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Risk Structures: Towards Engineering Risk-aware Autonomous Systems

Mario Gleirscher

TL;DR

Risk Structures presents a compositional, algebraic framework for qualitative risk modelling in autonomous systems by separating a process model $P$ from a modular risk model $\mathfrak{R}$ built from risk factors. Risk factors are formalized as labeled transition systems with phases and events, translated into CSP processes, and assembled into risk spaces $R(F)$ with operators like parallel composition $\parallel$ and constraints $[\cdot]_C$ to capture dependencies. The framework introduces qualitative and quantitative mitigation orders, proving properties such as linearity and lattice structure to support refinement and safety reasoning at design-time and run-time, and discusses integration with failure analysis and runtime monitoring. The work lays a foundation for scalable, compositional risk-aware design of autonomous systems and outlines pathways to probabilistic extensions, reachability analysis, and tool-supported monitor synthesis. This approach supports systematic, verifiable risk management in complex robot and autonomous-system deployments.

Abstract

Inspired by widely-used techniques of causal modelling in risk, failure, and accident analysis, this work discusses a compositional framework for risk modelling. Risk models capture fragments of the space of risky events likely to occur when operating a machine in a given environment. Moreover, one can build such models into machines such as autonomous robots, to equip them with the ability of risk-aware perception, monitoring, decision making, and control. With the notion of a risk factor as the modelling primitive, the framework provides several means to construct and shape risk models. Relational and algebraic properties are investigated and proofs support the validity and consistency of these properties over the corresponding models. Several examples throughout the discussion illustrate the applicability of the concepts. Overall, this work focuses on the qualitative treatment of risk with the outlook of transferring these results to probabilistic refinements of the discussed framework.

Risk Structures: Towards Engineering Risk-aware Autonomous Systems

TL;DR

Risk Structures presents a compositional, algebraic framework for qualitative risk modelling in autonomous systems by separating a process model from a modular risk model built from risk factors. Risk factors are formalized as labeled transition systems with phases and events, translated into CSP processes, and assembled into risk spaces with operators like parallel composition and constraints to capture dependencies. The framework introduces qualitative and quantitative mitigation orders, proving properties such as linearity and lattice structure to support refinement and safety reasoning at design-time and run-time, and discusses integration with failure analysis and runtime monitoring. The work lays a foundation for scalable, compositional risk-aware design of autonomous systems and outlines pathways to probabilistic extensions, reachability analysis, and tool-supported monitor synthesis. This approach supports systematic, verifiable risk management in complex robot and autonomous-system deployments.

Abstract

Inspired by widely-used techniques of causal modelling in risk, failure, and accident analysis, this work discusses a compositional framework for risk modelling. Risk models capture fragments of the space of risky events likely to occur when operating a machine in a given environment. Moreover, one can build such models into machines such as autonomous robots, to equip them with the ability of risk-aware perception, monitoring, decision making, and control. With the notion of a risk factor as the modelling primitive, the framework provides several means to construct and shape risk models. Relational and algebraic properties are investigated and proofs support the validity and consistency of these properties over the corresponding models. Several examples throughout the discussion illustrate the applicability of the concepts. Overall, this work focuses on the qualitative treatment of risk with the outlook of transferring these results to probabilistic refinements of the discussed framework.

Paper Structure

This paper contains 49 sections, 22 theorems, 53 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Abstractions for Machine Safety and Risk Awareness
  3. Related Work
  4. Algebraic Methods in System Risk Assessment.
  5. Dependability Methods for Repairable Systems.
  6. Safety Monitoring in Autonomous Systems.
  7. Risk-sensitive Control and Risk-aware Planning in Autonomous Systems.
  8. Contributions and Overview
  9. Background
  10. Notions of Risk
  11. The Risk of Undesired Events
  12. System Accidents, Dangerous Incidents and Failures.
  13. Analysis and Reduction of Random Failures.
  14. Analysis and Reduction of Systematic Failures.
  15. Analysis and Mitigation at Run-time.
  16. ...and 34 more sections

Key Result

Lemma 1

Figures (3)

  • Figure 1: Two abstraction levels: Simple risk model $\mathfrak{R}$ with a single risk factor partitioning the state space of process model $P$ and, this way, forming a view of $P$ with respect to this specific risk factor
  • Figure 2: Risk factor $\mathsf{f}$
  • Figure 3: Nondeterministic risk factor $\mathsf{f}$

Theorems & Definitions (70)

  • Definition 1: Process
  • Definition 2: Labelled Transition System, LTS
  • Definition 3: Risk Factor
  • Remark 1
  • Remark 2
  • Definition 4: Risk State
  • Definition 5: Risk Space
  • Remark 3
  • Definition 6: Equality and Compatibility of Risk States
  • Definition 7: Risk Space Composition
  • ...and 60 more