Lyapunov Stability-Driven Control Algorithm for Heterogeneous Multi-Robot Coordination
Fatemeh Rekabi Bana, Mazen Bahaidarah, Ognjen Marjanovic, Farshad Arvin
AI summary
Problem
Existing swarm control algorithms either lack formal stability guarantees or require complex optimization, making them unsuitable for large-scale, resource-constrained multi-robot systems. Practical deployment remains hindered by the challenge of ensuring mathematical stability while minimizing computational and control effort.
Approach
The authors model inter-robot interactions using a viscoelastic framework and derive control parameters analytically via Lyapunov stability theory, bypassing numerical optimization while mathematically guaranteeing asymptotic stability and robustness.
Key results
- Distributed viscoelastic coordination algorithm guaranteeing stable tracking of time-varying formations
- Analytical gain-tuning method using Lyapunov functions that eliminates complex parameter optimization
- Proven Input-to-State Stability demonstrating robustness to bounded perturbations and communication delays
- Experimental validation showing reduced control effort and improved swarm behavior versus state-of-the-art methods
Why it matters
Provides a mathematically rigorous, computationally efficient coordination framework for resource-constrained robotic applications like warehouse automation and intelligent transportation.
Abstract
Recent advancements in autonomous swarm sys- tems 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 al- gorithm’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. Note to Practitioners: This paper presents a viscoelastic swarm control algorithm for heterogeneous multi-robot coordination, emphasising stability, robustness, and reduced computational effort. Swarm robotics addresses complex tasks using simple autonomous agents, offering adaptability and resilience. How- ever, practical deployment faces challenges in ensuring sys- tem stability and optimising performance under resource con- straints. The proposed algorithm applies the Lyapunov method for a theoretical stability proof. Its robustness was validated through Monte Carlo simulations and real-world experiments using the Mona robot platform. Key findings demonstrate that increasing stiffness coefficients enhances swarm cohesiveness but may induce fluctuations in alignment, while a larger number of neighbours and scouts improves alignment stability and robustness. Practitioners in automation, robotics, and related fields can benefit from this work by applying the algorithm to distributed systems requiring efficient coordination under uncertain conditions, such as intelligent transportation and warehouse automation. The approach reduces control effort, a critical factor for battery-operated robots, and offers a sys- This work was supported by EU H2020-FET-OPEN RoboRoyale project number 964492. F. Rekabi-Bana and F. Arvin are with the Department of Computer Science, University of Durham, UK. (e-mails: {fatemeh.rekabi-bana, far- shad.arvin}@durham.ac.uk) Mazen Bahaidarah and Ognjen Marjanovic are with the Department of Electrical & Electronic Engineering, University of Manchester, UK. tematic framework for parameter tuning based on interaction graph properties. Future work will extend this framework to dynamic interaction networks, extending applicability to real- world scenarios with time-varying constraints.