Stigmergic optimal transport

TL;DR

This paper presents a theoretical framework for stigmergic transport in swarms, modeling it as a stochastic optimal control problem where agents collectively minimize traversal time through trail modification, leading to emergent geodesic paths.

Contribution

It introduces a novel stochastic control model for stigmergic transport, explaining emergent path behaviors without centralized control or global knowledge.

Findings

Path straightening in homogeneous environments

Path refraction at material interfaces

Emergence of geodesic trajectories from local interactions

Abstract

Efficient navigation in swarms often relies on the emergence of decentralized approaches that minimize traversal time or energy. Stigmergy, where agents modify a shared environment that then modifies their behavior, is a classic mechanism that can encode this strategy. We develop a theoretical framework for stigmergic transport by casting it as a stochastic optimal control problem: agents (collectively) lay and (individually) follow trails while minimizing expected traversal time. Simulations and analysis reveal two emergent behaviors: path straightening in homogeneous environments and path refraction at material interfaces, both consistent with experimental observations of insect trails. While reminiscent of Fermat's principle, our results show how local, noisy agent+field interactions can give rise to geodesic trajectories in heterogeneous environments, without centralized coordination or global knowledge, relying instead on an embodied slow fast dynamical mechanism.