A multi-agent coverage algorithm with connectivity maintenance

Sungjoon Choi, Kyungjae Lee, Songhwai Oh

Abstract: This paper presents a connectivity control algorithm of a multi-agent system. The connectivity of the multi-agent system can be represented by the second smallest eigenvalue λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> of the Laplacian matrix L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> and it is also referred to as algebraic connectivity. Unlike many of the existing connectivity control algorithms which adapt convex optimization technique to maximize algebraic connectivity, we first show that the algebraic connectivity can be maximized by minimizing the weighted sum of distances between the connected agents. We implement a hill-climbing algorithm that minimizes the weighted sum of distances. Semi-definite programming (SDP) is used for computing proper weight ω*. Our proposed algorithm can effectively be mixed with other cooperative applications such as covering an unknown area or following a leader.