多飞行器协同轨迹优化设计
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摘要
随着未来战场环境日趋复杂和防御体系的不断完善，未来战争将是系统与系统、体系与体系之间的对抗。在高度对抗的体系化作战环境中，单架飞行器已经难以甚至不能发挥预期的作战效果，只有通过飞行器之间的协同作战，才能获得最大的作战效果。因此，有必要开展多飞行器协同轨迹优化的研究工作。
本学位论文结合航空某所课题合作项目--“多飞行器攻防对抗仿真演示系统”与江苏省普通高校研究生科研创新计划资助项目--“多弹协同对抗轨迹全局优化与控制”，针对多飞行器协同轨迹多约束、强耦合的复杂多目标优化与决策问题，对多飞行器协同轨迹优化进行了较为系统的研究，提出了一套在随机环境中多飞行器协同轨迹优化的数值算法，并进行了大量地飞行数值仿真。论文的主要研究内容如下：
首先，对多飞行器协同轨迹优化进行了数学描述和对多飞行器航迹规划进行了数学建模。多飞行器协同轨迹优化的数学描述主要包括：多飞行器协同轨迹优化问题的一般数学描述、攻防双方拦截型飞行器协同轨迹优化与突防型飞行器协同轨迹优化的问题数学描述。多飞行器航迹规划的数学建模主要包括：静态/动态飞行任务、飞行环境（数字地图、随机风场模型、禁飞区、静态/动态威胁区）、飞行器运动方程等数学建模。
然后，提出了多飞行器协同任务规划系统优化设计的数值算法。其主要包括多飞行器协同任务分配算法与飞行器航迹最优规划。多飞行器协同任务分配算法主要给出了一种基于目标剩余时间的多飞行器协同任务分配算法，就攻击型飞行器与目标飞行器的飞行速度与数量的不同组合，分别给出了算例。基于目标剩余时间的多飞行器协同任务分配算法可以实时在线地计算各攻击型飞行器相对各目标飞行器的剩余飞行时间，得出当时的目标分配矩阵，从而实时地调整分配目标，得到最优的分配方案系列。飞行器航迹最优规划主要研究了在随机环境（如风场）中威胁区回避轨迹的飞行器航迹最优规划。即在随机多变敌雷达监测、敌防空武器拦截系统（动态可攻击与拦截区）、复杂地形、复杂恶劣的天气现象（随机风场）等各种威胁区条件下，可以为飞行器寻找准确地命中目标、同时危险度最小、可靠度最大、路径或时间最小的最优飞行轨迹。飞行器最优航迹规划算法采用的是改进的动态规划法与共轭梯度法的组合算法。该多飞行器协同任务规划系统优化设计的数值算法，是基于敌-我双方的动态可攻击与拦截区而实时调整进行的，其中，敌-我双方的动态可攻击区与动态拦截区是多飞行器协同（轨迹优化）作战的关键技术之一。
其次，研究了多飞行器协同作战动态攻防区。依据多飞行器协同作战中攻防双方需要及时动态获取可攻击空域的信息等特点，以空空导弹为例进行了动态可攻击区的研究；包括了空空导弹的射前可攻击区（包括前向攻击的可攻击区和全向攻击的可攻击区）、射后动态可攻击区。其中，全向攻击是对前向攻击的空空导弹不能攻击其后半球目标而进行的一项补充研究；为了获取多飞行器攻防对抗中空空导弹发射后动态可攻击空域的信息，提出了空空导弹射后动态可攻击区的概念并进行了数值仿真。同时，空空导弹的射前可攻击区是静态威胁区的一个组成部分，而空空导弹的射后动态可攻击区对于已方来说，是为了实时获取敌方目标是否在其攻击空域内，对于敌方来说，此射后动态可攻击区是动态的威胁区域。因此，在考虑敌方威胁区时，需要考虑敌方射前可攻击区所构成的静态威胁区以及敌方射后动态可攻击区所构成的动态威胁区。
最后，基于以上的研究，对多飞行器协同轨迹优化进行了飞行数值仿真。根据对抗飞行器的飞行环境与飞行目的不同组合分为四种情况：目标作有规则（非对抗）机动的多飞行器协同轨迹优化、目标作无规则随机（非对抗）机动的多飞行器协同轨迹优化、考虑射前可攻击区的多飞行器协同突防威胁区的轨迹优化、考虑射后动态可攻击区与静态威胁区的攻防双方对抗飞行的多飞行器协同轨迹优化。
值得指出的是：在研究多飞行器攻防协同对抗时，多飞行器攻防对抗的双方均应同时采用全局一体化优化。即当进攻方采用（轨迹与各子系统控制）全局一体化最优策略时，对抗方也应采用考虑全局的轨迹与控制的全局一体化优化；另外，在多飞行器协同作战中，攻防对抗双方均需考虑各种多维未知的随机干扰因素。
Because the future battlefield environments are complicating and the defense systems areupgraded and improved, the future war will be a confrontation in among systems. In the drasticcombat environment of fighting systems, a single flight vehicle has been difficult to achieve the flightmissions. Only through collaborative combat of the flight vehicles, can obtain the best fight effects.Therefore, it is necessary to do research on optimization design of cooperative trajectories andoptimal control for multiple flight vehicles.
The paper is based on several research projects, those research projects are ‘multiple flightvehicles attack-defense simulation demonstration system’ which supported by a aeronautics researchinstitute cooperation,‘the global trajectory optimization and control of multiple missilesattack-defense system’ which supported by Jiangsu province ordinary college graduate student ofscientific research innovation plan funded projects. This doctoral dissertation deeply and systemicallystudies optimization design of cooperative trajectories for multiple flight vehicles which aim at acomplicated multi-objective optimization and decision-making of cooperative trajectories for multipleflight vehicles. An algorithm is presented for multiple flight vehicles in random environment tooptimization design cooperative trajectories; and a large number of flight numerical simulationsare carried out. The main research contents of the dissertation are as follows.
Firstly, the problem is described as mathematical presetation regarding on the optimizationdesign of cooperative trajectories for multiple flight vehicles, and the mathematical models oftrajectory planning are presented for multiple flight vehicles in unknown environment. Themathematical description regarding on optimization design of cooperative trajectories for multipleflight vehicles mainly includes: a general mathematical description about optimization design ofcooperative trajectories for multiple flight vehicles, the mathematical description about theoptimization design of cooperative trajectories for interceptor-type flightvehicles and penetration about flight vehicles in attack and defense statuses. The detailedmathematical models of trajectory planning for multiple flight vehicles mainly include: themathematical description of dynamic/static flight missions, the flight environment (digitalmaps, stochastic wind model,the no-flight zone, and static/dynamic threat zone), the flightvehicle differential equations of motion, spacecraft orbit differential equations.
Secondly, the numerical algorithm of collaborative mission planning system design for multipleflight vehicles have been proposed. This algorithm mainly includes cooperative targets distribution method for multiple flight vehicles and the trajectory optimal planning for flight vehicle. Based on theremaining time of the target, the cooperative targets distribution algorithm is presented. The exampleswere presented for some cases regarding on multiple targets distribution algorithm based on thedifferent flight velocity combinations between attacking flight vehicle and target vehicle.Theremaining time of the targets is computed from each attacking flight vehicle to the correspondingtarget; and matrix of the remaining time for the targets was obtained, this matrix is created from thecombination of multiple targets and multiple attacking vehicles. The remaining time of each targetflight vehicle for each attacking flight vehicle has been real-time online calculated. The cooperativetarget distribution is adjusted in real-time, the optimal program series of cooperativetarget distribution is obtained online. The avoiding trajectory about threatened zones in stochasticflight environment (stochastic wind) is researched for flight vehicles to plan the optimal trajectory.The avoiding trajectory is optimized considering all kinds of possible conditions of threat zones, suchas the random and complex monitoring from enemy radars, the enemy air defense weaponinterception systems (dynamical attack and interception zones), complex and various terrain,stochastic flight environment (stochastic wind) and so on. The performance indexes of optimaltrajectory for flight vehicle are minimize risk, the maximize reliability to accurately hit target.A combination algorithm of the trajectory planning for flight vehicle is consist of improved dynamicprogramming method and conjugate gradient algorithm. The numerical algorithm ofcollaborative mission planning system design for multiple flight vehicles can be adjusted in real timeonline based on the dynamic attacked and intercepted zones of both attack and defense sides. Thatis, the dynamic attacked and intercepted zone of both attack and defense sides is one of the keytechnologies in cooperative fighting for multiple flight vehicles.
Furthermore, the key techniques of dynamic attack zones were researched for multiple flightvehicles of both offensive and defensive in cooperative combat. According to the characteristics ofcooperative fighting for multiple flight vehicles and dynamic attack zones of air-to-air missiles(AAMs), the dynamical attack zones at the time of being launched of AAMs (the forward-aspectattack zone and the all-aspect attack zone) and the dynamical attack zone after being launched ofAAM are researched. The all-aspect attacking is a new attacking method of the AAM to intercepttargets in the rear hemisphere. In order to obtain the information of how AAM can attack duringcooperative combat for multiple flight vehicles, a new concept, dynamic attack zone of AAMs afterbeing launched, was proposed, and was researched. At the same time, the attack zone at the time ofbeing launched of AAM is a component of of the static threat zone. For the offensive side, in order to real-time obtain information of the enemy target whether inside dynamic attack zoneof AAM, dynamic attack zone after being launched of AAM is calculated. For the enemy vehicles,however, the dynamic attack zones after being launched of the offensive side are dynamic threatzones of the intercept vehicles. Therefore, when considering the enemy threat zones, it is necessaryto calculate both the dynamic attack zones at the time of being launched and the dynamicattack zones after being launched of AAMs.
At the last, based on the above algorithms, four typical different kinds of cases were numericalsimulated and analyzed, those cases include different combination of the flight environment, targetsand waypoints maneuver type, static and dynamic threat areas, as well as the flight purposes for bothattacking and intercepting flight vehicles. The detailed information of the cases are as follows.
a) The cooperative trajectories optimization for flight vehicle when multiple targets fly bythe regularly maneuver law (Non-confrontational).
b) The cooperative trajectories optimization for multiple flight vehicles when multiple targets fly bythe non-regularly maneuver law, the the target flight vehicles are random maneuvering.(Non-confrontational).
c) Considering the attack zones before being launched of flight vehicles, the cooperative trajectorieswere optimized for multiple flight vehicles to penetrate threat zones with the minimum threat,passing all waypoints, and other environments, such as weather, terrain and so on.
d) Considering the attack zones after being launched and static threat zones of flight vehicles, thecooperative trajectories were optimized for multiple penetrating flight vehicles to penetratestatic and dynamic threat zones, as well as passing the waypoints; at the same time, thecooperative trajectories were also optimized for multiple intercepting flight vehicles to interceptthe penetrating flight vehicles, avoiding static and dynamic threat zones.
It is noticeable that, both of attack and defense flight vehicles are using the global integration ofoptimization algorithm at the same time. That means, when the offensive vehicles (trajectoriesand subsystem control) employ global integration of optimal algorithm strategy,intercept vehicles also employ the global trajectory and control of the global integration optimizationalgorithm. Both sides of attack and defense flight vehicles are considering a varietyof multi-dimensional random interference of all unknown possible factors.
本学位论文结合航空某所课题合作项目--“多飞行器攻防对抗仿真演示系统”与江苏省普通高校研究生科研创新计划资助项目--“多弹协同对抗轨迹全局优化与控制”，针对多飞行器协同轨迹多约束、强耦合的复杂多目标优化与决策问题，对多飞行器协同轨迹优化进行了较为系统的研究，提出了一套在随机环境中多飞行器协同轨迹优化的数值算法，并进行了大量地飞行数值仿真。论文的主要研究内容如下：
首先，对多飞行器协同轨迹优化进行了数学描述和对多飞行器航迹规划进行了数学建模。多飞行器协同轨迹优化的数学描述主要包括：多飞行器协同轨迹优化问题的一般数学描述、攻防双方拦截型飞行器协同轨迹优化与突防型飞行器协同轨迹优化的问题数学描述。多飞行器航迹规划的数学建模主要包括：静态/动态飞行任务、飞行环境（数字地图、随机风场模型、禁飞区、静态/动态威胁区）、飞行器运动方程等数学建模。
然后，提出了多飞行器协同任务规划系统优化设计的数值算法。其主要包括多飞行器协同任务分配算法与飞行器航迹最优规划。多飞行器协同任务分配算法主要给出了一种基于目标剩余时间的多飞行器协同任务分配算法，就攻击型飞行器与目标飞行器的飞行速度与数量的不同组合，分别给出了算例。基于目标剩余时间的多飞行器协同任务分配算法可以实时在线地计算各攻击型飞行器相对各目标飞行器的剩余飞行时间，得出当时的目标分配矩阵，从而实时地调整分配目标，得到最优的分配方案系列。飞行器航迹最优规划主要研究了在随机环境（如风场）中威胁区回避轨迹的飞行器航迹最优规划。即在随机多变敌雷达监测、敌防空武器拦截系统（动态可攻击与拦截区）、复杂地形、复杂恶劣的天气现象（随机风场）等各种威胁区条件下，可以为飞行器寻找准确地命中目标、同时危险度最小、可靠度最大、路径或时间最小的最优飞行轨迹。飞行器最优航迹规划算法采用的是改进的动态规划法与共轭梯度法的组合算法。该多飞行器协同任务规划系统优化设计的数值算法，是基于敌-我双方的动态可攻击与拦截区而实时调整进行的，其中，敌-我双方的动态可攻击区与动态拦截区是多飞行器协同（轨迹优化）作战的关键技术之一。
其次，研究了多飞行器协同作战动态攻防区。依据多飞行器协同作战中攻防双方需要及时动态获取可攻击空域的信息等特点，以空空导弹为例进行了动态可攻击区的研究；包括了空空导弹的射前可攻击区（包括前向攻击的可攻击区和全向攻击的可攻击区）、射后动态可攻击区。其中，全向攻击是对前向攻击的空空导弹不能攻击其后半球目标而进行的一项补充研究；为了获取多飞行器攻防对抗中空空导弹发射后动态可攻击空域的信息，提出了空空导弹射后动态可攻击区的概念并进行了数值仿真。同时，空空导弹的射前可攻击区是静态威胁区的一个组成部分，而空空导弹的射后动态可攻击区对于已方来说，是为了实时获取敌方目标是否在其攻击空域内，对于敌方来说，此射后动态可攻击区是动态的威胁区域。因此，在考虑敌方威胁区时，需要考虑敌方射前可攻击区所构成的静态威胁区以及敌方射后动态可攻击区所构成的动态威胁区。
最后，基于以上的研究，对多飞行器协同轨迹优化进行了飞行数值仿真。根据对抗飞行器的飞行环境与飞行目的不同组合分为四种情况：目标作有规则（非对抗）机动的多飞行器协同轨迹优化、目标作无规则随机（非对抗）机动的多飞行器协同轨迹优化、考虑射前可攻击区的多飞行器协同突防威胁区的轨迹优化、考虑射后动态可攻击区与静态威胁区的攻防双方对抗飞行的多飞行器协同轨迹优化。
值得指出的是：在研究多飞行器攻防协同对抗时，多飞行器攻防对抗的双方均应同时采用全局一体化优化。即当进攻方采用（轨迹与各子系统控制）全局一体化最优策略时，对抗方也应采用考虑全局的轨迹与控制的全局一体化优化；另外，在多飞行器协同作战中，攻防对抗双方均需考虑各种多维未知的随机干扰因素。
Because the future battlefield environments are complicating and the defense systems areupgraded and improved, the future war will be a confrontation in among systems. In the drasticcombat environment of fighting systems, a single flight vehicle has been difficult to achieve the flightmissions. Only through collaborative combat of the flight vehicles, can obtain the best fight effects.Therefore, it is necessary to do research on optimization design of cooperative trajectories andoptimal control for multiple flight vehicles.
The paper is based on several research projects, those research projects are ‘multiple flightvehicles attack-defense simulation demonstration system’ which supported by a aeronautics researchinstitute cooperation,‘the global trajectory optimization and control of multiple missilesattack-defense system’ which supported by Jiangsu province ordinary college graduate student ofscientific research innovation plan funded projects. This doctoral dissertation deeply and systemicallystudies optimization design of cooperative trajectories for multiple flight vehicles which aim at acomplicated multi-objective optimization and decision-making of cooperative trajectories for multipleflight vehicles. An algorithm is presented for multiple flight vehicles in random environment tooptimization design cooperative trajectories; and a large number of flight numerical simulationsare carried out. The main research contents of the dissertation are as follows.
Firstly, the problem is described as mathematical presetation regarding on the optimizationdesign of cooperative trajectories for multiple flight vehicles, and the mathematical models oftrajectory planning are presented for multiple flight vehicles in unknown environment. Themathematical description regarding on optimization design of cooperative trajectories for multipleflight vehicles mainly includes: a general mathematical description about optimization design ofcooperative trajectories for multiple flight vehicles, the mathematical description about theoptimization design of cooperative trajectories for interceptor-type flightvehicles and penetration about flight vehicles in attack and defense statuses. The detailedmathematical models of trajectory planning for multiple flight vehicles mainly include: themathematical description of dynamic/static flight missions, the flight environment (digitalmaps, stochastic wind model,the no-flight zone, and static/dynamic threat zone), the flightvehicle differential equations of motion, spacecraft orbit differential equations.
Secondly, the numerical algorithm of collaborative mission planning system design for multipleflight vehicles have been proposed. This algorithm mainly includes cooperative targets distribution method for multiple flight vehicles and the trajectory optimal planning for flight vehicle. Based on theremaining time of the target, the cooperative targets distribution algorithm is presented. The exampleswere presented for some cases regarding on multiple targets distribution algorithm based on thedifferent flight velocity combinations between attacking flight vehicle and target vehicle.Theremaining time of the targets is computed from each attacking flight vehicle to the correspondingtarget; and matrix of the remaining time for the targets was obtained, this matrix is created from thecombination of multiple targets and multiple attacking vehicles. The remaining time of each targetflight vehicle for each attacking flight vehicle has been real-time online calculated. The cooperativetarget distribution is adjusted in real-time, the optimal program series of cooperativetarget distribution is obtained online. The avoiding trajectory about threatened zones in stochasticflight environment (stochastic wind) is researched for flight vehicles to plan the optimal trajectory.The avoiding trajectory is optimized considering all kinds of possible conditions of threat zones, suchas the random and complex monitoring from enemy radars, the enemy air defense weaponinterception systems (dynamical attack and interception zones), complex and various terrain,stochastic flight environment (stochastic wind) and so on. The performance indexes of optimaltrajectory for flight vehicle are minimize risk, the maximize reliability to accurately hit target.A combination algorithm of the trajectory planning for flight vehicle is consist of improved dynamicprogramming method and conjugate gradient algorithm. The numerical algorithm ofcollaborative mission planning system design for multiple flight vehicles can be adjusted in real timeonline based on the dynamic attacked and intercepted zones of both attack and defense sides. Thatis, the dynamic attacked and intercepted zone of both attack and defense sides is one of the keytechnologies in cooperative fighting for multiple flight vehicles.
Furthermore, the key techniques of dynamic attack zones were researched for multiple flightvehicles of both offensive and defensive in cooperative combat. According to the characteristics ofcooperative fighting for multiple flight vehicles and dynamic attack zones of air-to-air missiles(AAMs), the dynamical attack zones at the time of being launched of AAMs (the forward-aspectattack zone and the all-aspect attack zone) and the dynamical attack zone after being launched ofAAM are researched. The all-aspect attacking is a new attacking method of the AAM to intercepttargets in the rear hemisphere. In order to obtain the information of how AAM can attack duringcooperative combat for multiple flight vehicles, a new concept, dynamic attack zone of AAMs afterbeing launched, was proposed, and was researched. At the same time, the attack zone at the time ofbeing launched of AAM is a component of of the static threat zone. For the offensive side, in order to real-time obtain information of the enemy target whether inside dynamic attack zoneof AAM, dynamic attack zone after being launched of AAM is calculated. For the enemy vehicles,however, the dynamic attack zones after being launched of the offensive side are dynamic threatzones of the intercept vehicles. Therefore, when considering the enemy threat zones, it is necessaryto calculate both the dynamic attack zones at the time of being launched and the dynamicattack zones after being launched of AAMs.
At the last, based on the above algorithms, four typical different kinds of cases were numericalsimulated and analyzed, those cases include different combination of the flight environment, targetsand waypoints maneuver type, static and dynamic threat areas, as well as the flight purposes for bothattacking and intercepting flight vehicles. The detailed information of the cases are as follows.
a) The cooperative trajectories optimization for flight vehicle when multiple targets fly bythe regularly maneuver law (Non-confrontational).
b) The cooperative trajectories optimization for multiple flight vehicles when multiple targets fly bythe non-regularly maneuver law, the the target flight vehicles are random maneuvering.(Non-confrontational).
c) Considering the attack zones before being launched of flight vehicles, the cooperative trajectorieswere optimized for multiple flight vehicles to penetrate threat zones with the minimum threat,passing all waypoints, and other environments, such as weather, terrain and so on.
d) Considering the attack zones after being launched and static threat zones of flight vehicles, thecooperative trajectories were optimized for multiple penetrating flight vehicles to penetratestatic and dynamic threat zones, as well as passing the waypoints; at the same time, thecooperative trajectories were also optimized for multiple intercepting flight vehicles to interceptthe penetrating flight vehicles, avoiding static and dynamic threat zones.
It is noticeable that, both of attack and defense flight vehicles are using the global integration ofoptimization algorithm at the same time. That means, when the offensive vehicles (trajectoriesand subsystem control) employ global integration of optimal algorithm strategy,intercept vehicles also employ the global trajectory and control of the global integration optimizationalgorithm. Both sides of attack and defense flight vehicles are considering a varietyof multi-dimensional random interference of all unknown possible factors.
引文
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