Conflict Detection and Resolution for 1 , 2 , . . . , N Aircraft Gilles

Formal methods in computer science refers to the use of logic and mathematics to verify that a system design and its implementation satisfy functional requirements and safety properties. Despite the fact that several Conflict Detection and Resolution (CD&R) systems have been proposed in the past few years, very few of these systems have been described and analyzed using formal methods. Therefore, it is not always clear what properties these algorithms satisfy. For instance, the notion of cooperative resolution is often used in the CD&R literature expressing different and, sometimes, contradictory concepts, e.g., it expresses exchange of intent information, degree of coordination, sharing of effort to achieve separation, and temporary delegation of responsibility for separation. This confusion could be avoided by providing rigorous definitions of the concepts and properties that are fundamental to all CD&R systems. This paper presents a mathematical framework for the formal specification and analysis of conflict detection and resolution algorithms and their properties. This framework applies to state-based, pairwise, geometric, and distributed conflict detection and resolution algorithms. State-based (or tactical) refers to the use of aircraft state information, e.g., position and velocity vectors, as opposed to strategic approaches that use intent information, e.g., flight plan. Pairwise refers the use of a conflict detection and resolution logic for two distinguished aircraft: the ownship and the traffic aircraft. Geometric refers to the use of linear projections to predict aircraft trajectories as opposed to probabilistic or performance-based trajectories. Finally, distributed refers to systems that are deployed on several aircraft detecting and solving conflicts for the ownship as opposed to centralized systems that detect and simultaneously solve conflicts for a large set of aircraft. The distributed approach that we consider in this framework requires minimal communication between the aircraft. In particular, the only information that is periodically exchanged between the aircraft is the state information, e.g., position and velocity vectors of the aircraft. Examples of algorithms and approaches that are included in this framework are the self-organizational approach, the modified potential algorithm, the geometric optimization approach, and the KB3D algorithm and its extensions. This paper is organized as follows. Section II provides the geometric background for state-based conflict detection and resolution. The CD&R framework is presented in Section III, for conflict detection, and Section IV, for conflict resolution. These sections illustrate the use of the framework with original conflict detection and resolution algorithms for multiple aircraft. The mathematical development presented in this paper has been formally verified in the Program Verification System (PVS).