Abstract
This paper studies the thrust regulation of the tethered space-tug in order to stabilize the target towed by a exible tether. To compromise between model accuracy and simplicity, a rigid- exible coupling multi-body model is proposed as the full model of the tethered space-tug. More specifically, the tug and the towed target are assumed as rigid bodies, whereas the exible tether is approximated as a series of hinged rods. The rods are assumed extensible but incompressible. Then the equations of motion of the multi-body system are derived based on the recursive dynamics algorithm. The attitude motion of the towed target is stabilized by regulating the thrust on the tug, whereas the tether-tension-caused perturbation to the tug's attitude motion is eliminated by the control torque on the tug. The regulated thrust is achieved by first designing an optimal control trajectory considering the simplified system model with constraints for both state variables and control input. Then the trajectory is tracked using a neural-network-based terminal sliding-mode controller. The radial basis function neural network is used to estimate the unknown nonlinear difference between the simple model and the full model, while the terminal sliding-mode controller ensures the rapid tracking control of the target's attitude motion. Thrust saturation and tether slackness avoidance are also considered. Finally, numerical simulations prove the effectiveness of the proposed controller using the regulated thrust. Without disturbing orbital motion much, the attitude motion of the tug and the target are well stabilized and the tether slackness is avoided.
Similar content being viewed by others
Change history
11 February 2022
A Correction to this paper has been published: https://doi.org/10.1007/s42064-022-0136-2
References
Bischof, B. ROGER -Robotic geostationary orbit restorer. In: Proceedings of the 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law, 2003: IAC-03-IAA.5.2.08.
Zhai, G., Zhang, J., Yao, Z. Circular orbit target capture using space tether-net system. Mathematical Problems in Engineering, 2013, 2013, Article ID601482.
Wen, H., Zhu, Z. H., Jin, D., Hu, H. Model predictive control with output feedback for a deorbiting electrodynamic tether system. Journal of Guidance, Control, and Dynamics, 2016, 39(10): 2455–2460.
Zhong, R., Zhu, Z. H. Timescale separate optimal control of tethered space-tug systems for space-debris removal. Journal of Guidance, Control, and Dynamics, 2016, 39(11): 2540–2545.
Jasper, L., Schaub, H. Tethered towing using open-loop input-shaping and discrete thrust levels. Acta Astronautica, 2014, 105(1): 373–384.
Aslanov, V. S., Ledkov, A. S. Dynamics of towed large space debris taking into account atmospheric disturbance. Acta Mechanica, 2014, 225(9): 2685–2697.
Krupa, M., Poth, W., Schagerl, M., Steindl, A., Troger, H., Wiedermann, G. Modeling, dynamics and control of tethered satellite systems. Nonlinear Dynamics, 2006, 43(1-2): 73–96.
Peng, J. H., Liu, Y. Z. Chaos in the tethered satellite system. Journal of Shanghai Jiaotong University, 1996, 30: 32–35. (in Chinese)
Banerjee, A. K. Dynamics of tethered payloads with deployment rate control. Journal of Guidance, Control, and Dynamics, 1990, 13(4): 759–762.
Biswell, B. L., Puig-Suari, J., Longuski, J. M., Tragesser, S. G. Three-dimensional hinged-rod model for elastic aerobraking tethers. Journal of Guidance, Control, and Dynamics, 1998, 21(2): 286–295.
Zhong, R. Rigid-exible coupling multibody model for the tethered satellite system based on recursive dynamics algorithm. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(7): 1188–1195. (in Chinese)
Ulrich, S., Sasiadek, J. Z., Barkana, I. Modeling and direct adaptive control of a fiexible-joint manipulator. Journal of Guidance, Control, and Dynamics, 2012, 35(1): 25–39.
Yu, S., Yu, X., Man, Z. Robust global terminal sliding mode control of SISO nonlinear uncertain systems. In: Proceedings of the 39th IEEE Conference on Decision and Control, 2000, 3: 2198–2203.
Lewis, F. L., Liu, K., Yesildirek, A. Neural net robot controller with guaranteed tracking performance. IEEE Transactions on Neural Networks, 1995, 6(3): 703–715.
Julian, K. D., Kochenderfer, M. J. Neural network guidance for UAVs. In: Proceedings of the AIAA Guidance, Navigation, and Control Conference, 2017: AIAA 2017–1743.
Narendra, K. S., Parthasarathy, K. Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1990, 1(1): 4–27.
Lee, M.-J., Choi, Y.-K. An adaptive neurocontroller using RBFN for robot manipulators. IEEE Transactions on Industrial Electronics, 2004, 51(3): 711–717.
Biannic, J.-M., Tarbouriech, S. Optimization and implementation of dynamic anti-windup compensators with multiple saturations in fight control systems. Control Engineering Practice, 2009, 17(6): 703–713.
Hu, Q., Jia, Y., Xu, S. Recursive dynamics algorithm for multibody systems with variable-speed control moment gyroscopes. Journal of Guidance, Control, and Dynamics, 2013, 36(5): 1388–1398.
Hughes, P. C. Spacecraft Attitude Dynamics. John Wiley & Sons, Inc., 1986.
Dorf, R. C., Bishop, R. H. Modern Control Systems, 12th edn. Publishing House of Electronics Industry, 2012.
Jin, D. P., Hu, H. Y. Optimal control of a tethered subsatellite of three degrees of freedom. Nonlinear Dynamics, 2006, 46(1-2): 161–178.
Zhong, R., Zhu, Z. H. Optimal control of nanosatellite fast deorbit using electrodynamic tether. Journal of Guidance, Control, and Dynamics, 2014, 37(4): 1182–1194.
Garg, D., Patterson, M., Hager, W. W., Rao, A. V., Benson, D. A., Huntington, G. T. A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica, 2010, 46(11): 1843–1851.
Gill, P. E., Murray, W., Saunders, M. A. SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM Journal on Optimization, 2002, 12(4): 979–1006.
Wang, L., Chai, T., Zhai, L. Neural-network-based terminal sliding-mode control of robotic manipulators including actuator dynamics. IEEE Transactions on Industrial Electronics, 2009, 56(9): 3296–3304.
Acknowledgements
The authors acknowledge the support of the National Natural Science Foundation of China (Grant No. 11402009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Rui Zhong received his Ph.D. degree in spacecraft design from Beijing University of Aeronautics and Astronautics, Beijing, China, in 2011. From 2011 to 2013, he worked as a postdoctoral fellow in the Department of Earth and Space Science and Engineering at York University. Since 2013, he has been an assistant professor in the School of Astronautics at Beijing University of Aeronautics and Astronautics, Beijing, China, where he is currently an associate professor. His research interests include tethered satellite system, spatial multi exible body dynamics, spacecraft dynamics and control.
Shijie Xu received his B.Eng. degree from the Department of Mechanical Engineering, Northeast Forestry University, Harbin, China, in 1976, M.S. degree from the Laboratory of Flight Dynamics, Harbin Institute of Technology, China, in 1983, and Ph.D. degree with a specialization in automatic controls from Henri Poincar University, Nancy, France, in 1995. From 1989 to 2000, he was with Harbin Institute of Technology, where he was an associate professor and then a professor. In 2000, he joined the School of Astronautics, Beihang University, Beijing, China, where he is currently a professor. He has authored or coauthored over 300 papers in journals and conferences. His research interests include robust control, astrodynamics, spacecraft guidance, navigation and control, and deep space exploration. He was a recipient of the Key Program Funding of the National Natural Science Foundation of China from 2015 to 2019.
Rights and permissions
About this article
Cite this article
Zhong, R., Xu, S. Neural-network-based terminal sliding-mode control for thrust regulation of a tethered space-tug. Astrodyn 2, 175–185 (2018). https://doi.org/10.1007/s42064-017-0019-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42064-017-0019-0