Automated generation of hybrid automata for multi-rigid-body mechanical systems and its application to the falsification of safety properties

What if we designed a tool to automatically generate a dynamical transition system for the formal specification of mechanical systems subject to multiple impacts, contacts and discontinuous friction? Such a tool would represent an advance in the description and simulation of these complex systems. This is precisely what this paper offers: Dyverse Rigid Body Toolbox (DyverseRBT). This tool requires a sufficiently expressive computational model that can accurately describe the behaviour of the system as it evolves over time. For this purpose, we propose an alternative abstraction of multi-rigid-body (MRB) mechanical systems with multiple contacts as an extended version of the classical hybrid automaton, which we call MRB hybrid automaton. One of the chief characteristics of the MRB hybrid automaton is the inclusion of computation nodes to encode algorithms to calculate the contact forces. The computation nodes consist of a set of non-dynamical discrete locations, discrete transitions and guards between these locations, and resets on transitions. They can account for the energy transfer not explicitly considered within the rigid-body formalism. The proposed modelling framework is well suited for the automated verification of dynamical properties of realistic mechanical systems. We show this by the falsification of safety properties over the transition system generated by DyverseRBT.

试想我们研发一款工具，可自动生成针对受多重冲击、接触与不连续摩擦约束的机械系统形式化规范的动态转换系统——此类工具将为这类复杂系统的描述与仿真带来突破性进展。本文所提供的正是这样一款工具：Dyverse刚体工具箱（Dyverse Rigid Body Toolbox，简称DyverseRBT）。该工具需要具备足够表达能力的计算模型，以精准刻画系统随时间演化的行为特性。为此，我们提出一种针对含多接触的多刚体（multi-rigid-body，MRB）机械系统的新型抽象建模方式，将其作为经典混合自动机（hybrid automaton）的扩展版本，并将其命名为MRB混合自动机。MRB混合自动机的核心特性之一，便是纳入了用于编码接触力计算算法的计算节点。此类计算节点由一组非动态离散位置、离散迁移以及这些位置间的警戒条件，与迁移重置操作共同构成。其可弥补刚体形式化体系中未被显式考虑的能量传递问题。所提出的建模框架非常适用于对实际机械系统的动态特性开展自动化验证。我们通过针对DyverseRBT生成的转换系统开展安全属性证伪实验，验证了该建模框架的适用性。