A Distributed Connectivity Maintenance Algorithm With Formal Guarantees for a Communication-Constrained Network of Unmanned Underwater Vehicles

This article presents a distributed connectivity maintenance algorithm for a multiagent system composed of unmanned underwater vehicles (UUVs). We consider a homogeneous network of UUVs that move on a 2-D plane with bounded linear speeds. The time-division multiple-access protocol, which is a commonly used communication protocol for UUVs, is used by the agents in the network to communicate with each other. Due to the communication constraints imposed by the protocol, the agents do not have access to the current positions of their neighbors. This presents a significant challenge in developing a connectivity maintenance algorithm that can be formally verified. Using only local information from an agent’s neighbors, the algorithm provides motion constraints for each agent in the network, which can then be used by each UUV’s motion planner to plan a connectivity-preserving reference trajectory. In addition to providing mathematical proofs expressed in a way that is typical in the systems and control community, we give formal proofs of the results that establish network connectivity for the presented algorithm under suitable assumptions on each agent’s motion planner and controller. The formal proofs are carried out using the KeYmaera X theorem prover, which is an interactive formal verification tool for hybrid systems. This article also highlights the utility of formal verification tools in identifying scenarios that could be overlooked when employing proofs that are not carried out in a formal system for complex distributed algorithms such as the one presented in this article.