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.

倘若我们设计一款工具，可自动生成针对受多重冲击、接触与间断摩擦影响的机械系统形式化规约的动态转换系统，将会如何？此类工具将为这类复杂系统的描述与仿真研究带来突破性进展。本论文正是提供了这样一款工具：Dyverse刚体工具箱（Dyverse Rigid Body Toolbox，缩写为DyverseRBT）。该工具需要具备足够强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，我们针对带多重接触的多刚体（multi-rigid-body, MRB）机械系统提出了一种替代抽象建模方案，将其作为经典混合自动机的扩展版本，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，便是引入计算节点以编码计算接触力的算法。此类计算节点由若干非动态离散位置、离散迁移及各位置间的警戒条件，以及迁移时的状态重置操作构成，可对刚体形式化体系中未被显式纳入考虑的能量传递过程进行建模。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。我们通过对DyverseRBT生成的转换系统进行安全属性证伪，验证了该框架的适用性。