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

Davis S. Catherman; Carlo Pinciroli

cs.ROFeb 24, 2026

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

Authors: Davis S. Catherman, Carlo Pinciroli

Organizations: Robotics Engineering, Worcester Polytechnic Institute, Worcester, MA, USA

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.

Figures & tables

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).

Parameter	Default	Parameter Study
$N$	20	{6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50 }
$C$ (m)	10	{6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50 }
$L$ (m)	200	{40, 60, 80, 100, 120, 140, 160, 180, 200, 220 }
$V$ (m/s)	0.05	{0.05 }
Walk	CRW ( $\rho=0.7$ )	$\begin{aligned} \{\hskip 2.84526ptCRW&(\rho=(0.1,0.9,0.1)),\\ LW&(\alpha=(1.4,2.8,0.1)),\\ Hybrid&(\rho=(0.2,0.8,0.2),\alpha=(1.4,2.4,0.2))\hskip 2.84526pt\}\\ \end{aligned}$

Table 1: For CRW, LW, and Hybrid walks, the parameters were studied across a range specified by

(start,stop,step)

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.

Panel of Figure 4 — 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.

Swarm Robotics

Swarm robotics studies how groups of robots coordinate through local sensing, communication, and interaction to accomplish shared tasks.

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A Kinetic Theory of Encounter-Based Information Propagation in Multi-Robot Systems

Alkesh K. Srivastava, Philip Dames

Temple University, Philadelphia, PA, 19122 USA

Multi-Robot Systems Age of Information

Open paper AskPDF arXiv

Multi-robot systems cannot assume persistent network connectivity. We study this problem through target tracking, where performance depends on how quickly target information is sensed, transported through the team, and used before it becomes stale. When robots exchange information only through physical encounters, tracking becomes a kinetic information-transport problem: robot motion induces encounters, encounters carry target-state estimates, information age determines staleness, and stale information produces tracking error. This paper develops a kinetic theory of encounter-based information propagation and identifies three limits. The first is an access limit -- information cannot support team-level coordination unless it spreads beyond the robots that sensed it. The second is a staleness limit -- even propagated information loses value as the target moves. The third is a geometry limit -- when target motion outpaces information transport, tracking error approaches a saturation regime where communication improvements alone have diminishing returns. We evaluate the theory through large-scale simulations varying team size, operating area, communication range, and target speed. Results support the proposed access-staleness-geometry decomposition: communication coverage governs the access transition; once information is accessible, tracking error is shaped by target displacement; and this response is locally linear in restricted regimes but nonlinear over broader ranges because of sensing refreshes and bounded geometry. Across controlled sweeps and joint variation, the derived access and staleness coordinates reliably describe tracking performance. Together, these results establish a kinetic-theoretic framework for predicting and designing encounter-based multi-robot systems.

Abstract

Swarm Robotics

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