Nonlinear dynamics and coupling effect of libration and vibration of tethered space robot in deorbiting process

In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the tethered combination system in the post-capture phase was established with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether.The motion law of the tethered combination in the deorbiting process with different disturbances was simulated and discussed on the premise that the platform was only controlled by a constant thrust force.It is known that the four motion freedoms of the tethered combination are coupled with each other in the deorbiting process from the simulation results.A noticeable phenomenon is that the tether longitudinal vibration does not decay to vanish even under the large tether damping with initial attitude disturbances due to the coupling effect.The approximate analytical solutions of the dynamics for a simplified model are obtained through the perturbation method.The condition of the inter resonance phenomenon is the frequency ratio λ_1=2.The case study shows good accordance between the analytical solutions and numerical results,indicating the effectiveness and correctness of approximate analytical solutions.

Dynamic analysis of tethered space system deployment process

Discusses in detail the deploying strategies and feature of the motion of the Tethered Space System and the effects of some parameters, such as the property and initial length of the tether, the perturbation of the atmosphere, the ellipse of the orbit and the mass distribution of the system and points out the deploying strategy is based on the controlling of tension and the length of tether. And concludes from the computer simulation results of a tethered atmosphere probing satellite deployment that the deploying strategy presented does work well.

Game theory based finite-time formation control using artificial potentials for tethered space net robot

The Tethered Space Net Robot(TSNR)is an innovative solution for active space debris capture and removal.Its large envelope and simple capture method make it an attractive option for this task.However,capturing maneuverable debris with the flexible and elastic underactuated net poses significant challenges.To address this,a novel formation control method for the TSNR is proposed through the integration of differential game theory and robust adaptive control in this paper.Specifically,the trajectory of the TSNR is obtained through the solution of a real-time feedback pursuit-evasion game with a dynamic target,where the primary condition is to ensure the stability of the TSNR.Furthermore,to minimize tracking errors and maintain a specific configuration,a robust adaptive formation control scheme with Artificial Potential Field(APF)based on a Finite-Time Convergent Extended State Observer(FTCESO)is investigated.The proposed control method has a key advantage in suppressing complex oscillations by a new adaptive law,thus precisely maintaining the configuration.Finally,numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.

Advances in dynamics and control of tethered satellite systems

The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.

Adaptive Optimal Control of Space Tether System for Payload Capture via Policy Iteration

The libration control problem of space tether system(STS)for post-capture of payload is studied.The process of payload capture will cause tether swing and deviation from the nominal position,resulting in the failure of capture mission.Due to unknown inertial parameters after capturing the payload,an adaptive optimal control based on policy iteration is developed to stabilize the uncertain dynamic system in the post-capture phase.By introducing integral reinforcement learning(IRL)scheme,the algebraic Riccati equation(ARE)can be online solved without known dynamics.To avoid computational burden from iteration equations,the online implementation of policy iteration algorithm is provided by the least-squares solution method.Finally,the effectiveness of the algorithm is validated by numerical simulations.

Strict finite-time sliding mode control for a tethered space net robot

Tethered Space Net Robot(TSNR)is considered to be a promising approach for space debris removal,and accordingly it is also an interesting control problem due to its time-varying disturbances caused by an elastic and flexible net and a main connected tether.In this situation,the control scheme should be robust enough,low-frequency,and finite-time convergent in presence of external disturbances.In this paper,a robust controller with an advanced adaptive scheme is proposed.To improve robustness,the disturbance is skillfully involved in the adaptive scheme.It is strictly proven that the closed-loop system can converge to the desired trajectory in finite time in both reaching and sliding processes.Based on the theoretical proof,adaptive gains and corresponding dynamic stability characteristics are further discussed.Finally,the efficiency of the proposed control scheme is numerically proven via a TSNR.The proposed control scheme utilizes small and continuous control forces to compensate for the disturbance efficiently and track the desired trajectory quickly.

Fuel-optimal deorbit scheme of space debris using tethered space-tug based on pseudospectral method

This paper proposes a fuel-optimal deorbit scheme for space debris deorbit using tethered space tug.The scheme contains three stages named respectively as dragging,maintenance and swinging.In the first stage,the tug,propelled by continuous thrust,tows deorbit to a transfer orbit with a tether.Then in the second stage,the combination of the tug and the debris flies unpowered and uncontrolled to a swing point on the transfer orbit.Finally,in the third stage,the tug is propelled at the swing point and the rotation speed of the tethered system increases such that the debris obtains enough velocity increment.The trajectory optimization of the first stage is established considering the total fuel consumption of the three stages,whereas the dynamic model is simplified for computation efficiency.The solution to the optimal problem is obtained using a direct method based on Gauss pesudospectral discretization.Then a model predictive controller is designed to track the open-loop optimal reference trajectories,reducing the states’deviations caused by model simplification and ignorance of perturbations.Furthermore,it is proved that the fuel-optimal swing point is the apogee of the transfer orbit.The paper analyzes the fuel consumption of a typical scenario and demonstrates effectiveness of the proposed deorbit scheme numerically.

Evaluation of E-sail parameters on central spacecraft attitude stability using a high-fidelity rigid–flexible coupling model

This study examines the impact of electric solar wind sail(E-sail)parameters on the attitude stability of E-sail’s central spacecraft by using a comprehensive rigid–flexible coupling dynamic model.In this model,the nodal position finite element method is used to model the elastic deformation of the tethers through interconnected two-node tensile elements.The attitude dynamics of the central spacecraft is described using a natural coordinate formulation.The rigid–flexible coupling between the central spacecraft and its flexible tethers is established using Lagrange multipliers.Our research reveals the significant influences of parameters such as tether numbers,tether’s electric potential,and solar wind velocity on attitude stability.Specifically,solar wind fluctuations and the distribution of electric potential on the main tethers considerably affect the attitude stability of the spacecraft.For consistent management,the angular velocities of the spacecraft must remain at target values.Moreover,the attitude stability of a spacecraft has a pronounced dependence on the geometrical configuration of the E-sail,with axisymmetric E-sails proving to be more stable.

Libration and end body swing stabilization of a parallel partial space elevator system

This paper studies the libration and stabilization of a parallel partial space elevator system in circular orbits. The system is made up of two paralleled partial space elevators, each of which consists of one main satellite, one end body and a climber moving along the tether between them.The libration characteristics of the elevator are studied through numerical analysis by a new dynamic model, and a novel control strategy is proposed to stabilize the swing of the end body by projecting the climber speeds only. Optimal control method is used to implement the new control strategy in the case where the climbers move in opposite direction. The simulation results validate the effectiveness of the proposed control strategy whose application will neither sacrifice the transport efficiency nor exacerbate libration significantly.

Wave control of a flexible space tether based on elastic metamaterials

This study proposes a spider‐web elastic metamaterial to suppress vibrations in space slender structures,such as flexible space tethers.The metamaterial consists of unit cells that are periodically distributed on the space tether to obtain band gaps.The finite element model of the unit cell is established by employing the absolute nodal coordinate formulation(ANCF)due to the large deformation of the structure.The eigenfrequencies and corresponding vibration modes of the unit cell are obtained by ANCF.Moreover,the band gap of the unit cell is calculated based on the phonon crystal theory.The relationship between the vibration modes and the band gaps is analyzed.Finally,an experiment is conducted to verify the vibration transmission characteristics of finite period cells.The results show the effectiveness of the spider‐web elastic metamaterial for vibration suppression of a flexible tether.This study provides insights into the use of elastic metamaterials for vibration isolation in space tether systems.