Eric Feron

Trajectory Clustering and an Application to Airspace Monitoring

This paper presents a framework aimed at monitoring the behavior of aircraft in a given airspace. Trajectories that constitute typical operations are determined and learned using data-driven methods. Standard procedures are used by air traffic controllers (ATCs) to guide aircraft, ensure the safety of the airspace, and maximize runway occupancy. Even though standard procedures are used by ATCs, control of the aircraft remains with the pilots, leading to large variability in the flight patterns observed. Two methods for identifying typical operations and their variability from recorded radar tracks are presented. This knowledge base is then used to monitor the conformance of current operations against operations previously identified as typical. A tool called AirTrajectoryMiner is presented, aiming at monitoring the instantaneous health of the airspace, in real time. The airspace is “healthy” when all aircraft are flying according to typical operations. A measure of complexity is introduced, measuring the conformance of current flight to typical flight patterns. When an aircraft does not conform, the complexity increases as more attention from ATC is required to ensure safe separation between aircraft.

On the Dubins Traveling Salesman Problem

We study the traveling salesman problem for a Dubins vehicle. We prove that this problem is NP-hard, and provide lower bounds on the approximation ratio achievable by some recently proposed heuristics. We also describe new algorithms for this problem based on heading discretization, and evaluate their performance numerically.

Detection of Driver Fatigue Caused by Sleep Deprivation

This paper aims to provide reliable indications of driver drowsiness based on the characteristics of driver-vehicle interaction. A test bed was built under a simulated driving environment, and a total of 12 subjects participated in two experiment sessions requiring different levels of sleep (partial sleep-deprivation versus no sleep-deprivation) before the experiment. The performance of the subjects was analyzed in a series of stimulus-response and routine driving tasks, which revealed the performance differences of drivers under different sleep-deprivation levels. The experiments further demonstrated that sleep deprivation had greater effect on rule-based than on skill-based cognitive functions: when drivers were sleep-deprived, their performance of responding to unexpected disturbances degraded, while they were robust enough to continue the routine driving tasks such as lane tracking, vehicle following, and lane changing. In addition, we presented both qualitative and quantitative guidelines for designing drowsy-driver detection systems in a probabilistic framework based on the paradigm of Bayesian networks. Temporal aspects of drowsiness and individual differences of subjects were addressed in the framework.

Multi-UAV dynamic routing with partial observations using restless bandit allocation indices

Motivated by the type of missions currently performed by unmanned aerial vehicles, we investigate a discrete dynamic vehicle routing problem with a potentially large number of targets and vehicles. Each target is modeled as an independent two-state Markov chain, whose state is not observed if the target is not visited by some vehicle. The goal for the vehicles is to collect rewards obtained when they visit the targets in a particular state. This problem can be seen as a type of restless bandits problem with partial information. We compute an upper bound on the achievable performance and obtain in closed form an index policy proposed by Whittle. Simulation results provide evidence for the outstanding performance of this index heuristic and for the quality of the upper bound.

From Control Systems to Control Software

This article describes an approach to documenting control programs, whereby the control program code is annotated with logical expressions describing the set of reachable program states. This approach constitutes the application of the Floyd-Hoare paradigm to control programs. It is shown that domain knowledge gathered by control theory about control-system specifications is applicable to developing stability and performance proofs of the corresponding control programs. The analyses discussed in this article can be used in various contexts. In particular, the analyses can be used in an autocoding environment, whereby diagram-based specifications in Simulink or other languages can be turned into formally annotated target codes with extensive proofs of stability and performance. These proofs are tightly woven in the codes, which can then be verified independently by a proof checker.

A generic ellipsoid abstract domain for linear time invariant systems

Embedded system control often relies on linear systems, which admit quadratic invariants. The parts of the code that host linear system implementations need dedicated analysis tools, since intervals or linear abstract domains will give imprecise results, if any at all, on these systems. Previous work by FERET proposes a specific abstraction for digital filters that addresses this issue on a specific class of controllers. This paper aims at generalizing the idea. It works directly on system representation, relying on existing methods from control theory to automatically generate quadratic invariants for linear time invariant systems, whose stability is provable. This class encompasses n-th order digital filters and, in general, controllers embedded in critical systems. While control theorists only focus on the existence of such invariants, this paper proposes a method to effectively compute tight ones. The method has been implemented and applied to some benchmark systems, giving good results. It also considers floating points issues and validates the soundness of the computed invariants.

Preventing Automotive Pileup Crashes in Mixed-Communication Environments

Recent news illustrates the frequent occurrence of pileup crashes on highways. A predominant reason for the occurrence of such crashes is that current vehicles (including those equipped with an automatic cruise control system) do not provide drivers with advance information of events occurring far ahead of them. The use of intervehicular communication to provide advance warnings to enhance automotive safety is therefore being actively discussed in the research community. In this paper, we investigate scenarios wherein only a subset of the vehicles in a multivehicle stream is equipped with such advance-warning capabilities. These vehicles (which are equipped with the capability to receive far-ahead information) are arbitrarily distributed among other unequipped vehicles that are capable of receiving only local near-neighbor information. It is seen that there are conditions wherein even a partial equipage of the system can be beneficial to both equipped and unequipped vehicles in a mixed-vehicle stream. We demonstrate this through both simulations and a theoretical analysis. We also developed a prototype of an advance-warning system and conducted road tests to test the concept. These road tests have demonstrated the systems performance to be satisfactory, subject to good communication links, for the class of scenarios tested.

PVS linear algebra libraries for verification of control software algorithms in C/ACSL

The problem of ensuring control software properties hold on their actual implementation is rarely tackled. While stability proofs are widely used on models, they are never carried to the code. Using program verification techniques requires express these properties at the level of the code but also to have theorem provers that can manipulate the proof elements. We propose to address this challenge by following two phases: first we introduce a way to express stability proofs as C code annotations; second, we propose a PVS linear algebra library that is able to manipulate quadratic invariants, i.e., ellipsoids. Our framework achieves the translation of stability properties expressed on the code to the representation of an associated proof obligation (PO) in PVS. Our library allows us to discharge these POs within PVS.

Multi-Agent Task Assignment in the Bandit Framework

We consider a task assignment problem for a fleet of UAVs in a surveillance/search mission. We formulate the problem as a restless bandits problem with switching costs and discounted rewards: there are TV sites to inspect, each one of them evolving as a Markov chain, with different transition probabilities if the site is inspected or not. The sites evolve independently of each other, there are transition costs c ij for moving between sites i and j isin {1,..., N}, rewards when visiting the sites, and we maximize a mixed objective function of these costs and rewards. This problem is known to be PSPACE-hard. We present a systematic method, inspired from the work of Bertsimas and Nino-Mora (2000) on restless bandits, for deriving a linear programming relaxation for such locally decomposable MDPs. The relaxation is computable in polynomial-time offline, provides a bound on the achievable performance, as well as an approximation of the cost-to-go which can be used online in conjunction with standard suboptimal stochastic control methods. In particular, the one-step lookahead policy based on this approximate cost-to-go reduces to computing the optimal value of a linear assignment problem of size N. We present numerical experiments, for which we assess the quality of the heuristics using the performance bound

Mathematical Models for Aircraft Trajectory Design: A Survey

Air tra c management ensure the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are ob- jects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of positions (and or speeds). In order to manipulate such objects with algorithms, one must reduce the dimension of the search space by using more e cient representations. Some dimen- sion reduction tricks are then presented for which advantages and drawbacks are presented. Then, front propagation approaches are introduced with a focus on Fast Marching Algorithms and Ordered upwind algorithms. An example of application of such algorithm to a real instance of air tra c control problem is also given. When aircraft dynamics have to be included in the model, optimal control approaches are really e cient. We present also some application to aircraft trajectory design. Finally, we introduce some path planning techniques via natural language processing and mathematical programming.