Formation tracking of mobile robots based on locally measured relative positions with velocity saturation
Author affiliations
DOI:
https://doi.org/10.15625/0866-7136/23630Keywords:
formation maneuvering, input saturation, multiagent systems, mobile robot, nonlinear stability analysisAbstract
This work addresses the formation tracking of a team of multiple mobile robots subject to nonholonomic constraints and velocity saturation. A leader robot is used that follows a straight line with a constant speed. The other follower robots maintain the formation geometry by regulatingthe desired relative positions to neighboring robots. {The measurement graph of the system is directed and contains a spanning tree rooted at the leader}. Such a task is called formation tracking (or formation maneuvering in some works). The tracking controllers for the follower robots are designed to provide each robot’s reference forward speed and angular rate, \added{with} \replaced{their}{and their} heading angles being estimated based on the robots’ global positions. Asymptotic convergence to the target formation of the system is established. Simulation results and experimental results on formation tracking of mobile robots are provided to support the effectiveness of the proposed controller. A video of the experiment is provided in \url{https://youtu.be/aKNtx02GNHQ}.
Downloads
References
Ahn, H.-S. (2019). Formation Control: Approaches for Distributed Agents. Springer International Publishing. https://doi.org/10.1007/978-3-030-15187-4
Bilello, C., & Bergman, L. A. (2004). Vibration of damaged beams under a moving mass: Theory and experimental validation. Journal of Sound and Vibration, 274(3), 567–582. https://doi.org/10.1016/j.jsv.2003.01.001
Cao, D. S., & Tran, Q. V. (2025). Adaptive path-following control of underactuated surface vessels subject to unknown disturbances with uniform bounded lateral motion. International Journal of Control, Automation and Systems, 23(6), 1641–1651. https://doi.org/10.1007/s12555-024-0916-y
Chen, J., Jayawardhana, B., & de Marina, H. G. (2024). Distributed Distance-based Formation-Motion Control of Unicycle Agents without Orientation Measurements. IEEE Transactions on Control of Network Systems, 1–8. https://doi.org/10.1109/TCNS.2024.3435148
Chen, L., & Cao, M. (2023). Angle Rigidity for Multiagent Formations in 3-D. IEEE Transactions on Automatic Control, 68(10), 6130–6145. https://doi.org/10.1109/TAC.2023.3237799
Chen, L., de Marina, H. G., & Cao, M. (2022). Maneuvering Formations of Mobile Agents Using Designed Mismatched Angles. IEEE Transactions on Automatic Control, 67(4), 1655–1668. https://doi.org/10.1109/TAC.2021.3066388
Chen, L., Xiao, J., Lin, R. C. H., & Feroskhan, M. (2023). Angle-constrained formation maneuvering of unmanned aerial vehicles. IEEE Transactions on Control Systems Technology, 31(4), 1733–1746. https://doi.org/10.1109/TCST.2023.3240286
Do, K. D. (2008). Formation Tracking Control of Unicycle-Type Mobile Robots With Limited Sensing Ranges. IEEE Transactions on Control Systems Technology, 16(3), 527–538. https://doi.org/10.1109/TCST.2007.908214
Doak, P. E. (1964). Notes on the theory of sound. University of Southampton, Institute of Sound and Vibration Research Memorandum ISAV 101.
Fryba, L. (1999). Vibration of solids and structures under moving loads. Thomas Telford.
Khaledyan, M., Liu, T., Fernandez-Kim, V., & de Queiroz, M. (2020). Flocking and Target Interception Control for Formations of Nonholonomic Kinematic Agents. IEEE Transactions on Control Systems Technology, 28(4), 1603–1610. https://doi.org/10.1109/TCST.2019.2914994
Kwon, S.-H., Sun, Z., Anderson, B. D. O., & Ahn, H.-S. (2022). Sign rigidity theory and application to formation specification control. Automatica, 141, 110291. https://doi.org/10.1016/j.automatica.2022.110291
Li, X., Wen, C., Fang, X., & Wang, J. (2022). Adaptive Bearing-Only Formation Tracking Control for Nonholonomic Multiagent Systems. IEEE Transactions on Cybernetics, 52(8), 7552–7562. https://doi.org/10.1109/TCYB.2020.3042491
Lu, K., Dai, S.-L., & Jin, X. (2024). Fixed-Time Rigidity-Based Formation Maneuvering for Nonholonomic Multirobot Systems With Prescribed Performance. IEEE Transactions on Cybernetics, 54(4), 2129–2141. https://doi.org/10.1109/TCYB.2022.3226297
Maghenem, M., Loría, A., & Panteley, E. (2018). A Cascades Approach to Formation-Tracking Stabilization of Force-Controlled Autonomous Vehicles. IEEE Transactions on Automatic Control, 63(8), 2662–2669. https://doi.org/10.1109/TAC.2017.2774003
Ribeiro, P. M. L. (1998). Geometrical non-linear vibration of beams and plates by the hierarchical finite element method [PhD Thesis]. University of Southampton.
Schuck, M., Dahanaggamaarachchi, D. O., Sprenger, B., Vyas, V., Zhou, S., & Schoellig, A. P. (2025). SwarmGPT: Combining Large Language Models with Safe Motion Planning for Drone Swarm Choreography. IEEE Robotics and Automation Letters. https://doi.org/10.1109/LRA.2025.3619745
Sun, G., Zhou, R., Ma, Z., Li, Y., Groß, R., Chen, Z., & Zhao, S. (2023). Mean-shift exploration in shape assembly of robot swarms. Nature Communications, 14(3476). https://doi.org/10.1038/s41467-023-39251-5
Sun, Z., de Marina, H. G., Seyboth, G. S., Anderson, B. D. O., & Yu, C. (2019). Circular Formation Control of Multiple Unicycle-Type Agents With Nonidentical Constant Speeds. IEEE Transactions on Control Systems Technology, 27(1), 192–205. https://doi.org/10.1109/TCST.2017.2763938
Tran, Q. V., & Ahn, H.-S. (2020). Distributed Formation Control of Mobile Agents via Global Orientation Estimation. IEEE Transactions on Control of Network Systems, 4(7), 1654–1664. https://doi.org/10.1109/tcns.2020.2993253
Tran, Q. V., Do, D.-K., & Pham, T.-T. (2025). Formation maneuver of wheeled mobile robots based on attitude estimation. Proceedings of the Fourth International Conference on Material, Machines, and Methods for Sustainable Development, 1–7. https://doi.org/10.1007/978-3-031-96126-7_1
Tran, Q. V., & Kim, J. (2022). Bearing-constrained Formation Tracking Control of Nonholonomic Agents without Inter-agent Communication. IEEE Control Systems Letters, 6, 2401–2406. https://doi.org/10.1109/LCSYS.2022.3159128
Tran, Q. V., Lee, C., Kim, J., & Nguyen, H. Q. (2023). Robust bearing-based formation tracking control of underactuated surface vessels: An output regulation approach. IEEE Transactions on Control of Network Systems, 10(4), 2048–2059. https://doi.org/10.1109/TCNS.2023.3259105
Valizadeh, N., Ghorashi, S. S., Yousefi, H., Bui, T. Q., & Rabczuk, T. (2012). Transient Analysis of Laminated Composite Plates using Isogeometric Analysis. Proceedings of the Eighth International Conference on Engineering Computational Technology.
Vu, H. M., Trinh, M. H., Van Tran, Q., & Ahn, H.-S. (2024). Distance-based formation tracking of single- and double-integrator agents. IEEE Transactions on Automatic Control, 69(2), 1332–1339. https://doi.org/10.1109/TAC.2023.3299817
Yan, L., Ma, B., Jia, Y., & Jia, Y. (2024). Observer-Based Trajectory Tracking Control of Nonholonomic Wheeled Mobile Robots. IEEE Transactions on Control Systems Technology, 32(3), 1114–1121. https://doi.org/10.1109/tcst.2024.3351073
Zhao, S., & Zelazo, D. (2015). Bearing rigidity and almost global bearing-only formation stabilization. IEEE Transactions on Automatic Control, 61(5), 1255–1268. https://doi.org/10.1109/tac.2015.2459191
Downloads
Published
How to Cite
License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.



