This paper presents DAIDALUS (Detect and Avoid Alerting Logic for Unmanned Systems), a reference implementation of a detect and avoid concept intended to support the integration of Unmanned Aircraft Systems into civil airspace. DAIDALUS consists of self-separation and alerting algorithms that provide situational awareness to UAS remote pilots. These algorithms have been formally specified in a mathematical notation and verified for correctness in an interactive theorem prover. The software implementation has been verified against the formal models and validated against multiple stressing cases jointly developed by the

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze infinite-state open systems, i.e., systems that interact with a non-deterministic environment. Such systems exhibit both internal non-determinism, which is proper to the system, and external non-determinism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of a real-time system that is beyond the scope of timed-automata methods.

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This paper introduces a static analysis technique for computing formally verified round-off error bounds of floating-point functional expressions. The technique is based on a denotational semantics that computes a symbolic estimation of floating-point round-off errors along with a proof certificate that ensures its correctness. The symbolic estimation can be evaluated on concrete inputs using rigorous enclosure methods to produce formally verified numerical error bounds. The proposed technique is implemented in the prototype research tool PRECiSA (Program Round-off Error Certifier via Static Analysis) and used in the verification of floating-point programs of interest to NASA.

The Traffic Alert and Collision Avoidance System (TCAS) is a family of airborne systems designed to reduce the risk of mid-air collisions between aircraft. TCAS II, the current generation of TCAS devices, provides resolution advisories that direct pilots to maintain or increase vertical separation when aircraft distance and time parameters are beyond designed system thresholds. This paper presents a mathematical model of the TCAS II Resolution Advisory (RA) logic that assumes accurate aircraft state information. Based on this model, an algorithm for RA detection is also presented. This algorithm is analogous to a conflict detection algorithm, but instead of predicting loss of separation, it predicts resolution advisories. It has been formally verified that for a kinematic model of aircraft trajectories, this algorithm completely and correctly characterizes all encounter geometries between two aircraft that lead to a resolution advisory within a given lookahead time interval. The RA detection algorithm proposed in this paper is a fundamental component of a NASA sense and avoid concept for the integration of Unmanned Aircraft Systems in civil airspace.

Abstract. Highly accurate positioning systems and new broadcasting technology have enabled air traffic management concepts where the responsibility for aircraft separation resides on pilots rather than on air traffic controllers. The Formal Methods Group at the National Institute of Aerospace and NASA Langley Research Center has proposed and formally verified an algorithm, called KB3D, for distributed three dimensional conflict resolution. KB3D computes resolution maneuvers where only one component of the velocity vector, i.e., ground speed, vertical speed, or heading, is modified. Although these maneuvers are simple to implement by a pilot, they are not necessarily optimal from a geometrical point of view. In general, optimal resolutions require the combination of all the components of the velocity vector. In this paper, we propose a two dimensional version of KB3D, which we call KB2D, that computes resolution maneuvers that are optimal with respect to ground speed and heading changes. The algorithm has been mechanically verified in the Prototype Verification System (PVS). The verification relies on algebraic proof techniques for the manipulation of the geometrical concepts relevant to the algorithm as well as standard deductive techniques available in PVS.

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The FAA-sponsored Sense and Avoid Workshop for Unmanned Aircraft Systems (UAS) defines the concept of sense and avoid for remote pilots as "the capability of a UAS to remain well clear from and avoid collisions with other airborne traffic." Hence, a rigorous definition of well clear is fundamental to any separation assurance concept for the integration of UAS into civil airspace. This paper presents a family of well-clear boundary models based on the TCAS II Resolution Advisory logic. For these models, algorithms that predict well-clear violations along aircraft current trajectories are provided. These algorithms are analogous to conflict detection algorithms but instead of predicting loss of separation, they predict whether well-clear violations will occur during a given lookahead time interval. Analytical techniques are used to study the properties and relationships satisfied by the models.