Distributed control design for formation control of double integrator mutli-agent systems based on graph rigidity

This paper addresses the challenge of controlling the formation of multi-agent system based only on the relative distances between agents obtained individually by local sensors mounted on each autonomous agent in the system. Based on the graph rigidity approach, the inter-agent sensing and communication topology is presented as a rigid graph, and the control model is designed for each agent as a distributed control scheme. This study shows the capability of utilizing graph rigidity in designing distance-based formation control for multi-agent system. It also shows the applicability of the approach to achieve formation control for more complex formations in both two and three-dimensional spaces. To validate the effectiveness and capability of the proposed formation control strategy, three complex formation scenarios are conducted and simulated using MATLAB. These scenarios involve both formation acquisition and maneuvering problems and consider double-integrator multi-agent systems with 5 and 12 agents. The simulation results show the effectiveness of the distance-based formation control based on the graph rigidity, by demonstrating the exponential stability of the controlled system and the convergence of the agents to the desired formation in less than 3 seconds even for a system of 12 agents. The system stability proof is provided using Lyapunov stability theorem. In addition to ensuring system stability, this study shows that the graph rigidity approach implicitly ensures inter-agent collision avoidance.This study demonstrates the effectiveness of using graph rigidity approach in designing formation control of multi-agent system based only on the relative distances between agents, which ensures system stability