Adaptive sliding mode formation control for space interferometer missions
Authors
Mauro Mancini, Giulia Alessandra Tataru, Satoshi Satoh, Elisa Capello
Abstract
This paper addresses high-precision formation control for spacecraft operating in low Earth orbit, motivated by the requirements of future space interferometry missions such as SILVIA. The proposed approach formulates the relative dynamics within a port-Hamiltonian framework and introduces an Adaptive Boundary-layer Sliding Mode Control (AB-SMC) law to overcome the limitations of conventional SMC with constant gains. The key innovation lies in a dynamic, error-dependent adjustment of the sliding manifold, enhancing transient performance while guaranteeing high-precision trajectory tracking. Rigorous Lyapunov-based analysis establishes explicit ultimate bounds on the tracking error and ensures closed-loop stability, while extensive Monte Carlo simulations further validate the proposed AB-SMC compared to standard control approaches. Results show that AB-SMC achieves faster convergence, lower control effort, and sub-millimeter tracking accuracy, demonstrating its practical robustness and implementation feasibility in realistic, uncertain orbital environments while respecting low-thrust constraints.
Keywords
aerospace, control of multi satellite systems, guidance, navigation and control of aircraft and spacecraft
Citation
- Journal: Control Engineering Practice
- Year: 2026
- Volume: 174
- Issue:
- Pages: 107025
- Publisher: Elsevier BV
- DOI: 10.1016/j.conengprac.2026.107025
BibTeX
@article{Mancini_2026,
title={{Adaptive sliding mode formation control for space interferometer missions}},
volume={174},
ISSN={0967-0661},
DOI={10.1016/j.conengprac.2026.107025},
journal={Control Engineering Practice},
publisher={Elsevier BV},
author={Mancini, Mauro and Tataru, Giulia Alessandra and Satoh, Satoshi and Capello, Elisa},
year={2026},
pages={107025}
}References
- Ahn, (2020)
- Bai, (2011)
- Bakhtiari M, Panahyazdan A, Abbasali E (2025) Finite-Time Control for Satellite Formation Reconfiguration and Maintenance in LEO: A Nonlinear Lyapunov-Based SDDRE Approach. Aerospace 12(3):201. https://doi.org/10.3390/aerospace1203020 – 10.3390/aerospace12030201
- Boiko, (2009)
- Min-Shin Chen, Yean-Ren Hwang, Tomizuka M (2002) A state-dependent boundary layer design for sliding mode control. IEEE Trans Automat Contr 47(10):1677–1681. https://doi.org/10.1109/tac.2002.80353 – 10.1109/tac.2002.803534
- D’Amico S, Montenbruck O (2006) Proximity Operations of Formation-Flying Spacecraft Using an Eccentricity/Inclination Vector Separation. Journal of Guidance, Control, and Dynamics 29(3):554–563. https://doi.org/10.2514/1.1511 – 10.2514/1.15114
- Danzmann K, R diger A (2003) LISA technology concept, status, prospects. Class Quantum Grav 20(10):S1–S9. https://doi.org/10.1088/0264-9381/20/10/30 – 10.1088/0264-9381/20/10/301
- Di Mauro G, Lawn M, Bevilacqua R (2018) Survey on Guidance Navigation and Control Requirements for Spacecraft Formation-Flying Missions. Journal of Guidance, Control, and Dynamics 41(3):581–602. https://doi.org/10.2514/1.g00286 – 10.2514/1.g002868
- Modeling and control of complex physical systems: The port-Hamiltonian approach. (2009)
- Fujimoto K, Sakurama K, Sugie T (2003) Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39(12):2059–2069. https://doi.org/10.1016/j.automatica.2003.07.00 – 10.1016/j.automatica.2003.07.005
- Gui Y, Jia Q, Li H, Cheng Y (2022) Reconfigurable Fault-Tolerant Control for Spacecraft Formation Flying Based on Iterative Learning Algorithms. Applied Sciences 12(5):2485. https://doi.org/10.3390/app1205248 – 10.3390/app12052485
- Ikari, Seirios: A demonstration of space infrared interferometer by formation flying of micro-satellites. (2021)
- Ito T, Izumi K, Kawano I, Funaki I, Sato S, Akutsu T, Komori K, Musha M, Michimura Y, Satoh S, Iwaki T, Yokota K, Goto K, Furukawa K, Matsuo T, Tsuzuki T, Yamada K, Sasaki T, Nishishita T, Matsumoto Y, Hirose C, Torii W, Ikari S, Nagano K, Ando M, Kawamura S, Kaneda H, Takeuchi S, Sakai S (2025) SILVIA: Ultra-precision formation flying demonstration for space-based interferometry. Publications of the Astronomical Society of Japan 77(5):1080–1089. https://doi.org/10.1093/pasj/psaf08 – 10.1093/pasj/psaf086
- Javanmardi N, Yaghmaei A, Yazdanpanah MJ (2020) Spacecraft formation flying in the port-Hamiltonian framework. Nonlinear Dyn 99(4):2765–2783. https://doi.org/10.1007/s11071-019-05445- – 10.1007/s11071-019-05445-0
- Kawamura, The Japanese space gravitational wave antenna - DECIGO. Journal of Physics: Conference Series (2008)
- Koenig AW, D’Amico S, Lightsey EG (2023) Formation Flying Orbit and Control Concept for Virtual Super Optics Reconfigurable Swarm Mission. Journal of Guidance, Control, and Dynamics 46(9):1657–1670. https://doi.org/10.2514/1.g00733 – 10.2514/1.g007334
- Hespanha JP (2005) Switching in Systems and Control [Book Review]. IEEE Control Syst 25(5):97–99. https://doi.org/10.1109/mcs.2005.151280 – 10.1109/mcs.2005.1512800
- Mancini M, Ruggiero D (2025) Artificial Potential Field and Sliding Mode Control for spacecraft attitude maneuver with actuation and pointing constraints. Control Engineering Practice 162:106373. https://doi.org/10.1016/j.conengprac.2025.10637 – 10.1016/j.conengprac.2025.106373
- Maschke, Port-controlled Hamiltonian systems: Modelling origins and system theoretic properties. (1992)
- Matsuo T, Ikari S, Kondo H, Ishiwata S, Nakasuka S, Yamamuro T (2022) High spatial resolution spectral imaging method for space interferometers and its application to formation flying small satellites. J Astron Telesc Instrum Syst 8(01). https://doi.org/10.1117/1.jatis.8.1.01500 – 10.1117/1.jatis.8.1.015001
- Molina, POC_ESSAIM: Close-formation flying demonstration of 3 nanosatellites in LEO. (2024)
- Morse AS, Mayne DQ, Goodwin GC (1992) Applications of hysteresis switching in parameter adaptive control. IEEE Trans Automat Contr 37(9):1343–1354. https://doi.org/10.1109/9.15957 – 10.1109/9.159571
- Pereira P, Guerreiro BJ, Lourenço P (2023) Distributed Model Predictive Control Method for Spacecraft Formation Flying in a Leader–Follower Formation. IEEE Trans Aerosp Electron Syst 59(3):3213–3223. https://doi.org/10.1109/taes.2022.322469 – 10.1109/taes.2022.3224692
- Plestan F, Shtessel Y, Brégeault V, Poznyak A (2010) New methodologies for adaptive sliding mode control. International Journal of Control 83(9):1907–1919. https://doi.org/10.1080/00207179.2010.50138 – 10.1080/00207179.2010.501385
- Pomares J, Felicetti L, García GJ, Ramón JL (2024) Spacecraft Formation Keeping and Reconfiguration Using Optimal Visual Servoing. J Astronaut Sci 71(2). https://doi.org/10.1007/s40295-024-00439- – 10.1007/s40295-024-00439-6
- Pomet J-B, Praly L (1992) Adaptive nonlinear regulation: estimation from the Lyapunov equation. IEEE Trans Automat Contr 37(6):729–740. https://doi.org/10.1109/9.25632 – 10.1109/9.256328
- Quanz SP, Ottiger M, Fontanet E, Kammerer J, Menti F, Dannert F, Gheorghe A, Absil O, Airapetian VS, Alei E, Allart R, Angerhausen D, Blumenthal S, Buchhave LA, Cabrera J, Carrión-González Ó, Chauvin G, Danchi WC, Dandumont C, Defrére D, Dorn C, Ehrenreich D, Ertel S, Fridlund M, García Muñoz A, Gascón C, Girard JH, Glauser A, Grenfell JL, Guidi G, Hagelberg J, Helled R, Ireland MJ, Janson M, Kopparapu RK, Korth J, Kozakis T, Kraus S, Léger A, Leedjärv L, Lichtenberg T, Lillo-Box J, Linz H, Liseau R, Loicq J, Mahendra V, Malbet F, Mathew J, Mennesson B, Meyer MR, Mishra L, Molaverdikhani K, Noack L, Oza AV, Pallé E, Parviainen H, Quirrenbach A, Rauer H, Ribas I, Rice M, Romagnolo A, Rugheimer S, Schwieterman EW, Serabyn E, Sharma S, Stassun KG, Szulágyi J, Wang HS, Wunderlich F, Wyatt MC (2022) Large Interferometer For Exoplanets (LIFE). A&A 664:A21. https://doi.org/10.1051/0004-6361/20214036 – 10.1051/0004-6361/202140366
- Satoh S, Hamanaka Y (2026) Nonlinear formation tracking control based on generalized canonical transformations with adaptive mechanism for atmospheric drag. Advances in Space Research 77(1):671–685. https://doi.org/10.1016/j.asr.2025.11.03 – 10.1016/j.asr.2025.11.031
- Schweighart, Satellite formation flying design and control using mean orbit elements. Journal of the Astronautical Sciences (2001)
- Serrano D, Scoarnec Y, Tiraplegui Riveras S, Gómez Ruiz V, Robert M, Negrete Solana JJ, Galano D, Rougeot R, Bozhanov T, Ilsen S, Beeckman MK, Scopelliti D (2025) Proba-3 Precise Formation Flying: An In-Flight Reality Now. IAF Space Systems Symposium 613–62 – 10.52202/083091-0060
- Shao X, Chen L, Chen J, Zhang D (2023) Prescribed-time spacecraft formation flying control with unknown disturbances by time-varying feedback. International Journal of Control 97(11):2677–2687. https://doi.org/10.1080/00207179.2023.229140 – 10.1080/00207179.2023.2291403
- Shi Y, Hu Q, Li D, Lv M (2023) Adaptive Optimal Tracking Control for Spacecraft Formation Flying With Event-Triggered Input. IEEE Trans Ind Inf 19(5):6418–6428. https://doi.org/10.1109/tii.2022.318106 – 10.1109/tii.2022.3181067
- Shtessel, (2014)
- Slotine, Tracking control of non-linear systems using sliding surfaces with application to robot manipulators. (1983)
- Tabuchi, Formation tracking control using generalized canonical transformations and sliding mode control of port-Hamiltonian systems. Journal of Evolving Space Activities (2024)
- Tokat, New approaches for on-line tuning of the linear sliding surface slope in sliding mode controllers. Turkish Journal of Electrical Engineering and Computer Sciences (2003)
- Tokat, A classification and overview of sliding mode controller sliding surface design methods. (2015)
- Utkin, (1992)
- Utkin V, Poznyak A, Orlov Y, Polyakov A (2020) Conventional and high order sliding mode control. Journal of the Franklin Institute 357(15):10244–10261. https://doi.org/10.1016/j.jfranklin.2020.06.01 – 10.1016/j.jfranklin.2020.06.018
- Wang G, Yuan W, Wang X (2024) Event‐Triggered Adaptive Neural Network Backstepping Sliding Fault‐Tolerant Control of Spacecraft Formation Flying With Input Saturation. International Journal of Aerospace Engineering 2024(1). https://doi.org/10.1155/2024/684706 – 10.1155/2024/6847067
- Wang W, Wu D, Baoyin H (2024) Fuel-Optimal Control for Multiple Spacecraft Formation Flying With Relative Motion Constraints. IEEE Trans Aerosp Electron Syst 60(6):8569–8582. https://doi.org/10.1109/taes.2024.343211 – 10.1109/taes.2024.3432115
- Xie, Low frequency hierarchical cooperative impulse control for gravitational wave detector formation keeping. Journal of Guidance, Control, and Dynamics (2024)
- Zhang Z, Deng L, Feng J, Chang L, Li D, Qin Y (2022) A Survey of Precision Formation Relative State Measurement Technology for Distributed Spacecraft. Aerospace 9(7):362. https://doi.org/10.3390/aerospace907036 – 10.3390/aerospace9070362