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A Micro-Macro Model of Encounter-Driven Information Diffusion in Robot Swarms

Davis S. Catherman, Carlo Pinciroli

TL;DR

A model of information diffusion that captures the essential dynamics of EDID, which is derived from first principles and is composed of two levels: a micro model, based on a generalization of the concept of `mean free path'; and a macro model, which captures the global dynamics of information diffusion.

Abstract

In this paper, we propose the problem of Encounter-Driven Information Diffusion (EDID). In EDID, robots are allowed to exchange information only upon meeting. Crucially, EDID assumes that the robots are not allowed to schedule their meetings. As such, the robots have no means to anticipate when, where, and who they will meet. As a step towards the design of storage and routing algorithms for EDID, in this paper we propose a model of information diffusion that captures the essential dynamics of EDID. The model is derived from first principles and is composed of two levels: a micro model, based on a generalization of the concept of `mean free path'; and a macro model, which captures the global dynamics of information diffusion. We validate the model through extensive robot simulations, in which we consider swarm size, communication range, environment size, and different random motion regimes. We conclude the paper with a discussion of the implications of this model on the algorithms that best support information diffusion according to the parameters of interest.

A Micro-Macro Model of Encounter-Driven Information Diffusion in Robot Swarms

TL;DR

A model of information diffusion that captures the essential dynamics of EDID, which is derived from first principles and is composed of two levels: a micro model, based on a generalization of the concept of `mean free path'; and a macro model, which captures the global dynamics of information diffusion.

Abstract

In this paper, we propose the problem of Encounter-Driven Information Diffusion (EDID). In EDID, robots are allowed to exchange information only upon meeting. Crucially, EDID assumes that the robots are not allowed to schedule their meetings. As such, the robots have no means to anticipate when, where, and who they will meet. As a step towards the design of storage and routing algorithms for EDID, in this paper we propose a model of information diffusion that captures the essential dynamics of EDID. The model is derived from first principles and is composed of two levels: a micro model, based on a generalization of the concept of `mean free path'; and a macro model, which captures the global dynamics of information diffusion. We validate the model through extensive robot simulations, in which we consider swarm size, communication range, environment size, and different random motion regimes. We conclude the paper with a discussion of the implications of this model on the algorithms that best support information diffusion according to the parameters of interest.
Paper Structure (15 sections, 13 equations, 5 figures, 1 table)

This paper contains 15 sections, 13 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Microscopic Model
  3. Encounters and mean free path
  4. Deriving the ideal mean free path
  5. The generalized mean free path
  6. The Macroscopic Model
  7. Low-density, well-mixed regime
  8. High-density, not-mixed regime
  9. Combined model
  10. Experimental Evaluation
  11. Experimental Setup
  12. Microscopic Model
  13. Macroscopic Model: Parameter Fit
  14. Macroscopic Model: Propagation Time
  15. Conclusion

Figures (5)

  • Figure 1: A representation of the mean free path $\tau$ as the average time between subsequent interactions between an agent (depicted in red) and surrounding agents (in blue).
  • Figure 2: Our macro model identifies two possible regimes: low-density, well mixed (left) and high-density, not-mixed (right).
  • Figure 3: Interaction interval for swarm configurations considering the number of robots ($N$), communication range ($C$) and the square-environment length ($L$) given the robot velocity ($v$). The plot reports means and inter-quartile ranges.
  • Figure 4: Message propagation over time for a subset of the various experimental conditions.
  • Figure 5: Parameter $\lambda$ for blending the Logistic and Gompertz as fit across all IVs.