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RiskStructures: A design algebra for risk-aware machines


Machines, such as mobile robots and delivery drones, incorporate controllers responsible for a task while handling risk (e.g. anticipating and mitigating hazards; preventing and alleviating accidents). We refer to machines with this capability as risk-awaremachines. 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.


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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.

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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".

Cliff Jones

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Gleirscher, M., Calinescu, R. & Woodcock, J. RiskStructures: A design algebra for risk-aware machines. Form Asp Comp 33, 763–802 (2021).

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