Parametric Statistical Model Checking of UAV Flight Plan

Abstract

Unmanned Aerial Vehicles (UAV) are now widespread in our society and are often used in a context where they can put people at risk. Studying their reliability, in particular in the context of flight above a crowd, thus becomes a necessity. In this paper, we study the modeling and analysis of UAV in the context of their flight plan. To this purpose, we build a parametric probabilistic model of the UAV and use it, as well as a given flight plan, in order to model its trajectory. This model takes into account parameters such as potential filter or sensor (like GPS) failure as well as wind force and direction. Because of the nature and complexity of the successive obtained models, their exact verification using tools such as PRISM or PARAM is impossible. We therefore develop a new approximation method, called Parametric Statistical Model Checking, in order to compute failure probabilities. This method has been implemented in a prototype tool, which we use to resolve complex issues in a practical case study.

Verification of Variability-Intensive Stochastic Systems with Statistical Model Checking

“…Recently, Delahaye et al [15,3] proposed an SMC approach to verify parametric Markov chains, that is, DTMCs whose transition probabilities depend on numeric parameters function such as P r : S × S → P oly(X) where X is the set of parameters p 0 , ..., p n . Then the -parametric -function f ∈ P oly(X) of a klength path ρ = s 0 , s 1 , .…”

“…Therefore, our work takes inspiration from the principles of Delahaye et al [15,3] but develops a novel SMC approach to verify FDTMCs. The implementation of our algorithms relies on a dedicated data structure -based on Algebraic Decision Diagrams (ADDs) [2] -to account for the binary nature and relationships of FDTMCs parameters.…”

“…Instead, we propose a new SMC method that can sample executions from all variants at once (i.e., directly in the FDTMC) regardless of the probabilistic differences across the variants. We rely on the theoretical results of Delahaye et al [15,3] and adapt their principles to FDTMC verification. Hence, our algorithm performs a uniform random walk to sample a path in the FDTMC.…”

End-to-End Statistical Model Checking for Parametric ODE Models

“…Because it is simulationbased, it can be applied to any stochastic model for which simulations can be performed. SMC has been successfully applied to perform parameterization of real-life models expressed using several formalisms such as parametric Markov chains [2], parametric Python programs [20], or even parametric Ordinary Differential Equation systems (ODEs) [15]. Unfortunately, the formal guarantees obtained through SMC are linked to the simulation space (i.e.…”

Strategy Synthesis for Autonomous Driving in a Moving Block Railway System with Uppaal Stratego

“…Related Work. At last year's FORTE, parametric statistical model checking was applied to Unmanned Aerial Vehicles (UAV) [4]. The model was formalised as a parametric Markov chain with the goal of reducing the probability of failure while varying parameters such as precision of the position.…”