Stochastic trajectory optimisation for aircraft in air combat

This paper proposes a novel approach to aircraft conflict resolution where the design of an optimal conflict resolution manoeuvre based on the aircraft intent information is robustified against the uncertainty affecting the aircraft future positions by a randomized stochastic optimization method. The goal is to account for a probabilistic description of the uncertainty affecting the aircraft motion, while avoiding the excessive computational load of a pure Monte Carlo stochastic optimization method.

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.

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.

TJPRC, 2013

Air Traffic control Strategy (ATCS) of the longer term permits for the likelihood of free flight, within which craft select their own best routes, altitudes, and velocities. The safe resolution of mechanical phenomenon conflicts between craft is important to the success of such a distributed system. During this paper, we present a technique to synthesize incontrovertibly safe conflict resolution maneuvers. The strategy models the craft and therefore the maneuver as a hybrid system and calculates the maximal set of safe initial conditions for every aircraft in order that separation is assured within the presence of uncertainties within the actions of the opposite aircraft. Samples of maneuvers victimization each speed and heading changes are figured out thoroughly.

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

IEEE Transactions on Intelligent Transportation Systems, 2006

The safety of flights, and, in particular, separation assurance, is one of the main tasks of air traffic control (ATC). Conflict resolution refers to the process used by ATCs to prevent loss of separation. Conflict resolution involves issuing instructions to aircraft to avoid loss of safe separation between them and, at the same time, direct them to their destinations. Conflict resolution requires decision making in the face of the considerable levels of uncertainty inherent in the motion of aircraft. In this paper, a framework for conflict resolution that allows one to take into account such levels of uncertainty using a stochastic simulator is presented. The conflict resolution task is posed as the problem of optimizing an expected value criterion. It is then shown how the cost criterion can be selected to ensure an upper bound on the probability of conflict for the optimal maneuver. Optimization of the expected value resolution criterion is carried out through an iterative procedure based on Markov chain Monte Carlo. Simulation examples inspired by current ATC practice in terminal maneuvering areas and approach sectors illustrate the proposed conflict resolution strategy

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.

Computing Research Repository, 2011

We show how to combine Bayes nets and game theory to predict the behavior of hybrid systems involving both humans and automated components. We call this novel framework "Semi Network-Form Games," and illustrate it by predicting aircraft pilot behavior in potential near mid-air collisions. At present, at the beginning of such potential collisions, a collision avoidance system in the aircraft cockpit advises the pilots what to do to avoid the collision. However studies of mid-air encounters have found wide variability in pilot responses to avoidance system advisories. In particular, pilots rarely perfectly execute the recommended maneuvers, despite the fact that the collision avoidance system's effectiveness relies on their doing so. Rather pilots decide their actions based on all information available to them (advisory, instrument readings, visual observations). We show how to build this aspect into a semi network-form game model of the encounter and then present computational simulations of the resultant model.

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.

International Journal of Computer and Electrical Engineering, 2017

Importance of Unmanned Combat Aerial Vehicles (UCAVs) in air combat has been increasing continuously. Dangerous nature of air combat, limits of human body, high cost of pilot training and combat readiness create a requirement for using (UCAV) in the battlefield. High speed, limited time for making decision and multivariable nature of the problem are the main challenges of the autonomous vehicle development problem. Another challenge is coordination of air combat when performed by multiple fighters. In this article, we propose a decision-making method for multi UCAV air combat. In our method, each UCAV chooses the best engagement for the advantage of team instead of its own advantage and provide a real time feedback for improving the engagement decision. An incomplete information zero sum game implemented to antagonistic team pair. And a reduction method is proposed for mixed Nash Equilibrium strategies when large number of agents is involved. Promising results have been obtained in multi-air engagement scenario, and our solution is based on game theory approaches.

Transportation Research Part C: Emerging Technologies, 2018

Conflict detection (CD) is one of the key functions used to ensure air transport safety and efficiency. In trajectory-based operation (TBO), aircraft are provided with more flexibility in en route trajectory planning and more responsibility for self-separation. The high flexibility in trajectory planning enables random changes in pilot intent, thus increasing the uncertainty in trajectory prediction and CD. This study proposes a novel probabilistic CD approach for TBO in which the uncertainty of pilot intent is taken into account by quantifying the aircraft reachable domain constrained by the flight plan. First, a probabilistic model for aircraft trajectory prediction is developed using the truncated Brownian bridge method. Based on this model, a novel conflict probability estimation method is developed. Finally, the performance of the proposed probabilistic CD approach is demonstrated through an illustrative air traffic scenario. 1. Introduction Conflict detection (CD) is the key function of the future Air Transport Management (ATM) 1 system envisioned by the Next Generation Air Transportation System (NextGen). 2 CD determines whether two aircraft would violate the safe separation criteria during the look-ahead period based on the predicted aircraft trajectory. This trajectory can be predicted based on the aircraft's current and historical trajectories, flight plan or intention, wind and other external environmental and regulatory information. Presently, CD is conducted by an air traffic controller, and pilots are required to follow the specific instructions of the air traffic controller. Aircraft trajectory prediction has been studied using deterministic models in which the aircraft is assumed to fly straight toward the target waypoint, and the future geographical location of the aircraft is predicted based on an aircraft dynamic model. Building on this approach, probabilistic trajectory predictions improve the prediction accuracy by considering the uncertainties caused by tracking, navigation, and positioning errors (Paielli and Erzberger, 1997). The classical aircraft position prediction model assumes that aircraft heading and lateral position prediction errors follow a Gaussian distribution with zero mean (Kuchar and Yang, 2000; Yepes et al., 2007). Variance in the aircraft heading position prediction error increases linearly with time, and variance in the lateral position prediction error is a constant value and does not increase over time (Paielli et al., 2009). Additionally, an aircraft position

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.

arXiv (Cornell University), 2023

Unmanned aerial vehicles (UAVs) have become increasingly prevalent in various domains, ranging from military operations to civilian applications. However, the proliferation of UAVs has also given rise to concerns regarding their potential misuse and security threats. As a result, the search and pursuit of UAVs have become crucial tasks for law enforcement agencies and security organizations. In this paper, we use a game theoretic approach to explore the problem of searching for and pursuing submarines and translate the problem into a UAV search and pursuit problem. Game theory provides a mathematical framework for modeling and analyzing strategic interactions among multiple decision makers. By applying game theoretic principles to the search and pursuit problem, we aim to improve the effectiveness of UAV detection and capture strategies. We begin by formulating the problem as a game, where the UAV represents the evader, and the search and pursuit team represents the pursuers. Each player's objective is to optimize their own utility while considering the actions and strategies of the other players. By leveraging game theory, we can gain insights into the optimal decision-making strategies for both the UAV and the pursuers, leading to improved search and pursuit outcomes and enhanced security in the face of UAV threats. CONTENTS DYNAMIC MODELS OF INSPECTIONS .

International Journal of Robust and Nonlinear Control, 2008

Autonomous aerial vehicles play an important role in military applications such as in search, surveillance and reconnaissance. Multi-player stochastic pursuit-evasion (PE) differential game is a natural model for such operations involving intelligent moving targets with uncertainties. In this paper, some fundamental issues of stochastic PE games are addressed. We first model a general stochastic multi-player PE differential game with perfect state information. To avoid the difficulty of multiplicity of the players, we extend the iterative method for deterministic multi-player PE games to the stochastic case. Starting from certain suboptimal solutions with an improving property, the optimization based on limited look-ahead can be used for improvement. The process converges when this improvement is applied iteratively. Furthermore, we introduce a hierarchical approach that can determine a valid starting point of the iterative process. As a basis for multi-player games, stochastic two-player PE games are also addressed. We also briefly discuss the games with imperfect state information and propose a suboptimal approach from a practical point of view. Finally, we demonstrate the usefulness and the feasibility of the method through simulations.

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...