Reachability Analysis Of Hybrid Automata Research Articles

Parametric formal verification: the robotic paint spraying case study

Abstract The design of robots in industrial automation is based on classical control theory approaches. Recently, formal verification methodologies have been introduced in the design flow, due to their ability of analyzing the model of the robot-environment system in a conservative way. In this paper we specifically explore the analysis of system parameters within a continuous space, by developing an extension of the tool Ariadne for reachability analysis of hybrid automata. Under this framework, the system takes the form of a composition of automata which model discrete control parts that operate in a continuous environment. In particular, the dynamics of the system includes parameters, i.e., unspecified constants for which we want to observe the effect on the dynamics, with the purpose of finding optimal design values. As a case study for this methodology, we consider a robotic paint sprayer, in which we use Ariadne to study the effect of choosing different values of a parameter that represents a point of observation for the system. Using the information gathered from this automated analysis, we provide an answer to the problem of optimizing the surface spraying speed while respecting a given measure of spraying quality.

ϵ-Semantics computations on biological systems

The assumption of being able to perform infinite precision measurements does not only lead to undecidability, but it also introduces artifacts in the mathematical models that do not correspond to observable behaviours of systems under study. When bounded spatial regions are involved, such issues can be avoided if arbitrarily small sets of points are not definable in the mathematical setting. ϵ-semantics were introduced in this spirit. In this paper we investigate the use of ϵ-semantics deeper, in the context of reachability analysis of hybrid automata. In particular, we focus on two ϵ-semantics and reason about their computability. We then try our approach on biological model analysis to give evidence about the effectiveness of the methodology.

Reachability computation for hybrid systems with Ariadne

Ariadne is an in-progress open environment to design algorithms for computing with hybrid automata, that relies on a rigorous computable analysis theory to represent geometric objects, in order to achieve provable approximation bounds along the computations. In this paper we discuss the problem of reachability analysis of hybrid automata to decide safety properties. We describe in details the algorithm used in Ariadne to compute over-approximations of reachable sets. Then we show how it works on a simple example. Finally, we discuss the lower-approximation approach to the reachability problem and how to extend Ariadne to support it.