Constrained Distributed Algebraic Connectivity Maximization in Robotic Networks

TL;DR

This paper presents a distributed optimization approach for mobile robot networks to enhance their communication connectivity by adjusting positions based on local semi-definite programs, ensuring monotonic improvement.

Contribution

It introduces a novel distributed SDP-based method for maximizing algebraic connectivity in robotic networks, enabling local computations and monotonic connectivity enhancement.

Findings

Distributed SDP approach effectively increases algebraic connectivity.

The method achieves comparable results to centralized solutions.

Adjustable communication load based on local measures improves efficiency.

Abstract

We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We define the Laplacian of the graph as dependent on the pairwise distance between the robots and we approximate the problem as a sequence of Semi-Definite Programs (SDP). We propose a distributed solution consisting of local SDP's which use information only from nearby neighboring robots. We show that the resulting distributed optimization framework leads to feasible subproblems and through its repeated execution, the algebraic connectivity increases monotonically. Moreover, we describe how to adjust the communication load of the robots based on locally computable measures. Numerical simulations show the performance of the algorithm with respect to the centralized solution.