Neural-network-based terminal sliding-mode control for thrust regulation of a tethered space-tug


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.

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The authors acknowledge the support of the National Natural Science Foundation of China (Grant No. 11402009).

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Corresponding author

Correspondence to Rui Zhong.

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.

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Zhong, R., Xu, S. Neural-network-based terminal sliding-mode control for thrust regulation of a tethered space-tug. Astrodyn 2, 175–185 (2018).

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  • tethered space-tug
  • thrust regulation
  • exible tether
  • recursive dynamics algorithm
  • neural network