In this paper, we show how classical tactical forma- tion patterns and flanking strategies, such as the line formation and the enveloping maneuver, can be seen as the result of maximizing a natural formation utility.

The problem of automatic formation keeping is extremely well studied within the areas of control and robotics, but the reasons for choosing a particular formation shape and position is much less so.

By analyzing a situation with two adversarial teams of agents facing each other, we show that natural assumptions regarding the target selection of the agents and decreasing weapon efficiency over distance, can be used to optimize a measure of utility over agent positions. This optimization in turn results in formations and positions that are very similar to the ones being used in practice. We present both analytical results for simple examples as well as numerical results for more complex situations.

Air Combat is a high-risk activity carried out by trained professionals operating sophisticated equipment. During this activity, a number of trade-offs have to be made, such as the balance between risk and efficiency. A policy that minimizes risk could have very low efficiency, and one that maximizes efficiency may involve very high risk.

In this study, we use Reinforcement Learning (RL) to create Control Barrier Functions (CBF) that captures the current risk, in terms of worst-case future separation between the aircraft and an enemy missile.

CBFs are usually designed manually as closed-form expressions, but for a complex system such as a guided missile, this is not possible. Instead, we solve an RL problem using high fidelity simulation models to find value functions with CBF properties, that can then be used to guarantee safety in real air combat situations. We also provide a theoretical analysis of what family of RL problems result in value functions that can be used as CBFs in this way.

The proposed approach allows the pilot in an air combat scenario to set the exposure level deemed acceptable and continuously monitor the risk related to his/her own safety. Given input regarding acceptable risk, the system limits the choices of the pilot to those that guarantee future satisfaction of the provided bound.

Military aircraft pilots need to adjust to a constantly changing battlefield. A system that aids in understanding challenging combat circumstances and suggests appropriate responses can considerably improve the effectiveness of pilots. In this paper, we provide a Reinforcement Learning (RL) based system that acts as an aid in determining if an afterburner should be turned on to escape an incoming air-to-air missile. An afterburner is a component of a jet engine that increases thrust at the expense of exceptionally high fuel consumption. Thus it provides a short-term advantage, at the cost of a longterm disadvantage, in terms of reduced mission time. Helping to choose when to use the afterburner may significantly lengthen the flight duration, allowing aircraft to support friendly aircraft for longer and suffer fewer friendly fatalities due to this extended ability to provide support. We propose an RL-based risk estimation approach to help determine whether additional thrust is required to escape an incoming missile and study the benefits of thrust-aided evasive maneuvers. The suggested technique gives pilots a risk estimate for the scenario and a recommended course of action. We create an environment in which a pilot must decide whether or not to activate additional thrust to achieve the intended aim at a potentially high fuel consumption cost. Additionally, we investigate various trade-offs of the generated evasive maneuver policies.

As the effective range of air-to-air missiles increases, it becomes harder for pilots and Unmanned aerial vehicle (UAV) operators to maintain the Situational Awareness (SA) needed to keep their aircraft safe. In this work, we propose a decision support tool to help pilots in Beyond Visual Range (BVR) air combat scenarios assess the risks of different options and make decisions based on those. Building upon earlier research that primarily addressed the threat of a single missile, we extend these ideas to encompass the complex scenario of multiple missile threats. The proposed method uses Deep Neural Networks (DNN) to learn from high-fidelity simulations and provide the pilots with an outcome estimate for a set of different strategies. Our results demonstrate that the proposed system can manage multiple incoming missiles, evaluate a family of options, and recommend the least risky course of action while accounting for all incoming air-to-air threats.

Tactical decisions in air combat are typically evaluated using experience as a basis. Pilots undergo frequent training in various air combat processes to enhance their combat proficiency and evaluation skills. Having the Situational Awareness (SA) necessary to evaluate the effects of multiple missile threats can often be challenging. This study provides a new method for calculating an aircraft fleet's maneuver flexibility in a Beyond-Visual-Range (BVR) setting. Sustaining a high degree of flexibility is necessary to adapt to unforeseen circumstances in BVR air combat. To do that, we employ Deep Neural Networks (DNN) to capture the result of a highperformance aircraft model in the presence of adversarial BVR missiles. We then modify our approach to calculate the aircraft's maneuverability concerning an opposing fleet, looking at the advantages and disadvantages of several flight formations. Finally, we consider the anticipated threat from an incoming opponent formation and optimize the counter-formation. This methodology offers a more sophisticated comprehension of aircraft maneuver flexibility within a BVR framework and aids in developing flexible and efficient decision-making techniques for air combat.

Creating new air combat tactics and discovering novel maneuvers can require numerous hours of expert pilots' time. Additionally, for each different combat scenario, the same strategies may not work since small changes in equipment performance may drastically change the air combat outcome. For this reason, we created a reinforcement learning environment to help investigate potential air combat tactics in the field of beyond-visual-range (BVR) air combat: the BVR Gym. This type of air combat is important since long-range missiles are often the first weapon to be used in aerial combat. Some existing environments provide high-fidelity simulations but are either not open source or are not adapted to the BVR air combat domain. Other environments are open source but use less accurate simulation models. Our work provides a high-fidelity environment based on the open-source flight dynamics simulator JSBSim and is adapted to the BVR air combat domain. This article describes the building blocks of the environment and some use cases.