To accomplish cooperative tasks, robotic systems are often required to communicate with each other. Thus, maintaining connectivity of the communication graph is a fundamental issue in the field of multi-robot systems. In this paper we present a completely decentralized control strategy for global connectivity maintenance of the communication graph. Considering the disk communication model, we describe a gradient-based control strategy that exploits decentralized estimation of the algebraic connectivity. Unlike previous approaches available in the literature, the proposed control algorithm solves the global connectivity problem in a decentralized manner providing theoretical guarantees, without requiring maintenance of the local connectivity between robotic systems. Moreover, results obtained with simulations and experiments on real robots are described for demonstrating the efficacy of the proposed algorithm.

This study introduces a control algorithm that, exploiting a completely decentralized estimation strategy for the algebraic connectivity of the graph, ensures the connectivity maintenance property for multi robot systems, in the presence of a generic (bounded) additional control term. This result is obtained by driving the robots along the negative gradient of an appropriately defined function of the algebraic connectivity. The proposed strategy is then enhanced with the introduction of the concept of critical robots, that is robots for which the loss of a single communication link might cause the disconnection of the communication graph. Limiting the control action to critical robots will be shown to reduce the control effort that is introduced by the proposed connectivity maintenance control law and to mitigate its effect on the additional (desired) control term.

In modern manufacturing plants, automation is widely adopted in the production phases, which leads to a high level of productivity and efficiency. However, the same level of automation is generally not achieved in logistics, typically performed by human operators and manually driven vehicles. In fact, even though automated guided vehicles (AGVs) have been used for a few decades for goods transportation in industrial environments [1], they do not yet represent a widespread solution and are typically applied only in specific scenarios.

In order to accomplish cooperative tasks, decentralized systems are required to communicate among each other. Thus, maintaining the connectivity of the communication graph is a fundamental issue. Connectivity maintenance has been extensively studied in the last few years, but generally considering undirected communication graphs. In this paper, we introduce a decentralized control and estimation strategy to maintain the strong connectivity property of directed communication graphs. In particular, we introduce a hierarchical estimation procedure that implements power iteration in a decentralized manner, exploiting an algorithm for balancing strongly connected directed graphs. The output of the estimation system is then utilized for guaranteeing preservation of the strong connectivity property. The control strategy is validated by means of analytical proofs and simulation results.