CONTROL OF A MULTI-ROBOT SYSTEM BASED ON HIGHER-ORDER SLIDING MODES
Abstract
The article addresses the control problem of a second-order multi-agent robotic system with discrete time under network-induced delays. A novel approach to formation control is proposed, based on higher-order sliding mode control and cloud technologies. The interaction between agents is described using graph theory, where the Laplacian matrix represents the communication channel between agents and the leader. The system dynamics are modeled by motion equations for the position and velocity of each agent. Special attention is paid to the impact of network-induced delays that occur during data transmission from sensors to the controller and from the controller to actuators. A multi-stage state predictor is developed, utilizing prediction methods to compensate for random delays in the network. The proposed control algorithm ensures rapid convergence of the system to the desired formation even in the presence of significant network delays. For each agent, a sliding surface and a reaching law are defined, taking into account multiple timestamps. A detailed stability analysis of the closed-loop system confirms the asymptotic stability of the developed control algorithm. Simulation results in MATLAB demonstrate the high efficiency of the proposed approach: a system consisting of five followers and one leader achieves the desired formation in 10.3 seconds and successfully maintains it despite random network delays. Compared to traditional first-order control methods, the new approach shows significantly improved performance, particularly in reducing chattering effects in control signals. The use of cloud technologies enables efficient real-time processing of large data volumes and implementation of complex prediction algorithms without overloading the local computational resources of the agents. The obtained results confirm the potential of the proposed approach for controlling multi-agent systems under real-world network constraints. The work also demonstrates the feasibility of using prediction methods to compensate for random packet losses and communication delays, ensuring reliable control and communication in dynamic, unpredictable scenarios
References
1. Nazarova A.V., Ryzhova T.P. Metody i algoritmy mul'tiagentnogo upravleniya robototekhnicheskoy sistemoi [Methods and algorithms of multi-agent control of a robotic system], Inzhenernyy zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation], 2012, No. 6 (6), pp. 93-105.
2. Naserian M., Ramazani A., Khaki A., Moarefianpour A. Leader–follower consensus control for a non-linear multi-agent robot system with input saturation and external disturbance, Systems Science & Con-trol Engineering, 2021, Vol. 9 (1), pp. 260-271.
3. Xiong F., Zhang Y., Kuang X., He L., Han X. Multi-agent dual actor-critic framework for reinforcement learning navigation, Applied Intelligence, 2024, Vol. 55 (2). pp. 104-124.
4. Ahmed S., Karsiti M., Loh R. Multiagent Systems, InTech, 2009, pp. 428.
5. Mousavi A., Davaie Markazi A. H. A new control method for leader-follower consensus problem of uncertain constrained nonlinear multi-agent systems, Journal of the Franklin Institute, 2024, Vol. 361 (9).
6. Behera L., Rybak L., Malyshev D.I., Khalapyan S. Numerical simulation of the workspace of robots with moving bases in the multi-agent system, Procedia Computer Science, 2021, Vol. 186 (6),
pp. 431-439.
7. Nandanwar A., Dhar N.K., Malyshev D., Rybak L., Behera L. Finite-Time Robust Admissible Consen-sus Control of Multirobot System under Dynamic Events, IEEE Systems Journal, 2021, Vol. 15 (1), pp. 780-790.
8. Kim J. Three-dimensional multi-robot control to chase a target while not being observed, International Journal of Advanced Robotic Systems, 2019, Vol. 16 (1), pp. 1-11.
9. Azid S., Raghuwaiya K., Javed A., Kumari E. Autonomous Leader–Follower Formation of Vehicular Robots Using the Lyapunov Method, Unmanned Systems, 2022, Vol. 12 (01), pp. 75-85.
10. Yang H., Li S., Yang L., Ding Z. Leader-Following Consensus of Fractional-Order Uncertain Multi-Agent Systems with Time Delays, Neural Processing Letters, 2022, Vol. 54 (6), pp. 4829-4849.
11. Chen B., Qi X., Li C., Qi X., Ma H. Observer-Based Distributed Adaptive Consensus Tracking of Non-linear Multi-agent Systems on Directed Graphs, IEEE Access, 2022, Vol. PP (99), pp. 1-1.
12. Ma J., Sun D., Haibo J., Feng G. Leader-following consensus of multi-agent systems with limited data rate, Journal of the Franklin Institute, 2016, Vol. 354 (1), pp. 184-196.
13. Kim J. Three dimensional motion camouflage guidance utilizing multiple leaders and one interceptor, IET Radar, Sonar & Navigation, 2021, Vol. 16 (3), pp. 617-631.
14. Ramachandran R., Fronda N., Preiss J., Dai Z., Sukhatme G. Resilient Multi-Robot Multi-Target Tracking, IEEE Transactions on Automation Science and Engineering, 2024, Vol. 21 (3), pp. 1-17.
15. Rehak B., Lynnyk A., Lynnyk V. Synchronization of Multi-Agent Systems Composed of Second-Order Underactuated Agents, Mathematics, 2024, Vol. 12 (21), pp. 3424.
16. Kou L., Huang Y., Zuo G., Jian L., Dou Y. Fixed‐time rotating consensus control of second‐order mul-ti‐agent systems, International Journal of Robust and Nonlinear Control, 2024, Vol. 34 (18),
pp. 12031-12049.
17. Chen J., Yang Y., Qin S. A Distributed Optimization Algorithm for Fixed-Time Flocking of Second-Order Multiagent Systems, IEEE Transactions on Network Science and Engineering, 2023, Vol. 11 (1), pp. 152-162.
18. Yin Y, Shi Y, Liu F, [et al.]. Second-order consensus for heterogeneous multi-agent systems with input constraints, Neurocomputing, 2019, Vol. 351, pp. 43–50.
19. Nataliia Y., Zababurin K. Matrix Laplace transform, Boletín de la Sociedad Matemática Mexicana, 2023, Vol. 29 (3), pp. 1-21.
20. Olson N., Andrews J. A Matrix Exponential Generalization of the Laplace Transform of Poisson Shot Noise, IEEE Transactions on Information Theory, 2024, Vol. 71 (1), pp. 396-412.
21. Bouchenak A., Horani M. Al H., Younis J. [et al.]. Fractional Laplace transform for matrix valued func-tions with applications, Arab Journal of Basic and Applied Sciences, 2022, Vol. 29 (1), pp. 330-336.
22. Rani D., Mishra V. Laplace Transform Inversion using Bernstein Operational Matrix of Integration and its Application to Differential and Integral Equations, Proceedings Mathematical Sciences, 2020, Vol. 130 (1), pp. 60-89.
