大规模空中集群的稀疏图使能编队规划
Sparse-Graph-Enabled Formation Planning for Large-Scale Aerial Swarms
AI总结：
针对大规模无人机编队轨迹规划中的维度灾难问题，提出一种保留全局刚性的稀疏图构建方法，在保留30%连接边时实现与完全图相当的误差和恢复性能，并将规划效率提升近一个数量级。
摘要：
随着无人机数量增加，使用完全图对协作约束进行建模的编队轨迹规划因维度灾难而在计算上变得不可行。为解决此问题，本文提出了一种用于编队规划的稀疏图构建方法，以实现更好的效率与性能折中。首先，设计了完全图的稀疏化机制，以确保稀疏图的全局刚性，这是唯一对应几何形状的必要条件。其次，构建了一个良好的稀疏图，以充分保留完全图的主要结构特征。由于基于图的编队约束由 Laplacian 矩阵描述，稀疏图构建问题等价于子矩阵选择，该问题具有组合时间复杂度且需要一个评分指标。通过对比仿真，Max-Trace 矩阵揭示指标展现出优异的性能。该稀疏图被集成到编队规划中。在复杂环境中使用 72 架无人机的仿真结果表明，当保留 30% 的连接边时，本方法相对于完全图具有可比的编队误差和恢复性能。同时，规划效率提高了近一个数量级。进行了基准比较和消融研究以充分验证本方法的优点。
英文摘要：
The formation trajectory planning using complete graphs to model collaborative constraints becomes computationally intractable as the number of drones increases due to the curse of dimensionality. To tackle this issue, this paper presents a sparse graph construction method for formation planning to realize better efficiency-performance trade-off. Firstly, a sparsification mechanism for complete graphs is designed to ensure the global rigidity of sparsified graphs, which is a necessary condition for uniquely corresponding to a geometric shape. Secondly, a good sparse graph is constructed to preserve the main structural feature of complete graphs sufficiently. Since the graph-based formation constraint is described by Laplacian matrix, the sparse graph construction problem is equivalent to submatrix selection, which has combinatorial time complexity and needs a scoring metric. Via comparative simulations, the Max-Trace matrix-revealing metric shows the promising performance. The sparse graph is integrated into the formation planning. Simulation results with 72 drones in complex environments demonstrate that when preserving 30\% connection edges, our method has comparative formation error and recovery performance w.r.t. complete graphs. Meanwhile, the planning efficiency is improved by approximate an order of magnitude. Benchmark comparisons and ablation studies are conducted to fully validate the merits of our method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
