Lyapunov Stability-Driven Control Algorithm for Heterogeneous Multi-Robot Coordination (I)

Abstract

Recent advancements in autonomous swarm systems mark a pivotal point in robotic science. Using a large-scale swarm of simple robots for complex tasks offers efficient, robust, and reliable solutions, inspired by natural phenomena. While bio-inspired methods are effective, approaches inspired by physical interactions in viscoelastic materials offer more structured ways to prove stability and robust performance mathematically. This paper proposes a new viscoelastic swarm algorithm applicable to heterogeneous swarm systems. The algorithm's development utilises the Lyapunov method to determine stability criteria and conditions, thereby avoiding reliance on complex optimisation to ensure stable performance parameters. A series of Monte Carlo simulations assessed the algorithm's performance and sensitivity to key variables. Furthermore, experiments with real robots evaluated the effects of variables like neighbourhood conditions and the stiffness coefficient on the algorithm's output. The results from simulations and experiments demonstrate the algorithm's stable, bounded performance and show how key variables, such as the stiffness coefficient and the number of neighbours, influence swarm performance. In real-world experiments, the proposed framework significantly reduces the robots' control effort while improving swarm behaviour, compared with a state-of-the-art algorithm.