Flat Tension Functions and Minimally Rigid Graphs for Tasks of Synchronization and Control of Multi-Agent Robotic Systems

This work focuses on the development of a synchronization and formation control method for multi-agent systems. The method is based on a modified consensus equation, the implementation of minimally rigid graphs and the use of flat tension functions. The goal is to bring a group of agents to a certain formation, and then lead them to a common goal, while avoiding obstacles. The use of minimally rigid graphs makes obstacle avoidance easier, compared to using totally rigid graphs, given the looser constraints for the swarms of robots. Using flat tension functions helps dealing with issues that minimally rigid graphs may present due to the lack of edges in the graphs. As a consequence, agents will keep the formation as closely as possible in the absence of obstacles, and they will adjust their positions and even switch formation if needed, when obstacles are present.