基于几何方法的洲际航空编队飞行路径规划

Geometric approach for intercontinental formation flight path planning

针对洲际航空编队飞行路径规划,首先,基于编队飞行空气动力学的研究结论和球面度量特征,建立了编队飞行路径规划的基本模型;其次,基于编队路径的拓扑特征,将编队路径规划问题抽象为球面点集上基于测地线的加权Steiner最小树规划问题(WGSMT),建立了WGSMT的有限几何简化原则;针对避障编队路径规划,证明衔接点的引入仅改变紧邻的Steiner点的拓扑特征,而不降低规划结果的准确性,以支持OAWGSMT编队路径规划.最后,构造一种基于"构造-修复"思想的编队路径规划方法,通过实际算例验证了算法的有效性.研究形成洲际航空编队路径规划的几何基础,使问题复杂度依赖于航班集规模而非球面离散化网格规模.

For intercontinental formation flight path planning problem, a basic model was developed based on the aerodynamic models and spherical metric characteristics of formation flight. The problem was then abstracted as the weighted geodesic Steiner minimum tree （WGSMT） problem in spherical point set due to its topological characteristics. The principles of simplifying WGSMT to a finite geometry planning problem were proposed. We also proved that the connecting points induced by obstacles only changed the topology of their adjacent Steiner points while did not lose the accuracy of solution. Finally, a two stage formation path planning algorithm based on ＂construct-repair＂ approach was developed, whose validity was verified by an ex- ample. Significance of the study is that the sphere geometric fundamentals of intercontinental formation path planning are built,which therefore makes the complexity of the problem depend on the scale of flight set rather than that of geographic grids, thereby reduces the complexity of the problem dramatically.