Collision analysis for an UAV

International audienceThe Sense and Avoid capacity of Unmanned Aerial Vehicles (UAV) is one of the key elements to open the access to airspace for UAVs. In order to replace a pilot's See and Avoid capacity such a system has to be certified "as safe as a human pilot on-board". The problem is to prove that an unmanned aircraft equipped with a S and A system can comply with the actual air transportation regulations. This paper aims to provide mathematical and numerical tools to link together the safety objectives and sensors specifications. Our approach starts with the natural idea of a specified "safety volume" around the aircraft: the safety objective is to guarantee that no other aircraft can penetrate this volume. We use a general reachability and viability concepts to define nested sets which are meaningful to allocate sensor performances and manoeuvring capabilities necessary to protect the safety volume. Using the general framework of HJB equations for the optimal control and differential games, we give a rigorous mathematical characterization of these sets. Our approach allows also to take into account some uncertainties in the measures of the parameters of the incoming traffic. We also provide numerical tools to compute the defined sets, so that the technical specifications of a S and A system can be derived in accordance with a small set of intuitive parameters. We consider several dynamical models corresponding to the different choices of maneuvers (lateral, longitudinal and mixed). Our numerical simulations show clearly that the nature of used maneuvers is an important factor in the specifications of sensor's performances

A time-triggered dimension reduction algorithm for the task assignment problem

The task assignment problem is fundamental in combinatorial optimisation, aiming at allocating one or more tasks to a number of agents while minimizing the total cost or maximizing the overall assignment benefit. This problem is known to be computationally hard since it is usually formulated as a mixed-integer programming problem. In this paper, we consider a novel time-triggered dimension reduction algorithm (TTDRA). We propose convexification approaches to convexify both the constraints and the cost function for the general non-convex assignment problem. The computational speed is accelerated via our time-triggered dimension reduction scheme, where the triggering condition is designed based on the optimality tolerance and the convexity of the cost function. Optimality and computational efficiency are verified via numerical simulations on benchmark examples

Explicit solutions for safety problems using control barrier functions

The control Barrier function approach has been widely used for safe controller synthesis. By solving an online convex quadratic programming problem, an optimal safe controller can be synthesized implicitly in state-space. Since the solution is unique, the mapping from state-space to control inputs is injective, thus enabling us to evaluate the underlying relationship. In this paper we aim at explicitly synthesizing a safe control law as a function of the state for nonlinear control-affine systems with limited control ability. We propose to transform the online quadratic programming problem into an offline parameterized optimisation problem which considers states as parameters. The obtained explicit safe controller is shown to be a piece-wise Lipschitz continuous function over the partitioned state space if the program is feasible. We address the infeasible cases by solving a parameterized adaptive control Barrier function-based quadratic programming problem. Extensive simulation results show the state-space partition and the controller properties

Evaluating Chicago's success in reaching the Healthy People 2000 goal of reducing health disparities.

OBJECTIVE: This study was designed to assess Chicago's progress from 1980 to 1998 in addressing the Healthy People 2000 goal of reducing health disparities. METHODS: Chicago vital statistics and surveillance data were used to calculate black:white rate ratios of mortality and morbidity for 1980-1998. Mortality and morbidity rate ratios were also used to compare people living in areas with the lowest median household income with those living in the highest for 1979-1981, 1991-1993, and 1996-1998. The health measures included mortality associated with leading causes of death; all-cause mortality, incidence rates for two communicable diseases; and two birth outcomes. RESULTS: Both black:white and low-income:high-income rate ratios monotonically increased for virtually all measures of mortality and morbidity. Almost all of the rate ratios and linear trends were statistically significant. From 1980 to 1998, the black:white rate ratio for all-cause mortality increased by 57% to 2.03. From 1979-1981 to 1996-1998, the low-income:high-income rate ratio for all-cause mortality increased by 56% to 2.68. CONCLUSIONS: These findings provide clear evidence that disparities in health did not decrease in Chicago. Instead, racial and economic disparities increased for almost all measures of mortality and morbidity used in this study. The fact that the Healthy People 2000 campaign to reduce and then eliminate health disparities was not effective must serve as a stimulus for improved strategies