Potential Fields for Maintaining Connectivity of Mobile Networks

TLDR

Controlling mobile multi‑agent networks presents novel challenges in shaping the dynamic graph structure. The study aims to design control strategies that maintain network connectivity during agent motion. The authors formulate connectivity as differentiable constraints derived from Laplacian dynamics and employ artificial potential fields to steer agents away from disconnection while preventing collisions. The paper demonstrates that various tasks can be performed while enforcing connectivity constraints.

Abstract

The control of mobile networks of multiple agents raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In this paper, we consider the problem of controlling a network of agents so that the resulting motion always preserves the connectivity property of the network. In particular, the connectivity condition is translated to differentiable constraints on individual agent motion by considering the dynamics of the Laplacian matrix and its spectral properties. Artificial potential fields are then used to drive the agents to configurations away from the undesired space of disconnected networks while avoiding collisions with each other. We conclude by illustrating a class of interesting problems that can be achieved while preserving connectivity constraints.