The focus of this paper is to present a game theoretical modeling framework for the integration of unmanned aircraft systems into the National Airspace System. The problem of predicting the outcome of complex scenarios, where manned and unmanned air vehicles coexist, is the research problem of this work. The fundamental gap in the literature is that the models of interaction between manned and unmanned vehicles are insufficient: 1) They assume that pilot behavior is known a priori, and 2) They disregard pilot reaction and the decision-making process. The contribution of this paper is to propose a realistic modeling framework that will fill this gap. The foundations of the proposed method are formed by game theory, which investigates strategic decision making between intelligent agents; bounded rationality concept, which is based on the fact that humans cannot always make perfect decisions; and reinforcement learning, which is shown to be effective in human learning in psychology literature. An analysis of integration is conducted using an example scenario in the presence of manned aircraft and fully autonomous unmanned aircraft systems equipped with sense-and-avoid algorithms.Nomenclature m = message P = probability Q = value function for state-action pairs R = minimum safety distance, nm r = relative position vector between the unmanned aircraft system and the intruder, nm r m = minimum relative position vector between the unmanned aircraft system and the intruder, nm r 0 = initial relative position vector between the unmanned aircraft system and the intruder, nm s = state V = value function for states ϵ = learning rate ζ = angle between r and v AB , rad v = velocity vector, m∕s v A = velocity vector of the unmanned aircraft system, m∕s v B = velocity vector of the intruder, m∕s v AB = relative velocity vector between the unmanned aircraft system and the intruder, m∕s v x = X component of the velocity vector, m∕s v y = Y component of the velocity vector, m∕s v d A = velocity adjustment command vector for the unmanned aircraft system, m∕s π· = policy Ψ = heading angle, rad Ψ d = desired heading angle, rad

The focus of this paper is to present a game theoretical modeling and simulation framework for the integration of Unmanned Aircraft Systems (UAS) into the National Airspace system (NAS). The problem of predicting the outcome of complex scenarios, where UAS and manned air vehicles co-exist, is the research problem of this work. The fundamental gap in the literature in terms of developing models for UAS integration into NAS is that the models of interaction between manned and unmanned vehicles are insufficient. These models are insufficient because a) they assume that human behavior is known a priori and b) they disregard human reaction and decision making process. The contribution of this paper is proposing a realistic modeling and simulation framework that will fill this gap in the literature. The foundations of the proposed modeling method is formed by game theory, which analyzes strategic decision making between intelligent agents, bounded rationality concept, which is based on the fact that humans cannot always make perfect decisions, and reinforcement learning, which is shown to be effective in human behavior in psychology literature. These concepts are used to develop a simulator which can be used to obtain the outcomes of scenarios consisting of UAS, manned vehicles, automation and their interactions. An analysis of the UAS integration is done with a specifically designed scenario for this paper. In the scenario, a UAS equipped with sense and avoid algorithm, moves along a predefined trajectory in a crowded airspace. Then the effect of various system parameters on the safety and performance of the overall system is investigated.