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. 2021 Aug 18:8:559380.
doi: 10.3389/frobt.2021.559380. eCollection 2021.

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

Renita Murimi  1
Affiliations

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

Renita Murimi. Front Robot AI. .

Abstract

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.

Keywords: blockchain; imperfect information; irrationality; robotics; sheaf theory; smart contracts.

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Conflict of interest statement

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Figures

FIGURE 1
FIGURE 1
A representation of task collaboration among sensors of a robot using simplicial complexes.
FIGURE 2
FIGURE 2
Abstract representation of the blockchain. Each block contains transactions, and a block’s hash is included in the header of the successive block.
FIGURE 3
FIGURE 3
Graph representation of the blockchain. IP addresses, represented as nodes n1−n7 engage in transactions t1−t6. Transactions attributes are shown.
FIGURE 4
FIGURE 4
An analogy describing stalks and blocks. Left: Blockchain as a stalk. The shaded portion represents the hash functions that link blocks to their successors and predecessors, thus forming a central spine around which transactions are linked. Middle: An individual stalk with seeds. Right: A sheaf of blockchain stalks bound by a smart contract tuned with imperfect information (p) and irrationality (r).
FIGURE 5
FIGURE 5
Left: A block of transactions represented as a stalk. Individual transactions contain varying attributes. Right: A blockchain of n blocks represented as a stalk. Block-level and transaction-level attributes can be adequately represented in the sheaf-theoretic model.
FIGURE 6
FIGURE 6
Stalks representing social robots. Left: A controller robot. Right: A lower-level robot.
FIGURE 7
FIGURE 7
Blockchain sheaf of multiple robot interactions.
FIGURE 8
FIGURE 8
A sheaf representation of transactions.
FIGURE 9
FIGURE 9
Representing blocks, transactions and hashes as a sheaf.
FIGURE 10
FIGURE 10
A sheaf containing blocks in series.
FIGURE 11
FIGURE 11
Composition of a sheaf of parallel chains
FIGURE 12
FIGURE 12
Composition of sheaves in a voice assistant social robot.
FIGURE 13
FIGURE 13
Stimulus sheaf as a blockchain.
See this image and copyright information in PMC

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