Advanced Leader-Follower Control Strategies: Integrating Adaptation Laws with Model Predictive Control

Abstract

This article investigates the intricate dynamics of the leader-follower problem within the framework of model predictive control (MPC). The study focuses on a scenario where a leader, characterized by a differential dynamic model, is diligently followed by a follower vehicle with a distinct differential dynamic model. The follower has full access to the leader's state information, facilitating real-time informed decision-making. A novel adaptation law is introduced to adjust the weighting matrix of the MPC controller, ensuring the follower approaches the leader in the tangent plane manifold by prioritizing the heading angle error. The control strategy is designed to synchronize the follower's trajectory with that of the leader, which performs various maneuvers such as lane changes, abrupt heading angle alterations, and sudden shifts in linear velocity. The leader-follower formation control problem is thoroughly investigated across diverse scenarios, including straight-line movements, circular trajectories, and intricate S-shaped paths. Comprehensive analysis demonstrates the effectiveness of MPC and the proposed adaptation law in achieving precise and adaptable formation control, significantly enhancing the understanding of leader-follower dynamics under varying conditions. This research contributes to the field by offering a robust solution for precise and reliable formation control in dynamic environments, showcasing the potential of MPC in autonomous systems.

Keywords

• Adaptation Law
• Leader-Follower
• MPC
• Optimal Control

References

1. [1] Macit, E., Vural, A., "Modelling and simulation of 1 MW grid-connected PV system regulated by sliding mode control, model predictive control, and PI control", Gazi University Journal of Science, 35(4): 1433–1452, (2022). DOI: https://doi.org/10.35378/gujs.899799
2. [2] Naregalkar, A., Subbulekshmi, D., "Least square support vector machines Laguerre Hammerstein model identification and non-linear model predictive controller design for pH neutralization process", Gazi University Journal of Science, 36(1): 80–94, (March 2023). DOI: https://doi.org/10.35378/gujs.798451
3. [3] Franze, G., Lucia, W., Tedesco, F., Scordamaglia, V., "A distributed obstacle avoidance MPC strategy for leader-follower formations", IFAC Proceedings Volumes, 47(3): 2570–2575, (2014). DOI: https://doi.org/10.3182/20140824-6-ZA-1003.01481
4. [4] Franze, G., Lucia, W., Tedesco, F., "A distributed model predictive control scheme for leader-follower multi-agent systems", International Journal of Control, 91(2): 369–382, (2018). DOI: https://doi.org/10.1080/00207179.2017.1282178
5. [5] Xiao, H., Li, Z., Chen, C. P., "Formation control of leader–follower mobile robots systems using model predictive control based on neural-dynamic optimization", IEEE Transactions on Industrial Electronics, 63(9): 5752–5762, (2016). DOI: https://doi.org/10.1109/TIE.2016.2542788
6. [6] Zhao, W., Go, T. H., "Quadcopter formation flight control combining MPC and robust feedback linearization", Journal of the Franklin Institute, 351(3): 1335–1355, (2014). DOI: https://doi.org/10.1016/j.jfranklin.2013.10.021
7. [7] Kuriki, Y., Namerikawa, T., "Formation control with collision avoidance for a multi-UAV system using decentralized MPC and consensus-based control", SICE Journal of Control, Measurement, and System Integration, 8(4): 285–294, (2015). DOI: https://doi.org/10.9746/jcmsi.8.285
8. [8] Yan, C., Fang, H., Chao, H., "Energy-aware leader-follower tracking control for electric-powered multi-agent systems", Control Engineering Practice, 79: 209–218, (2018). DOI: https://doi.org/10.1016/j.conengprac.2018.07.013

9. [9] He, D., Qiu, T., Luo, R., "Fuel efficiency-oriented platooning control of connected nonlinear vehicles: a distributed economic MPC approach", Asian Journal of Control, 22(4): 1628–1638, (2020). DOI: https://doi.org/10.1002/asjc.2049
10. [10] Lin, S., Jia, R., Yue, M., Xu, Y., "On composite leader–follower formation control for wheeled mobile robots with adaptive disturbance rejection", Applied Artificial Intelligence, 33(14): 1306–1326, (2019). DOI: https://doi.org/10.1080/08839514.2019.1685182
11. [11] Ma, L., Zhu, F., Zhang, J., Zhao, X. "Leader–follower asymptotic consensus control of multi-agent systems: An observer-based disturbance reconstruction approach", IEEE Transactions on Cybernetics, 53(2):1311–1323, (2021). DOI: https://doi.org/10.1109/TCYB.2021.3125332
12. [12] Qian, Z., Lyu, W., Dai, Y., Xu, J. "A consensus-based model predictive control with optimized line-of-sight guidance for formation trajectory tracking of autonomous underwater vehicles", Journal of Intelligent & Robotic Systems, 106(1):15, (2022). DOI: https://doi.org/10.1007/s10846-022-01710-4
13. [13] Xu, T., Liu, J., Zhang, Z., Chen, G., Cui, D., Li, H. "Distributed MPC for trajectory tracking and formation control of multi-UAVs with leader-follower structure", IEEE Access, (2023). DOI: https://doi.org/10.1109/ACCESS.2023.3329232
14. [14] Franze, G., Lucia, W., Venturino, A., "A distributed model predictive control strategy for constrained multi-vehicle systems moving in unknown environments", IEEE Transactions on Intelligent Vehicles, 6(2): 343–352, (2020). DOI: https://doi.org/10.1109/TIV.2020.3029746
15. [15] Pereira, P., Guerreiro, B. J., Lourenço, P., "Distributed model predictive control method for spacecraft formation flying in a leader-follower formation", IEEE Transactions on Aerospace and Electronic Systems, 59(3): 3213–3223, (2022). DOI: https://doi.org/10.1109/TAES.2022.3224692
16. [16] Sun, X., Wang, G., Fan, Y., Mu, D., Qiu, B., "A formation collision avoidance system for unmanned surface vehicles with leader-follower structure", IEEE Access, 7: 24691–24702, (2019). DOI: https://doi.org/10.1109/ACCESS.2019.2900280
17. [17] Li, Z., Yuan, Y., Ke, F., He, W., Su, C.-Y., "Robust vision-based tube model predictive control of multiple mobile robots for leader–follower formation", IEEE Transactions on Industrial Electronics, 67(4): 3096–3106, (2019). DOI: https://doi.org/10.1109/TIE.2019.2913813
18. [18] Ferraz, H., Hespanha, J. P., "Iterative algorithms for distributed leader-follower model predictive control", in 2019 IEEE 58th Conference on Decision and Control (CDC), IEEE, 3533–3539, (2019). DOI: https://doi.org/10.1109/CDC40024.2019.9029618
19. [19] Lim, H., Kang, Y., Kim, J., Kim, C., "Formation control of leader following unmanned ground vehicles using nonlinear model predictive control", in 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, IEEE, 945–950, (2009). DOI: https://doi.org/10.1109/AIM.2009.5229887