Optimal Design Of Cooperative Trajectories For Multiple Flight Vehicles

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.