Geometric approach for intercontinental formation flight path planning
-
摘要: 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.
-
关键词:
- 航空运输 /
- 编队飞行 /
- 路径规划 /
- Steiner最小树 /
- 几何方法
Abstract: 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 example. 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.-
Key words:
- air transportation /
- formation flight /
- path planning /
- Steiner minimal tree(SMT) /
- geometric approach
-
[1] Airport Council International. Global traffic forecast 2006—2025 executive summary, Edition 2007[R].Montreal: Airport Council International, 2007. [2] Rojo J J. Future trends in local air quality impacts of aviation[D].Massachusetts: Massachusetts Institute of Technology, 2007. [3] Blake W, Multhopp D.Design, performance and modeling considerations for close formation flight, AIAA-1998-4343[R].Reston: AIAA, 1998. [4] Dijkers H P A, Van Nunen R, Bos D A, et al.Integrated design of a long-haul commercial aircraft optimized for formation flying, AIAA-2011-6969[R].Reston: AIAA, 2011. [5] Nehrbass J G, Frommer J B, Garison L A, et al.Point to point commercial aircraft service design study including formation flight and morphing[C]//AIAA 4th Aviation Technology, Integration and Operations(ATIO)Forum.Reston: AIAA, 2004: 20-22. [6] Ning S A. Aircraft drag reduction through extended formation flight[D].Stanford: Stanford University, 2011. [7] Ning S A, Flanzer T C, Kroo I M, et al.Aerodynamic performance of extended formation flight[J].Journal of Aircraft, 2011, 48(3): 855-865. [8] Ning S A, Kroo I M.Compressibility effects of extended formation flight, AIAA-2011-3812[R].Reston: AIAA, 2011. [9] Flanzer T C, Bieniawski S R, Blake W B, et al.Operational analysis for the formation flight for aerodynamic benefit program, AIAA-2014-1460[R].Reston: AIAA, 2014. [10] Xue M, Hornby G.An analysis of the potential savings from using formation flight in the NAS, AIAA-2012-4524[R].Reston: AIAA, 2012. [11] Ribichini G, Frazzoli E.Efficient coordination of multiple-aircraft systems[C]//Proceedings of IEEE Conference on Decision and Control.Piscataway, NJ: IEEE Press, 2003, 1: 1035-1040. [12] Bower G C, Flanzer T C, Kroo I M.Formation geometries and route optimization for commercial formation flight, AIAA-2009-3615[R].Reston: AIAA, 2009. [13] Kent T, Richards A.A geometric approach to optimal routing for commercial formation flight, AIAA-2012-4769[R].Reston: AIAA, 2012. [14] Kent T E, Richards A G.On optimal routing for commercial formation flight, AIAA-2013-4889[R].Reston: AIAA, 2013. [15] Hino T.Real time path planning method of aircraft formations[C]//28th International Congress of the Aeronautical Scicences.Brisbane: ICAS, 2012: 1-5. [16] Xu J S, Ning S A, Bower G C, Kroo I M, et al.Aircraft route optimization for formation flight[J].Journal of Aircraft, 2014, 51(2): 490-501. [17] Chiles P. ETOPS redefined[J].AeroSafety World, 2007, 2(3): 88-92. [18] Courant R, Robbins H.What is mathematics [M].New York: Oxford University Press, 1951. [19] Melzak Z A. On the problem of Steiner[J].Canadian Mathematical Bulletin, 1961, 4(2): 143-148. [20] Dolan J, Weiss R, Smith J M G.Minimal length tree networks on the unit sphere[J].Annals of Operations Research, 1991, 33(7): 501-535. [21] Cockayne E J. On fermat's problems on the surface of a sphere[J].Mathematics Magazine, 1972, 45(4): 216-219. [22] Weng J F. Steiner trees on curved surfaces[J].Graphs and Combinatorics, 2001, 17(2): 353-363.
点击查看大图
计量
- 文章访问数: 964
- HTML全文浏览量: 23
- PDF下载量: 648
- 被引次数: 0