Methods of aircraft trajectory optimisation in air combat

AIAA AVIATION 2022 Forum, 2022

Today, survival depends on seconds in air combats. The delay in communication of unmanned aerial vehicles with pilots in the ground station is the most important shortcoming in terms of survivability. One solution to this shortcoming is to develop autonomous operation methods for all possible types of missions that onboard computers will process the information collected by the aircraft's sensors and to take countermeasures against the threats without human input. With this regard, unmanned combat aerial vehicles (UCAVs) will take a more active role in air combat and contribute to air superiority in the future. In this study, various combat scenarios are generated and trajectory optimization solutions are obtained to perform autonomous evasive maneuvers for UCAVs against air-to-air missiles without human input. To accomplish this objective, an engagement geometry that includes details of a UCAV and a missile is introduced. This geometry is constructed by employing factors such as line-of-sight (LOS), velocity vectors, angle of attack, flight path angle, and heading angle, which expresses the relative positions of the missile and the UCAV in 3-dimensional space. The UCAV and missile are represented as point-mass models using the given geometry. Along with point-mass models, the commonly used Proportional Navigation (PN) method for missiles guidance is implemented. An energy formulation is incorporated into the model to calculate the instantaneous energy consumption of the missile. An optimization algorithm is developed so that the UCAV can automatically command the angle of attack and the bank angle to maximize the instantaneous energy consumption of the missile at every time step using the generated model. Optimal trajectories for different engagement scenarios are automatically generated by the optimization algorithm for variable initial conditions such as the missile's heading angle, altitude, and distance from the UCAV. Finally, the UCAV performed successful evasive maneuvers to evade the missile in all of its medium/long-range engagements and one of the short-range engagements which demonstrates that adaptive maneuvers suitable for real combat situations are produced for different initial condition sets.

This article consisders the problem of cooperative motion of two aircraft, Protected Entity and Electronic Attack/ Jammer asset, negotiating a terrain seeded with threat emitters toward the predefined stationary goal. The developed control algorithm utilizes a hybrid approach to navigation and subsequent optimal path generation, supplementing the reactive component with deliberative elements as well as considering kinematic and dynamic constraints of the moving assets. That way common pitfalls such as generating impossible paths, losing the goal, and getting trapped in the local minima are avoided, whereas the necessary ability to react quickly to changes in the environment is ensured. The described approach is based on providing discrete, in predefined intervals (time steps) updates of navigation parameters that include asset's state vector, next possible waypoint cost matrix, and goal vector. Hence, the navigation component is discrete, computed once per time step, while the trajectory generation component is continuous, governed by the continuous equations of motion. Generation of the pair of next waypoints involves constructing waypoint cost matrices for each asset, defining the acceptable pairs and assigning their weights using heuristic function. Selection of waypoint pair minimizes that weight. Asset alignment geometry for successful jamming together with terrain and inter-asset collision avoidance are involved in waypoint cost determination. The developed functionality for rollback and subsequent branching is essential for optimal path generation. Software implementation of the presented control algorithm is discussed. Case studies and system performance analysis is presented.

Dynamic game theory has received considerable attention as a promising technique for formulating control actions for agents in an extended complex enterprise that involves an adversary. At each decision making step, each side seeks the best scheme with the purpose of maximizing its own objective function. In this paper, a game theoretic approach based on predator-prey particle swarm optimization (PP-PSO) is presented, and the dynamic task assignment problem for multiple unmanned combat aerial vehicles (UCAVs) in military operation is decomposed and modeled as a two-player game at each decision stage. The optimal assignment scheme of each stage is regarded as a mixed Nash equilibrium, which can be solved by using the PP-PSO. The effectiveness of our proposed methodology is verified by a typical example of an air military operation that involves two opposing forces: the attacking force Red and the defense force Blue. Citation: Haibin Duan, Pei Li, Yaxiang Yu. A predator-prey particle swarm optimization approach to multiple UCAV air combat modeled by dynamic game theory. IEEE/CAA Journal of Automatica Sinica, 2015, 2(1): 11-18

Sensors (Basel, Switzerland), 2019

In recent years, the use of modern technology in military operations has become standard practice. Unmanned systems play an important role in operations such as reconnaissance and surveillance. This article examines a model for planning aerial reconnaissance using a fleet of mutually cooperating unmanned aerial vehicles to increase the effectiveness of the task. The model deploys a number of waypoints such that, when every waypoint is visited by any vehicle in the fleet, the area of interest is fully explored. The deployment of waypoints must meet the conditions arising from the technical parameters of the sensory systems used and tactical requirements of the task at hand. This paper proposes an improvement of the model by optimizing the number and position of waypoints deployed in the area of interest, the effect of which is to improve the trajectories of individual unmanned systems, and thus increase the efficiency of the operation. To achieve this optimization, a modified simulat...

2007

The optimisation of air combat manoeuvre using standard evolutionary programming (EP) algorithm is discussed. The objective is to increase the level of realism in the simulation. This is achieved via employing the nonlinear six degree-of-freedom equations of motion to represent the vehicle. The evader is modelled as a six degree of freedom generic jet fighter aircraft. The aileron, elevator, rudder and throttle setting of the aircraft are set as control variables. The pursuer is a medium range generic air-to-air missile and modelled as a point-mass. The air combat is played in three dimensions. The pursuer seeks to intercept the evader and the evader seeks to avoid interception. The search for optimal evasion solution is conducted utilising evolutionary programming (EP). The optimisation algorithm developed aims to maximise the objective function. The objective function is a self-play simulation between the players. The value of the game is demonstrated as the outcome of the game. The solution that produces the maximum value of fitness is considered to be the best. The optimal solution found is found to be highly dependent on the initial condition. A slight change of the initial condition will result a completely different set of optimal solutions. The computing time is further improved through parallel computing. This is achieved via dividing the solutions into smaller groups and sending each group to different processors for evaluation. As the numbers of processors increase, the time taken to search for optimal solution was found to decrease.

A new computational technique based on Pseudospectral Discretisation (PSD) and adaptive bisection-constraint methods is proposed to solve multi-objective aircraft trajectory optimisation problems formulated as nonlinear optimal control problems. This technique is applicable to a variety of next-generation avionics and Air Traffic Management (ATM) Decision Support Systems (DSS) for strategic and tactical replanning operations. These include the future Flight Management Systems (FMS) and the 4-Dimensional Trajectory (4DT) planning and intent negotiation/validation tools envisaged by SESAR and NextGen for a global implementation. In particular, after describing the implemented PSD method, the adaptive bisection-constraint method is presented to allow an efficient solution of problems in which two or multiple performance indices are to be minimized simultaneously. Initial simulation case studies were performed adopting suitable aircraft dynamics models and addressing a classical vertical trajectory optimisation problem with two objectives simultaneously. Subsequently, a more advanced 4DT simulation case study is presented with a focus on representative ATM optimisation objectives in the Terminal Manoeuvring Area (TMA). The simulation results are analysed in-depth and corroborated by flight performance analysis, supporting the validity of the proposed computational techniques.

EURASIP Journal on Wireless Communications and Networking, 2017

We solve a communication problem between a UAV and a set of receivers, in the presence of a jamming UAV, using differential game theory tools. We propose a new approach in which this kind of games can be approximated as pursuit-evasion games. The problem is posed in terms of optimizing capacity, and it is solved in two ways: firstly, a surrogate function approach is used to approximate it as a pursuit-evasion game; secondly, the game is solved without that approximation. In both cases, Isaacs equations are used to find the solution. Finally, both approaches are compared in terms of relative distance and complexity.

IEEE Transactions on Aerospace and Electronic Systems, 2004

A Command and Control (C 2) problem for Military Air Operations is addressed. Specifically, we consider C 2 problems for air vehicles against ground based targets and defensive systems. The problem is viewed as a stochastic game. In this paper, we restrict our attention to the C 2 level where the problem may consist of a few UCAVs or aircraft (or possibly teams of vehicles); less than say, a half-dozen enemy SAMs; a few enemy assets (viewed as targets from our standpoint); and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are mapped out and possible SAM sites that are unavoidably part of the situation are known. One may then employ a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged (if any), and by what series of air vehicle operations. Since this is a game model, the optimal opponent strategy is also determined. We provide analysis, numerical implementation, and simulation for full state feedback and measurement feedback control within this C 2 context.

IEEE Transactions on Aerospace and Electronic Systems, 2001

Civilians are not just passively static but might purposefully take actions to help one side in a battle. Sometimes civilians might directly join one side if they are excessively agitated by the other side. In this paper, a three-player attrition-type discrete time dynamic game model is formulated, in which there are two opposing forces and one civilian player that might be neutral, biased, or even joining one side publicly. Emotions of civilians are dynamically updated via anger mechanism. An example scenario and extensive simulations illustrate possible applications of this model, and comparative discussions further clarify the benefits.

Dynamic Games and Applications, 2018

A novel pursuit-evasion differential game involving three agents is considered. An Attacker missile is pursuing a Target aircraft. The Target aircraft is aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while at the same time the Attacker tries to minimize said distance. A long-range Beyond Visual Range engagement which is in line with current CONcepts of OPeration is envisaged, and it is therefore assumed that the players have simple motion kinematics á la Isaacs. Also, the speed of the Attacker is equal to the speed of the Defender and the latter is interested in point capture. It is also assumed that at all time the Attacker is aware of the Defender's position, i.e., it is a perfect information game. The analytic/closedform solution of the target defense pursuit-evasion differential game delineates the state space region where the Attacker can reach the Target without being intercepted by the Defender, thus disposing of the Game of Kind. The target defense Game of Degree is played in the remaining state space. The analytic solution of the Game of Degree yields the agents' optimal state feedback strategies, that is, the instantaneous heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker at the instant of Electronic supplementary material The online version of this article (

Naval Research Logistics (NRL), 2018

This article provides a modeling framework for quantifying cost and optimizing motion plans in combat situations with rapid weapon fire, multiple agents, and attacker uncertainty characterized by uncertain parameters. Recent developments in numerical optimal control enable the efficient computation of numerical solutions for optimization problems with multiple agents, nonlinear dynamics, and a broad class of objectives. This facilitates the application of more realistic, equipment-based combat models, which track both more realistic models, which track both agent motion and dynamic equipment capabilities. We present such a framework, along with a described algorithm for finding numerical solutions, and a numerical example.

2013

In this paper a numerical study is provided to solve the aircraft conflict avoidance problem through velocity regulation maneuvers. Starting from optimal controlbased model and approaches in which aircraft accelerations are the controls, and by applying the direct shooting technique, we propose to study two different largescale nonlinear optimization problems. In order to compare different possibilities of implementation, two environments (AMPL and MATLAB) and deterministic local optimization solvers are used. Numerical results are discussed. They show that the considered problem is really difficult to solve to global optimality, as different local minima are found using different methods.

It is well known that civilians often play an active role in wars. That is, they are not just passively static but might purposefully take actions to help one side in a battle to minimize their losses or achieve some political purpose. Unfortunately, existing game theoretic models usually do not consider this situation, even though collateral damage has been considered in a paper on a two-player game model. In this paper, a three-player attrition-type discrete time dynamic game model is formulated, in which there are two opposing forces and one civilian player that might be either neutral or slightly biased. We model the objective functions, control strategies of different players, and identify the associated constraints on the control and state variables. Existing attrition-like state space models can be regarded as a special case of the model proposed in this paper. An example scenario and extensive simulations illustrate possible applications of this model, and comparative discussions further clarify the benefits.

2002

System optimization is a process of translating the dynamics of a system and its desired objectives into the mathematical language, which give rise to what is called a control problem and then to find the solution of this problem. Such a solution is called optimal control and the path it follows to achieve the desired objectives is called optimal trajectory. Trajectory optimization is an optimal transfer problem. For any specified end condition and performance index, the problem of determining the optimal trajectory in powered flight of an aircraft in atmospheric conditions, subject to certain physical constraints, is very complex problem. In general it cannot be solved without using numerical computation based on a specified model of the atmosphere and aircraft aerodynamic and engine characteristics. In the past an intensive research has been carried out in the area of system optimization and optimal trajectories. In the work presented in this paper, emphasis is made on generalizat...

2007

Non-neutral civilians often play an active role in wars. That is, they are not just passively static but might dynamically take non-neutral actions to retaliate against the Forces who create collateral damage for them. Unfortunately, existing game theoretic models usually do not consider this situation. In this paper, an attrition-type discrete time dynamic game model is formulated, in which two opposing forces fight under reactive civilian environments that might be either neutral or slightly biased. We model the objective functions, control strategies of different players, and identify the associated constraints on the control and state variables. Existing attrition-like state space models can be regarded as a special case of the model proposed in this paper. An example scenario and extensive simulations illustrate possible applications of this model and comparative discussions further clarify the benefits. 1 2 TABLE OF CONTENTS 1. INTRODUCTION.