Formation Matrix and Energy-based Control of Multi-Agent Systems
2026-09-03 • Robotics
Robotics
AI summaryⓘ
The authors developed a method to control multiple robots so they move together in a specific pattern without crashing. They treated the connections between robots like springs and dampers, which helps the group keep its shape and avoid collisions. Using advanced math tools like bond graphs and graph theory, they created a model that links the robots’ positions and speeds. They also designed leader-follower setups and analyzed the system’s stability to ensure the formation holds over time. Their ideas were tested with computer simulations showing the approach works in different situations.
multiagent robotic systemsformation controlspring-damper modelbond graphsgraph theoryport-Hamiltonian systemscontrol-by-interconnection (CbI)IDA-PBC theorystability analysisleader-follower control
Authors
Martín Crespo, Sergio Junco, Matías Nacusse
Abstract
This paper presents an energy-based controller for a multiagent robotic system designed to achieve and maintain a specific formation while moving on a plane and avoiding collisions between agents. The controller emulates a network of elementary spring-damper modules connecting pairs of agents. This network, with its de-energized states representing the desired formation, determines the system's dynamics, which is fully encapsulated by a bond graph model. The modeling is further enhanced through the introduction of a formation matrix, using a graph-theoretic approach, that describes both the distances and relative velocities among the agents of the arrangement. This matrix mathematically represents the interconnection and energy-exchange structure of the bond graph, allowing us to put it in correspondence with the control-by-interconnection CbI-scheme of the IDA-PBC theory, facilitating the solution of the formation control problem within the port-Hamiltonian system framework. Furthermore, the paper presents leader-following and position-based formation control systems based on the CbI scheme, including a stability analysis of the corresponding closed-loop systems. The theoretical findings are validated through numerical simulations across various scenarios.