Lyapunov Stability-Driven Control Algorithm for Heterogeneous Multi-Robot Coordination

Recent advancements in autonomous swarm systems have made a pivotal point in robotic science. Utilising a large-scale swarm of simple robots to accomplish complex tasks offers efficient, robust, and reliable solutions inspired by natural phenomena. Although bio-inspired methodologies have presented competent algorithms, those approaches inspired by the physical interactions in viscoelastic materials demonstrate more structured methods to prove the stability and robust performance of the algorithms mathematically. This paper proposes a new viscoelastic swarm algorithm which applies to heterogeneous swarm systems. In this paper, the algorithm development utilises the Lyapunov method to determine stability criteria and corresponding conditions. Therefore, the resulting approach does not rely on complex optimisation to obtain the parameters that guarantee stable performance. In addition to the theoretical framework, a series of Monte Carlo simulations have been conducted to assess the algorithm’s performance and its sensitivity to the key variables. Furthermore, the algorithm’s performance has been evaluated by a series of experiments with real robots to examine the effect of different variables, such as neighbourhood conditions and the stiffness coefficient, on the algorithm’s output. The results obtained from the simulations and experiments demonstrate the stable and bounded performance of the algorithm and how the key variables, such as stiffness coefficient and number of neighbours for each robot, affect the swarm performance. The comparison results, obtained from real-world experiments with a state-of-the-art algorithm, show that the proposed framework significantly reduces the control effort for the robots while improving the swarm behaviour.