Safe Formation Tracking Control for Multi-Agent Euler-Lagrange Systems in Environments With Static and Dynamic Obstacles

Wei Cui; Yikang Yang; Yuxuan Guo; Ye Cao; Yongduan Song; Frank L. Lewis

doi:10.1109/JAS.2026.126038

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 18.3, Top 1 (SCI Q1)

CiteScore: 28.2, Top 1% (Q1)
Google Scholar h5-index: 95， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > In Press, Accepted Manuscript

W. Cui, Y. Yang, Y. Guo, Y. Cao, Y. Song, and F. L. Lewis, “Safe formation tracking control for multi-agent Euler-lagrange systems in environments with static and dynamic obstacles,” IEEE/CAA J. Autom. Sinica, early access, 2026. doi: 10.1109/JAS.2026.126038

Citation:

W. Cui, Y. Yang, Y. Guo, Y. Cao, Y. Song, and F. L. Lewis, “Safe formation tracking control for multi-agent Euler-lagrange systems in environments with static and dynamic obstacles,” IEEE/CAA J. Autom. Sinica, early access, 2026. doi: 10.1109/JAS.2026.126038

Citation:

W. Cui, Y. Yang, Y. Guo, Y. Cao, Y. Song, and F. L. Lewis, “Safe formation tracking control for multi-agent Euler-lagrange systems in environments with static and dynamic obstacles,” IEEE/CAA J. Autom. Sinica, early access, 2026. doi: 10.1109/JAS.2026.126038

PDF( 3225 KB)

Safe Formation Tracking Control for Multi-Agent Euler-Lagrange Systems in Environments With Static and Dynamic Obstacles

doi: 10.1109/JAS.2026.126038

Funds: This work was supported in part by the National Natural Science Foundation of China (62573340), the National Science and Technology Major Projects (2025ZD0805901), and the Natural Science Foundation of Chongqing (CSTB2023NSCQ-LZX0026)

More Information

Author Bio:
Wei Cui received the B.S. degree in nuclear engineering and technology and the M.S. and Ph.D. degrees in control science and engineering from Xi’an Jiaotong University in 2018, 2020, and 2025, respectively. She is currently a Lecturer with the College of Intelligent Systems Science and Engineering, Harbin Engineering University. Her research interests include distributed task allocation, control systems and applications

Yikang Yang received the B.S., M.S., and Ph.D. degrees in electronic engineering from Xi’an Jiaotong University in 1996, 1999, and 2003, respectively. He is currently a Professor with the School of Automation Science and Engineering, Xi’an Jiaotong University. His research interests include satellite navigation, intersatellite link, spacecraft telemetry, tracking, and command (TT&C), and signal processing

Yuxuan Guo received his B.S. degree in Engineering from Xi’an Jiaotong University in 2024. He is currently pursuing his M.S. degree at the School of Automation Science and Engineering, Xi’an Jiaotong University. His research interests include space traffic management, orbital perturbation evolution, and physics-informed neural networks

Ye Cao received the M.S. degree in applied mathematics from Shaanxi Normal University in 2016, and the Ph.D. degree in control theory and control engineering from Chongqing University in 2020. She was a Visiting Scholar with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, from 2019 to 2020. She is currently an Associate Professor with the School of Automation Science and Engineering, Xi’an Jiaotong University. Her research interests include control systems and applications, autonomous robotic systems, cyber-physical systems, complex systems, and networks. Dr. Cao was awarded the Young Talents Lifting Project by the China Association for Science and Technology (CAST). She currently serves as an Associate Editor for the Journal of Automation and Intelligence

Yongduan Song (Fellow, IEEE) received the Ph.D. degree in electrical and computer engineering from Tennessee Technological University, Cookeville, USA, in 1992. He was a tenured Full Professor with North Carolina A&T State University, Greensboro, USA, from 1993 to 2008 and a Langley Distinguished Professor with the National Institute of Aerospace (NIA), Hampton, VA, USA, from 2005 to 2008. He is currently the Dean of School of Automation, Chongqing University, and the Founding Director of the Institute of Smart Systems and Renewable Energy, Chongqing University. He was one of the six Langley Distinguished Professors and the Founding Director of Cooperative Systems with NIA. His research interests include intelligent systems, guidance navigation and control, bio-inspired adaptive and cooperative systems, rail traffic control and safety, and smart grids. He has received several competitive research awards from the National Science Foundation, the National Aeronautics and Space Administration, the U.S. Air Force Office, the U.S. Army Research Office, and the U.S. Naval Research Office. He has served as an associate editor/guest editor for several prestigious scientific journals

Frank L. Lewis (Life Fellow, IEEE) received the bachelor’s degree in physics/electrical engineering and the M.S.E.E. degree in electrical engineering from Rice University, Houston, TX, USA, in 1971, the M.S. degree in aeronautical engineering from the University of West Florida, Pensacola, FL, USA, in 1977, and the Ph.D. degree in electrical engineering from Georgia Institute of Technology, Atlanta, GA, USA, in 1981. He is currently a Distinguished Scholar Professor and Distinguished Teaching Professor with the University of Texas at Arlington, Fort Worth, TX, USA, the Moncrief-O’Donnell Chair of the University of Texas at Arlington Research Institute, Fort Worth, where he is involved in feedback control, intelligent systems, cooperative control systems, and nonlinear systems. He has authored six U.S. patents, numerous journal special issues, journal papers, and 20 books, including Optimal Control, Aircraft Control, Optimal Estimation, and Robot Manipulator Control. Prof. Lewis is a member of the National Academy of Inventors, a Fellow of the International Federation of Automatic Control and the Institute of Measurement and Control, U.K., a Texas Board of Professional Engineer, a U.K. Chartered Engineer, and a Founding Member of the Board of Governors of the Mediterranean Control Association. He was a recipient of the Fulbright Research Award, the NSF Research Initiation Grant, the Terman Award from the American Society for Engineering Education, the Gabor Award from the International Neural Network Society, the Honeywell Field Engineering Medal from the Institute of Measurement and Control, U.K., the Neural Networks Pioneer Award from IEEE Computational Intelligence Society, the Outstanding Service Award from the Dallas IEEE Section, and the Texas Regents Outstanding Teaching Award in 2013. He was elected as the Engineer of the Year by the Fort Worth IEEE Section. He was listed in the Fort Worth Business Press Top 200 Leaders in Manufacturing
Corresponding author: Ye Cao, e-mail: caoye62@126.com
Received Date: 2025-12-08
Revised Date: 2026-02-06
Accepted Date: 2026-03-25

Available Online: 2026-10-09

Abstract

Abstract

Existing studies primarily address obstacle avoidance at the trajectory planning level and often neglect the subsequent tracking stage. However, inevitable tracking errors can still cause collisions even when the planned trajectory is deemed safe. This paper develops a safe formation-tracking control scheme for multi-agent Euler-Lagrange (EL) systems operating among multiple obstacles, resolving conflicts between formation tracking and collision avoidance. The obstacles considered include other agents, borders, enclosed static obstacles, and moving obstacles with unknown velocities. We propose an adaptive, distributed method that ensures collision avoidance while achieving asymptotic formation tracking. The key features are: i) it requires neither pre-acquired obstacle maps nor precise obstacle-velocity information; ii) unsafe reference trajectories are modified online based on locally sensed data to reconcile tracking and safety; and iii) integral barrier functions enter as multiplicative gains in the virtual control law, together with adaptive estimation of upper bounds on velocity-related terms, yielding safe formation tracking.
- Collision avoidance,
- Euler-Lagrange systems,
- formation tracking,
- moving obstacles,
- multi-agent systems,
- prescribed-time observer

FullText(HTML)

References(39)

References

[1]	L. An, G.-H. Yang, C. Deng, and C. Wen, “Event-triggered reference governors for collisions-free leader-following coordination under unreliable communication topologies,” IEEE Trans. Autom. Control, vol. 69, no. 4, pp. 2116–2130, Apr. 2024. doi: 10.1109/TAC.2023.3291654
[2]	L. Liu, Y. Huang, and C. Deng, “Accelerated distributed cooperative energy management for integrated energy systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 12, pp. 2589–2601, Dec. 2025. doi: 10.1109/jas.2025.125489
[3]	X. Hou, X. Li, S. Zhao, Y. Zhang, and L. Wang, “High-precision Bi-directional beam-pointing measurement method based on space solar power station system,” Sensors, vol. 24, no. 18, Art. no. 6135, Sep. 2024. doi: 10.3390/s24186135
[4]	C.-C. Wang, Y.-L. Wang, and L. Jia, “Multi-USV formation collision avoidance via deep reinforcement learning and COLREGs,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 11, pp. 2349–2351, Nov. 2024. doi: 10.1109/JAS.2023.123846
[5]	H. Ma, M. Chen, and Q. Wu, “Disturbance observer-based safe tracking control for unmanned helicopters with partial state constraints and disturbances,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2056–2069, Nov. 2023. doi: 10.1109/JAS.2022.105938
[6]	Y. Cao, Y. Song, and C. Wen, “Practical tracking control of perturbed uncertain nonaffine systems with full state constraints,” Automatica, vol. 110, Art. no. 108608, Dec. 2019. doi: 10.1016/j.automatica.2019.108608
[7]	L. Xue, X. Li, W. Wu, Z. Zhang, and H. Li, “A parallel composite pseudo-noise code for deep space ranging,” IEEE Commun. Lett., vol. 26, no. 4, pp. 872–876, Apr. 2022. doi: 10.1109/LCOMM.2021.3125325
[8]	S. J. Yoo and B. S. Park, “Distributed adaptive formation tracking for a class of uncertain nonlinear multiagent systems: Guaranteed connectivity under moving obstacles,” IEEE Trans. Cybern., vol. 54, no. 6, pp. 3431–3443, Jun. 2024. doi: 10.1109/TCYB.2023.3265405
[9]	H. Zhang, J. Huo, Y. Huang, J. Cheng, and X. Li, “Perception-aware-based UAV trajectory planner via generative adversarial self-imitation learning from demonstrations,” IEEE Internet Things J., vol. 12, no. 3, pp. 3248–3260, Feb. 2025. doi: 10.1109/JIOT.2024.3477450
[10]	H. Zhang, J. Huo, Y. Huang, and D. Wang, “Perception-aware based quadrotor translation and yaw angle planner in unpredictable dynamic situations,” IEEE Trans. Aerosp. Electron. Syst., vol. 61, no. 1, pp. 47–60, Feb. 2025. doi: 10.1109/TAES.2024.3439673
[11]	A. Naderolasli and H. Shirzadfar, “Different applications of the gyroscope sensors data fusion in distinctive systems: An extended Kalman filter approach,” Comp. y Sist., vol. 28, no. 1, pp. 189–196, Jun. 2024. doi: 10.13053/cys-28-1-4308
[12]	Q. Zhang, S. Wu, Y. Jia, Y. Xu, and J. Liu, “Improve computing efficiency and motion safety by analyzing environment with graphics,” IEEE Trans. Autom. Sci. Eng., vol. 21, no. 3, pp. 4613–4626, Jul. 2024. doi: 10.1109/TASE.2023.3299962
[13]	N. Malone, H.-T. Chiang, K. Lesser, M. Oishi, and L. Tapia, “Hybrid dynamic moving obstacle avoidance using a stochastic reachable set-based potential field,” IEEE Trans. Rob., vol. 33, no. 5, pp. 1124–1138, Oct. 2017. doi: 10.1109/TRO.2017.2705034
[14]	Y. Wan, Y. Zhong, A. Ma, and L. Zhang, “An accurate UAV 3-D path planning method for disaster emergency response based on an improved multiobjective swarm intelligence algorithm,” IEEE Trans. Cybern., vol. 53, no. 4, pp. 2658–2671, Apr. 2023. doi: 10.1109/TCYB.2022.3170580
[15]	W. Xiao and C. Belta, “High-order control barrier functions,” IEEE Trans. Autom. Control, vol. 67, no. 7, pp. 3655–3662, Jul. 2022. doi: 10.1109/TAC.2021.3105491
[16]	Z. Peng, D. Wang, T. Li, and M. Han, “Output-feedback cooperative formation maneuvering of autonomous surface vehicles with connectivity preservation and collision avoidance,” IEEE Trans. Cybern., vol. 50, no. 6, pp. 2527–2535, Jun. 2020. doi: 10.1109/TCYB.2019.2914717
[17]	H. Wang, J. Peng, F. Zhang, and Y. Wang, “High-order control barrier function-based safety control of constrained robotic systems: An augmented dynamics approach,” IEEE/CAA J. Autom. Sinica, vol. 11, pp. 2487–2496, Dec. 2024. doi: 10.1109/jas.2024.124524
[18]	A. Naderolasli, K. Shojaei, and A. Chatraei, “Platoon formation control of autonomous underwater vehicles under LOS range and orientation angles constraints,” Ocean Eng., vol. 271, Art. no. 113674, Mar. 2023. doi: 10.1016/j.oceaneng.2023.113674
[19]	A. Naderolasli, K. Shojaei, and A. Chatraei, “Terminal sliding-mode disturbance observer-based finite-time adaptive-neural formation control of autonomous surface vessels under output constraints,” Robotica, vol. 41, no. 1, pp. 236–258, Jan. 2023. doi: 10.1017/S0263574722001266
[20]	C. K. Verginis and D. V. Dimarogonas, “Closed-form barrier functions for multi-agent ellipsoidal systems with uncertain Lagrangian dynamics,” IEEE Control Syst. Lett., vol. 3, no. 3, pp. 727–732, Jul. 2019. doi: 10.1109/LCSYS.2019.2917822
[21]	X. Xue, X. Yue, and J. Yuan, “Connectivity preservation and collision avoidance control for spacecraft formation flying in the presence of multiple obstacles,” Adv. Space Res., vol. 67, no. 11, pp. 3504–3514, Jun. 2021. doi: 10.1016/j.asr.2020.05.036
[22]	X. Liu, S. S. Ge, and C.-H. Goh, “Formation potential field for trajectory tracking control of multi-agents in constrained space,” Int. J. Control, vol. 90, no. 10, pp. 2137−2151, 2017.
[23]	S. S. Ge, X. Liu, C.-H. Goh, and L. Xu, “Formation tracking control of multiagents in constrained space,” IEEE Trans. Control Syst. Technol., vol. 24, no. 3, pp. 992–1003, May 2016. doi: 10.1109/TCST.2015.2472959
[24]	C. Li and H. G. Tanner, “Navigation functions with time-varying destination manifolds in star worlds,” IEEE Trans. Rob., vol. 35, no. 1, pp. 35–48, Feb. 2019. doi: 10.1109/TRO.2018.2875421
[25]	L. An, G.-H. Yang, and S. Wasly, “Obstacle avoidance in distributed optimal coordination of multirobot systems: A trajectory planning and tracking strategy,” IEEE Trans. Control Network Syst., vol. 11, no. 3, pp. 1335–1344, Sep. 2024. doi: 10.1109/TCNS.2023.3337715
[26]	L. Zhang and G.-H. Yang, “Secure adaptive trajectory tracking control for nonlinear robot systems under multiple dynamic obstacles: Safety barrier certificates,” IEEE Trans. Ind. Electron., vol. 69, no. 11, pp. 11549–11559, Nov. 2022. doi: 10.1109/TIE.2021.3123641
[27]	A. Naderolasli, K. Shojaei, and A. Chatraei, “Fixed-time multilayer neural network-based leader-follower formation control of autonomous surface vessels with limited field-of-view sensors and saturated actuators,” Neural Comput. Appl., vol. 37, no. 21, pp. 16071–16091, Jul. 2025. doi: 10.1007/s00521-024-10575-7
[28]	D. Li, W. Zhang, W. He, C. Li, and S. S. Ge, “Two-layer distributed formation-containment control of multiple Euler-Lagrange systems by output feedback,” IEEE Trans. Cybern., vol. 49, no. 2, pp. 675–687, Feb. 2019. doi: 10.1109/TCYB.2017.2786318
[29]	P. Lu, H. Wang, F. Zhang, W. Yu, and G. Chen, “Formation control of nonholonomic mobile robots using distributed estimators,” IEEE Trans. Circ. Syst. II: Express Briefs, vol. 67, no. 12, pp. 3162–3166, Dec. 2020. doi: 10.1109/chicc.2006.4347420
[30]	Y. Cao, W. Ren, and Z. Meng, “Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking,” Syst. Control Lett., vol. 59, no. 9, pp. 522–529, Sep. 2010. doi: 10.1016/j.sysconle.2010.06.002
[31]	A. Naderolasli, “Indirect self-tuning controller for a two degree of freedom tracker model,” Int. J. Veh. Auton. Syst., vol. 16, no. 1, pp. 15–37, Sep. 2021. doi: 10.1504/ijvas.2021.118028
[32]	L. An and G.-H. Yang, “Collisions-free distributed optimal coordination for multiple Euler-Lagrangian systems,” IEEE Trans. Autom. Control, vol. 67, no. 1, pp. 460–467, Jan. 2022. doi: 10.1109/TAC.2021.3079284
[33]	D. Li, S. Sam Ge, G. Ma, W. He, J. Mei, and W. Zhang, “Formation-containment control of networked collision-free Lagrangian systems,” Int. J. Robust Nonlin.Control, vol. 30, no. 6, pp. 2399–2412, Apr. 2020.
[34]	X. Li, L. Wang, and Y. Zhang, “Distributed continuous-time containment control of heterogeneous multiagent systems with nonconvex control input constraints,” Complexity, vol. 2022, Art. no. 7081091, Apr. 2022. doi: 10.1155/2022/7081091
[35]	Y. Zhang, X. Li, and L. Wang, “Distributed H_∞ consensus of heterogeneous multi-agent systems with nonconvex constraints,” ISA Trans., vol. 131, pp. 160–166, Dec. 2022. doi: 10.1016/j.isatra.2022.05.007
[36]	Y. Cao, J. Cao, and Y. Song, “Practical prescribed time control of Euler-Lagrange systems with partial/full state constraints: A settling time regulator-based approach,” IEEE Trans. Cybern., vol. 52, no. 12, pp. 13096–13105, Dec. 2022. doi: 10.1109/TCYB.2021.3100764
[37]	D. Li, G. Ma, Y. Xu, W. He, and S. S. Ge, “Layered affine formation control of networked uncertain systems: A fully distributed approach over directed graphs,” IEEE Trans. Cybern., vol. 51, no. 12, pp. 6119–6130, Dec. 2021. doi: 10.1109/TCYB.2020.2965657
[38]	Y. Wang, Y. Song, D. J. Hill, and M. Krstic, “Prescribed-time consensus and containment control of networked multiagent systems,” IEEE Trans. Cybern., vol. 49, no. 4, pp. 1138–1147, Apr. 2019. doi: 10.1109/TCYB.2017.2788874
[39]	M. M. Polycarpou, “Stable adaptive neural control scheme for nonlinear systems,” IEEE Trans. Autom. Control, vol. 41, no. 3, pp. 447–451, Mar. 1996. doi: 10.1109/9.486648

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(10) / Tables(1)

Get Citation

PDF

XML

Article Metrics

Article views (46) PDF downloads(17)

Safe Formation Tracking Control for Multi-Agent Euler-Lagrange Systems in Environments With Static and Dynamic Obstacles

doi: 10.1109/JAS.2026.126038

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content