Learning-based data-driven control for micro-nano free-floating space robots in Cartesian space

Abstract

This paper addresses the problem of end-effector position-tracking control for micro-nano free-floating space robots in Cartesian space without relying on explicit analytical kinematic or dynamic models. To address this challenge, we develop a two-layer learning architecture. In the first layer, a deep neural network is used for kinematic learning to capture the nonlinear mapping from end-effector Cartesian coordinates to joint angular velocities and to generate reference joint trajectories. In the second layer, a Koopman-operator-based network is employed to construct an approximately linearized representation of the joint-space dynamics of free-floating space robots. Based on this model, we propose a terminal fractional-order model predictive control scheme that incorporates the Grünwald-Letnikov fractional-order operator, thereby enhancing online control performance and improving tracking speed and accuracy relative to conventional model predictive control. Simulation results verify the effectiveness of the proposed method, demonstrating accurate and rapid end-effector trajectory tracking, all without requiring explicit analytical kinematic and dynamic models in the controller design, while the training pipeline relies solely on input-output trajectories.

Keywords

Free-floating space robot / Deep neural networks / Model learning for control / Model predictive control

References

[1] Al Ali A , Shi JF , Zhu ZH , 2024. Path planning of 6-DOF free-floating space robotic manipulators using reinforcement learning. Acta Astronaut, 224: 367- 378.

[2] Bruder D , Fu X , Vasudevan R , 2021. Advantages of bilinear Koopman realizations for the modeling and control of systems with unknown dynamics. IEEE Rob Autom Lett, 6 (3): 4369- 4376.

[3] Chen B , Wang MB , Hu L , et al., 2024. Data-driven Koopman model predictive control for hybrid energy storage system of electric vehicles under vehicle-following scenarios. Appl Energy, 365: 123218.

[4] Dou B , Yue XK , 2023. Disturbance observer-based fractional-order sliding mode control for free-floating space manipulator with disturbance. Aerosp Sci Technol, 132: 108061.

[5] Fallahiarezoodar N , Zhu ZH , 2025. Review of autonomous space robotic manipulators for on-orbit servicing and active debris removal. Space Sci Technol, 5: 0291.

[6] Gong K , 2025. Robust proximity rendezvous and coordinated control of space robots. Adv Space Res, 75 (3): 2856- 2873.

[7] Huang ZX , Wang HQ , Niu B , et al., 2024. Practical fixed-time adaptive fuzzy control of uncertain nonlinear systems with timevarying asymmetric constraints: a unified barrier function based approach. Front Inform Technol Electron Eng, 25 (9): 1282- 1294.

[8] Jin A , Zhang F , Huang PF , 2024. Learning-based data-driven optimal deployment control of tethered space robot. Adv Space Res, 74 (5): 2214- 2224.

[9] Jin RY , Rocco P , Geng YH , 2021. Observer-based fixed-time tracking control for space robots in task space. Acta Astronaut, 184: 35- 45.

[10] Koopman BO , 1931. Hamiltonian systems and transformation in Hilbert space. Proc Natl Acad Sci USA, 17 (5): 315- 318.

[11] Korda M , Mezić I , 2018. Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control. Automatica, 93: 149- 160.

[12] Lavín-Delgado JE , Chávez-Vázquez S , Gómez-Aguilar JF , et al., 2023. Intelligent neural integral sliding-mode controller for a space robotic manipulator mounted on a free-floating satellite. Adv Space Res, 71 (9): 3734- 3747.

[13] Lei WX , Zhao TY , Sun GH , 2023. Image based target capture of free floating space manipulator under unknown dynamics. Adv Space Res, 72 (11): 4923- 4933.

[14] Li CP , Qian DL , Chen YQ , 2011. On Riemann-Liouville and Caputo derivatives. Discrete Dyn Nat Soc, 2011 (1): 562494.

[15] Liu RP , Guo J , Gill E , 2025. Motion planning of free-floating space robots through multi-layer optimization using the RRT* algorithm. Acta Astronaut, 228: 940- 956.

[16] Mao RH , Meng T , Wang K , et al., 2024. Deep Koopman-operatorbased model predictive control for free-floating space robots with disturbance observer. Aerosp Sci Technol, 154: 109515.

[17] Nekoo SR , 2022. Output- and state-dependent Riccati equation: an output feedback controller design. Aerosp Sci Technol, 126: 107649.

[18] Papadopoulos E , Aghili F , Ma O , et al., 2021. Robotic manipulation and capture in space: a survey. Front Rob AI, 8: 686723.

[19] Prakash A , Giri DK , Kumar SR , 2022. Dynamic velocity error based trajectory tracking for space robotic manipulator. Aerosp Sci Technol, 126: 107650.

[20] Rahmani M , Redkar S , 2024a. Deep neural data-driven Koopman fractional control of a worm robot. Expert Syst Appl, 256: 124916.

[21] Rahmani M , Redkar S , 2024b. Enhanced Koopman operator-based robust data-driven control for 3 degree of freedom autonomous underwater vehicles: a novel approach. Ocean Eng, 307: 118227.

[22] Rybus T , Wojtunik M , Basmadji FL , 2022. Optimal collision-free path planning of a free-floating space robot using spline-based trajectories. Acta Astronaut, 190: 395- 408.

[23] Shao XY , Sun GH , Yao WR , et al., 2021. Fractional-order resolved acceleration control for free-floating space manipulator with system uncertainty. Aerosp Sci Technol, 118: 107041.

[24] Shao YC , Jin YB , Huang ZL , et al., 2024. A learning-based control pipeline for generic motor skills for quadruped robots. J Zhejiang Univ-Sci A, 25 (6): 443- 454.

[25] Shenwai PG , Choudhary A , Pokuri T , et al., 2025. On the role of artificial intelligence in aerospace engineering: current state of the art and future trajectories. Aeronaut J, 129 (1342): 3506- 3532.

[26] Tang M , Xia WQ , Deng JQ , et al., 2025. An error-based observer improved by the repetitive control strategy for electro-optical tracking systems. Front Inform Technol Electron Eng, 26 (3): 441- 455.

[27] Tao R , Ding YB , Li HY , et al., 2025. Predefined-time controller design for a multiple space transportation robots system based on Lpnorm-normalized sign function. Chin J Aeronaut, 38 (2): 103285.

[28] Tu SL , Wang HQ , Huang Y , et al., 2024. A spaceborne advanced storage system for remote sensing microsatellites. Front Inform Technol Electron Eng, 25 (4): 600- 615.

Rights & permissions

The Authors. Published by Zhejiang University Press Co., Ltd.