RiskStructures: A Design Algebra for Risk-Aware Machines

Mario Gleirscher*, Radu Calinescu, Jim Woodcock

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Machines, such as mobile robots and delivery drones, incorporate controllers responsible for a task while handling risk (e.g. anticipating and mitigating hazards; and preventing and alleviating accidents). We refer to machines with this capability as risk-aware machines. Risk awareness includes robustness and resilience, and complicates monitoring (i.e., introspection, sensing, prediction), decision making, and control. From an engineering perspective, risk awareness adds a range of dependability requirements to system assurance. Such assurance mandates a correct-by-construction approach to controller design, based on mathematical theory. We introduce RiskStructures, an algebraic framework for risk modelling intended to support the design of safety controllers for risk-aware machines. Using the concept of a risk factor as a modelling primitive, this framework provides facilities to construct, examine, and assure these controllers. We prove desirable algebraic properties of these facilities, and demonstrate their applicability by using them to specify key aspects of safety controllers for risk-aware automated driving and collaborative robots.
Original languageEnglish
Pages (from-to)763-802
JournalFormal Aspects of Computing
Issue number4-5
Early online date26 May 2021
Publication statusPublished - Aug 2021

Bibliographical note

Funding Information:
Mario Gleirscher was supported in part by the German Research Foundation (DFG) under the Fellowship Grant no. 381212925. Work by Radu Calinescu and Mario Gleirscher was partially supported by the Lloyd's Register Foundation under the Autonomy Assurance International Programme (AAIP) Grant CSI:Cobot. Radu Calinescu was additionally supported by the UKRI Project EP/V026747/1 "Trustworthy Autonomous Systems Node in Resilience". We would like to thank Simon Foster for inspiring discussions on the use of relational specification; Ana Cavalcanti and Cliff Jones for insightful questions about the abstraction, composition, and methodology underlying RiskStructures; James Baxter, AlvaroMiyazawa, and Pedro Ribeiro for enlightening conversations about CSP. We are also thankful to Sam Clark for helpful feedback on an early version of the introductory and closing sections.

Funding Information:
Radu Calinescu was additionally supported by the UKRI Project EP/V026747/1 "Trustworthy Autonomous Systems Node in Resilience". Acknowledgements

Publisher Copyright:
© 2021, The Author(s).


  • Correct construction
  • Formal development
  • Risk awareness
  • Run-time mitigation
  • Safety controllers
  • Robots and autonomous systems

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