算挑战。因此，我们进行了这项研究，以了解最佳解决空中走廊规划问题所需的复杂性和计算资源。在本文中，我们使用最低成本的多商品网络流 （MCNF） 模型（一种数学模型）对问题进行建模，并通过 MCNF 的复杂性来展示空中走廊规划的复杂性。然后，我们应用 Gurobi 和 GLPK 的整数规划 （IP） 求解器来找到最优解。此外，我们提出了两种现有的多路径图搜索算法，即顺序路由网络规划 （SRP） 算法和分布式路由网络规划 （DRP） 算法，以解决这个走廊规划问题。使用 IP 求解器和图形搜索算法在各种尺度和设置下进行的数值实验表明，找到最佳解决方案需要大量的计算资源，并且与图形搜索算法相比，最优性仅略有提高。 因此，空中走廊规划在理论和数值上都很复杂，而图形搜索算法可以为实际场景中的走廊规划提供具有足够最优性的可行解决方案。此外，多路径图搜索算法可以轻松整合已知无法用多项式算法解决的侧约束，使其在实际应用中更加实用。最后，我们演示了 SRP 和 DRP 在真实 3D 城市场景中的应用。