飞行冲突解脱的几何优化模型
|
摘要
针对空中交通管制中的冲突探测与解脱问题,提出了一种几何最优的冲突探测与解脱方法。首先定义了该问题的冲突解脱点,在该点处预判飞机之间可能存在的飞行冲突。其次,采取同向同角度的方式解决飞行冲突,即在原航迹上两机同时向同一侧改变相同角度,得到新的航迹交叉点,即航迹恢复点,使得两机之间始终保持最小安全距离。通过几何分析,理论推导了两机航迹距离之和与各自改变航向角度之间的关系,该模型能够有效地解决飞行和冲突,并且具体给出冲突解脱和航迹恢复的位置,以及所涉及到的参数求解过程。最后通过仿真分析,结果显示该方法简单高效。
A geometrically optimal conflict detection and resolution method is proposed to make up for the defect of current methods in air traffic control.Firstly,the conflict resolution point of the problem is defined,at which the possible flight conflicts between aircrafts are predicted.Secondly,the same direction same angle is adopted to solve the flight conflicts;that is,the two aircrafts turn the same angle to the same side at the same time on the original track to obtain a new track crossing point,namely a track recovery point.Thus the minimum separation between the two planes is always maintained.Through geometric analysis,the relationship between the sum of the track distances of the two aircrafts and their respective change of heading is theoretically deduced.The model can effectively solve the flight and conflicts,and specifically give the position of the conflict resolution and track recovery,as well as the parameter solving process involved.Finally,the simulation results show that the method is simple and efficient.
A geometrically optimal conflict detection and resolution method is proposed to make up for the defect of current methods in air traffic control.Firstly,the conflict resolution point of the problem is defined,at which the possible flight conflicts between aircrafts are predicted.Secondly,the same direction same angle is adopted to solve the flight conflicts;that is,the two aircrafts turn the same angle to the same side at the same time on the original track to obtain a new track crossing point,namely a track recovery point.Thus the minimum separation between the two planes is always maintained.Through geometric analysis,the relationship between the sum of the track distances of the two aircrafts and their respective change of heading is theoretically deduced.The model can effectively solve the flight and conflicts,and specifically give the position of the conflict resolution and track recovery,as well as the parameter solving process involved.Finally,the simulation results show that the method is simple and efficient.
引文
[1]KUCHAR J K,YANG L C.A review of conflict detection and resolution modeling methods[J].IEEE Trans.on Intelligent Transportation Systems,2000,1(4):179-189.
[2]朱承元,孟旭.飞行冲突解脱与恢复几何模型及管制策略[J].武汉理工大学学报(交通科学与工程版),2013,37(2):307-310.ZHU C Y,MENG X.Automatic obstacle avoidance algorithm for UAV in dynamic uncertain environment[J].Journal of Wuhan University of Technology(Transportation Science&Engineering),2013,37(2):307-310.
[3]张建英,赵志萍,刘暾.基于人工势场法的机器人路径规划[J].哈尔滨工业大学学报,2006,38(8):1306-1309.ZHANG J Y,ZHAO Z P,LIU T.A path planning method for mobile robot based on artificial potential field[J].Journal of Harbin Institute of Technology,2006,38(8):1306-1309.
[4]张建英,刘暾.基于人工势场法的移动机器人最优路径规划[J].航空学报,2007,28(S):183-188.ZHANG J Y,LIU T.Optimized path planning of mobile robot based on artificial potential field[J].Acta Aeronauticaet Astronautica Sinica,2007,28(S):183-188.
[5]刘星,胡明华,董襄宁.遗传算法在飞行冲突解脱中的应用[J].南京航空航天大学学报,2002,34(1):35-39.LIU X,HU M H,DONG X N.Application of genetic algorithms for solving flight conflicts[J].Journal of Nanjing University of Aeronautics and Astronautics,2002,34(1):35-39.
[6]DELAHAYE D,PEYRONNE C,MONGEAU M,et al.Aircraft conflict resolution by genetic algorithm and B-spline approximation[C]∥Proc.of the 2nd ENRI International Workshop on ATM/CNS,2010:71-78.
[7]程丽媛,韩松臣,刘星.采用内点约束的最优冲突解脱方法[J].交通运输工程学报,2005,5(2):80-84.CHENG L Y,HAN S C,LIU X.Optimal conflict resolution method based on inner-point restriction[J].Journal of Traffic and Transportation Engineering,2005,5(2):80-84.
[8]TANG X M,CHEN P,LI B.Optimal air route flight conflict resolution based on receding horizon control[J].Aerospace Science and Technology March 2016,50:77-87.
[9]韩云祥,汤新民,韩松臣,等.固定航路最优飞行冲突解脱模型[J].交通运输工程学报,2012,12(1):115-120.HAN Y X,TANG X M,HAN S C.Conflict resolution model of optimal flight for fixation airway[J].Journal of Traffic and Transportation Engineering,2012,12(1):115-120.
[10]管祥民,吕人力.基于满意博弈论的复杂低空飞行冲突解脱方法[J].航空学报,2017,38(S):721475-721475.GUAN X M,LYU R L.Aircraft conflict resolution method based on satisfying game theory[J].Acta Aeronautica et Astronautica Sinica,2017,38(S):721475-721475.
[11]XU K J,YIN H,ZHANG L,et al.Game theory with probabilistic prediction for conflict resolution in air traffic management[C]∥Proc.of the 10th International Conference on Intelligent Systems and Knowledge Engineering,2015:94-98.
[12]BILLIMORIA K D.A geometric optimization approach to aircraft conflict resolution[C]∥Proc.of the 18th Applied Aerodynamics Conference,2000:AIAA-2000-4265.
[13]BILIMORIA K D,SRIDHAR B,CHATTERJI G B,et al.Facet:future ATM concepts evaluation tool[J].Air Traffic Control Quarterly,2001,9(1):1-20.
[14]HWANG I,KIM J,TOMLIN C.Protocol-based conflict resolution for air traffic control[J].Air Traffic Control Quarterly,2007,15(1):1-34.
[15]VAN DEN B J,GUY S J,LIN M,et al.Reciprocal n-body collision avoidance[M]∥PRADALIER C,SIEGWART R,HIRZINGER G.Robotics Research.Berlin:Springer,2011:3-19.
[16]DURAND N,BARNIER N.Does ATM need centralized coordination?Autonomous conflict resolution analysis in a constrained speed environment[J].Air Traffic Control Quarterly,2015,23(4):325-346.
[17]ALLIGNOL C,BARNIER N,DURAND N,et al.Assessing the robustness of a UAS detect&avoid algorithm[C]∥Proc.of the 12th USA/Europe Air Traffic Management Research and Development Seminar,2017:1-9.
[18]ALLIGNOL C,BARNIER N,DURAND N,et al.Integration of UAS in terminal control area[C]∥Proc.of the 35th IEEEDigital Avionics Systems Conference,2016:886-891.
[19]杨秀霞,周硙硙,张毅.基于速度障碍圆弧法的UAV自主避障规划研究[J].系统工程与电子技术,2017,39(1):168-176.YANG X X,ZHOU W W,ZHANG Y.Automatic obstacle-avoidance planning for UAV based on velocity obstacle arc method[J].Systems Engineering and Electronics,2017,39(1):168-176.
[20]杨秀霞,张毅,周硙硙.一种动态不确定环境下UAV自主避障算法[J].系统工程与电子技术,2017,39(11):2546-2552.YANG X X,ZHANG Y,ZHOU W W.Automatic obstacle avoidance algorithm for UAV in dynamic uncertain environment[J].Systems Engineering and Electronics,2017,39(11):2546-2552.
[21]GESER A,MUNOZ C.A geometric approach to strategic conflict detection and resolution[C]∥Proc.of the IEEE Digital Avionics Systems Conference,2002:6B1-1-6B1-11.
[22]OMER J.A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers[J].Computers&Operations Research,2015,58:75-86.
[23]GOSS J,RAJVANSHI R,SUBBARAO K.Aircraft conflict detection and resolution using mixed geometric and collision cone approaches[C]∥Proc.of the AIAA Guidance,Navigation,and Control Conference and Exhibit,2004:AIAA 2004-4879.
[24]MUELLER T,SCHLEICHER D,BILIMORIA K.Conflict detection and resolution with traffic flow constraints[J].Proc.of the AIAA Guidance,Navigation,and Control Conference and Exhibit,2002:AIAA 2002-4445.
[25]ZHANG Y,ZHANG M,YU J.Real-time flight conflict detection and release based on Multi-Agent system[C]∥Proc.of the IOP Conference Series Earth and Environmental Science2018:032053.
[26]ZHANG M,YU J,ZAHNG Y F,et al.Flight conflict resolution during low-altitude rescue operation based on ensemble conflict models[J].Advances in Mechanical Engineering,2017,94(4):168781401769665.
[27]李雄,徐肖豪,朱承元.基于几何算法的空中交通改航路径规划[J].系统工程,2008,26(8):37-40.LI X,XU X H,ZHU C Y.Air traffic reroute planning based on geometry algorithm[J].Systems Engineering,2008,26(8):37-40.
[28]李雄,徐肖豪,赵嶷飞,等.散点状分布危险天气区域下的航班改航路径规划[J].航空学报,2009,30(12):2342-2347.LI X,XU X H,ZHAO Y F,et al.Flight rerouting path planning in dispersedly distributed severe weather areas[J].Acta Aeronautica et Astronautica Sinica,2009,30(12):2342-2347.
[29]王莉莉,杨惠东.飞行冲突条件下基于几何算法的改航策略研究[J].飞行力学,2012,30(5):466-469.WANG L L,YANG H D.Rerouting strategy research based on geometry algorithm in flight conflict[J].Flight Dynamics,2012,30(5):466-469.
[30]蒋旭瑞,吴明功,温祥西,等.基于合作博弈的多机飞行冲突解脱策略[J].系统工程与电子技术,2018,40(11):2482-2489.JIANG X R,WU M G,WEN X X,et al.Conflict resolution of multi-aircraft based on the cooperative game[J].Systems Engineering and Electronics,2018,40(11):2482-2489.
[2]朱承元,孟旭.飞行冲突解脱与恢复几何模型及管制策略[J].武汉理工大学学报(交通科学与工程版),2013,37(2):307-310.ZHU C Y,MENG X.Automatic obstacle avoidance algorithm for UAV in dynamic uncertain environment[J].Journal of Wuhan University of Technology(Transportation Science&Engineering),2013,37(2):307-310.
[3]张建英,赵志萍,刘暾.基于人工势场法的机器人路径规划[J].哈尔滨工业大学学报,2006,38(8):1306-1309.ZHANG J Y,ZHAO Z P,LIU T.A path planning method for mobile robot based on artificial potential field[J].Journal of Harbin Institute of Technology,2006,38(8):1306-1309.
[4]张建英,刘暾.基于人工势场法的移动机器人最优路径规划[J].航空学报,2007,28(S):183-188.ZHANG J Y,LIU T.Optimized path planning of mobile robot based on artificial potential field[J].Acta Aeronauticaet Astronautica Sinica,2007,28(S):183-188.
[5]刘星,胡明华,董襄宁.遗传算法在飞行冲突解脱中的应用[J].南京航空航天大学学报,2002,34(1):35-39.LIU X,HU M H,DONG X N.Application of genetic algorithms for solving flight conflicts[J].Journal of Nanjing University of Aeronautics and Astronautics,2002,34(1):35-39.
[6]DELAHAYE D,PEYRONNE C,MONGEAU M,et al.Aircraft conflict resolution by genetic algorithm and B-spline approximation[C]∥Proc.of the 2nd ENRI International Workshop on ATM/CNS,2010:71-78.
[7]程丽媛,韩松臣,刘星.采用内点约束的最优冲突解脱方法[J].交通运输工程学报,2005,5(2):80-84.CHENG L Y,HAN S C,LIU X.Optimal conflict resolution method based on inner-point restriction[J].Journal of Traffic and Transportation Engineering,2005,5(2):80-84.
[8]TANG X M,CHEN P,LI B.Optimal air route flight conflict resolution based on receding horizon control[J].Aerospace Science and Technology March 2016,50:77-87.
[9]韩云祥,汤新民,韩松臣,等.固定航路最优飞行冲突解脱模型[J].交通运输工程学报,2012,12(1):115-120.HAN Y X,TANG X M,HAN S C.Conflict resolution model of optimal flight for fixation airway[J].Journal of Traffic and Transportation Engineering,2012,12(1):115-120.
[10]管祥民,吕人力.基于满意博弈论的复杂低空飞行冲突解脱方法[J].航空学报,2017,38(S):721475-721475.GUAN X M,LYU R L.Aircraft conflict resolution method based on satisfying game theory[J].Acta Aeronautica et Astronautica Sinica,2017,38(S):721475-721475.
[11]XU K J,YIN H,ZHANG L,et al.Game theory with probabilistic prediction for conflict resolution in air traffic management[C]∥Proc.of the 10th International Conference on Intelligent Systems and Knowledge Engineering,2015:94-98.
[12]BILLIMORIA K D.A geometric optimization approach to aircraft conflict resolution[C]∥Proc.of the 18th Applied Aerodynamics Conference,2000:AIAA-2000-4265.
[13]BILIMORIA K D,SRIDHAR B,CHATTERJI G B,et al.Facet:future ATM concepts evaluation tool[J].Air Traffic Control Quarterly,2001,9(1):1-20.
[14]HWANG I,KIM J,TOMLIN C.Protocol-based conflict resolution for air traffic control[J].Air Traffic Control Quarterly,2007,15(1):1-34.
[15]VAN DEN B J,GUY S J,LIN M,et al.Reciprocal n-body collision avoidance[M]∥PRADALIER C,SIEGWART R,HIRZINGER G.Robotics Research.Berlin:Springer,2011:3-19.
[16]DURAND N,BARNIER N.Does ATM need centralized coordination?Autonomous conflict resolution analysis in a constrained speed environment[J].Air Traffic Control Quarterly,2015,23(4):325-346.
[17]ALLIGNOL C,BARNIER N,DURAND N,et al.Assessing the robustness of a UAS detect&avoid algorithm[C]∥Proc.of the 12th USA/Europe Air Traffic Management Research and Development Seminar,2017:1-9.
[18]ALLIGNOL C,BARNIER N,DURAND N,et al.Integration of UAS in terminal control area[C]∥Proc.of the 35th IEEEDigital Avionics Systems Conference,2016:886-891.
[19]杨秀霞,周硙硙,张毅.基于速度障碍圆弧法的UAV自主避障规划研究[J].系统工程与电子技术,2017,39(1):168-176.YANG X X,ZHOU W W,ZHANG Y.Automatic obstacle-avoidance planning for UAV based on velocity obstacle arc method[J].Systems Engineering and Electronics,2017,39(1):168-176.
[20]杨秀霞,张毅,周硙硙.一种动态不确定环境下UAV自主避障算法[J].系统工程与电子技术,2017,39(11):2546-2552.YANG X X,ZHANG Y,ZHOU W W.Automatic obstacle avoidance algorithm for UAV in dynamic uncertain environment[J].Systems Engineering and Electronics,2017,39(11):2546-2552.
[21]GESER A,MUNOZ C.A geometric approach to strategic conflict detection and resolution[C]∥Proc.of the IEEE Digital Avionics Systems Conference,2002:6B1-1-6B1-11.
[22]OMER J.A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers[J].Computers&Operations Research,2015,58:75-86.
[23]GOSS J,RAJVANSHI R,SUBBARAO K.Aircraft conflict detection and resolution using mixed geometric and collision cone approaches[C]∥Proc.of the AIAA Guidance,Navigation,and Control Conference and Exhibit,2004:AIAA 2004-4879.
[24]MUELLER T,SCHLEICHER D,BILIMORIA K.Conflict detection and resolution with traffic flow constraints[J].Proc.of the AIAA Guidance,Navigation,and Control Conference and Exhibit,2002:AIAA 2002-4445.
[25]ZHANG Y,ZHANG M,YU J.Real-time flight conflict detection and release based on Multi-Agent system[C]∥Proc.of the IOP Conference Series Earth and Environmental Science2018:032053.
[26]ZHANG M,YU J,ZAHNG Y F,et al.Flight conflict resolution during low-altitude rescue operation based on ensemble conflict models[J].Advances in Mechanical Engineering,2017,94(4):168781401769665.
[27]李雄,徐肖豪,朱承元.基于几何算法的空中交通改航路径规划[J].系统工程,2008,26(8):37-40.LI X,XU X H,ZHU C Y.Air traffic reroute planning based on geometry algorithm[J].Systems Engineering,2008,26(8):37-40.
[28]李雄,徐肖豪,赵嶷飞,等.散点状分布危险天气区域下的航班改航路径规划[J].航空学报,2009,30(12):2342-2347.LI X,XU X H,ZHAO Y F,et al.Flight rerouting path planning in dispersedly distributed severe weather areas[J].Acta Aeronautica et Astronautica Sinica,2009,30(12):2342-2347.
[29]王莉莉,杨惠东.飞行冲突条件下基于几何算法的改航策略研究[J].飞行力学,2012,30(5):466-469.WANG L L,YANG H D.Rerouting strategy research based on geometry algorithm in flight conflict[J].Flight Dynamics,2012,30(5):466-469.
[30]蒋旭瑞,吴明功,温祥西,等.基于合作博弈的多机飞行冲突解脱策略[J].系统工程与电子技术,2018,40(11):2482-2489.JIANG X R,WU M G,WEN X X,et al.Conflict resolution of multi-aircraft based on the cooperative game[J].Systems Engineering and Electronics,2018,40(11):2482-2489.