A Compositional Sheaf-Theoretic Framework for Event-Based Systems

Zardini, Gioele; Spivak, David I.; Censi, Andrea

doi:10.4204/eptcs.333.10

Cited by 7 publications

(6 citation statements)

References 20 publications

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“…Outlook: This work fits in our vision of compositional robotics, where we want to describe and co-design robots all the way from signals characterising a single component [38] to networks and fleet effects [39]. We want to leverage compositionality properties of our framework to interconnect the co-design problem of a robot in the co-design problem of an urban robot-enabled mobility system, to assess how local trade-offs influence fleet-level operations [40].…”

Section: Discussionmentioning

confidence: 99%

Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis

Zardini

Censi

2021

2021 European Control Conference (ECC)

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Designing cyber-physical systems is a complex task which requires insights at multiple abstraction levels. The choices of single components are deeply interconnected and need to be jointly studied. In this work, we consider the problem of co-designing the control algorithm as well as the platform around it. In particular, we leverage a monotone theory of codesign to formalize variations of the LQG control problem as monotone feasibility relations. We then show how this enables the embedding of control co-design problems in the higher level co-design problem of a robotic platform. We illustrate the properties of our formalization by analyzing the co-design of an autonomous drone performing search-and-rescue tasks and show how, given a set of desired robot behaviors, we can compute Pareto efficient design solutions.Definition 8 (Product poset). Let P, P and Q, Q be posets. Then, P × Q, P ×Q is a poset with p 1 , q 1 P ×Q p 2 , q 2 ⇔ (p 1 P p 2 ) ∧ (q 1 Q q 2 ). This is called the product poset of P, P and Q, Q .Definition 9 (Monotonicity). A map f : P → Q between two posets P, P , Q, Q is monotone iff x P y implies f (x) Q f (y). Monotonicity is compositional.

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Section: Discussionmentioning

confidence: 99%

Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis

Zardini

Censi

2021

2021 European Control Conference (ECC)

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“…More broadly, the analytic strength of category theory to express compositionality and functorial semantics is explored in numerous recent applied works, e.g. engineering diagrams [29,[53][54][55][56][57][58], Markov processes [59,60], database integration [27,29,31,33,[61][62][63], behavioural logic [29,[64][65][66], natural language processing [67][68][69], machine learning [70,71], cybersecurity [51,[72][73][74], quantum computation [75][76][77] and open games [78][79][80].…”

Section: (I) Related Analytic Applicationsmentioning

confidence: 99%

Operads for complex system design specification, analysis and synthesis

et al. 2021

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As the complexity and heterogeneity of a system grows, the challenge of specifying, documenting and synthesizing correct, machine-readable designs increases dramatically. Separation of the system into manageable parts is needed to support analysis at various levels of granularity so that the system is maintainable and adaptable over its life cycle. In this paper, we argue that operads provide an effective knowledge representation to address these challenges. Formal documentation of a syntactically correct design is built up during design synthesis, guided by semantic reasoning about design effectiveness. Throughout, the ability to decompose the system into parts and reconstitute the whole is maintained. We describe recent progress in effective modelling under this paradigm and directions for future work to systematically address scalability challenges for complex system design.

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“…The localglobal properties inherent to sheaves were shown to be useful in modeling the communication and interaction between cooperating robots. The study of event-based systems using sheaves is described in Zardini et al (2020), where events belonging to a system denoted by time stamps and the transition between these events can be depicted in a topological space. Examples of event-based systems that are analyzed in this paper include the representation of background on event cameras and robotic system description.…”

Section: Related Workmentioning

confidence: 99%

“…In this section, we describe our approach to incorporating robotics applications on the blockchain that will focus on modeling the blockchain as a topological structure of sheaves. We build upon work in Zardini et al (2020) for a quick overview of underlying topics in category theory, and refer the reader to Riehl (2017) for a detailed exposition of category theory.…”

Section: A Unifying Framework For Blockchain Robotics and Sheavesmentioning

confidence: 99%

On the Design of Social Robots Using Sheaf Theory and Smart Contracts

Murimi

2021

Front. Robot. AI

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The incorporation of robots in the social fabric of our society has taken giant leaps, enabled by advances in artificial intelligence and big data. As these robots become increasingly adept at parsing through enormous datasets and making decisions where humans fall short, a significant challenge lies in the analysis of robot behavior. Capturing interactions between robots, humans and IoT devices in traditional structures such as graphs poses challenges in the storage and analysis of large data sets in dense graphs generated by frequent activities. This paper proposes a framework that uses the blockchain for the storage of robotic interactions, and the use of sheaf theory for analysis of these interactions. Applications of our framework for social robots and swarm robots incorporating imperfect information and irrationality on the blockchain sheaf are proposed. This work shows the application of such a framework for various blockchain applications on the spectrum of human-robot interaction, and identifies key challenges that arise as a result of using the blockchain for robotic applications.

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A Compositional Sheaf-Theoretic Framework for Event-Based Systems

Cited by 7 publications

References 20 publications

Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis

Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis

Operads for complex system design specification, analysis and synthesis

On the Design of Social Robots Using Sheaf Theory and Smart Contracts

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