In this paper, a novel fractional-order fuzzy sliding mode control strategy is developed to realize the deployment of the tethered satellite system (TSS) with input saturation. The considered TSS is modeled as an underactuated system. By decoupling the underactuated system into two subsystems, a fractional-order and a constrained integer-order sliding surfaces are designed for the actuated and unactuated subsystems, respectively. Then, a new hybrid sliding manifold is obtained by coupling the two subsliding surfaces. Adaptive fuzzy algorithm is used to regulate the coupling coefficient in the newly proposed hybrid sliding manifold in order to procure satisfactory performance. Meanwhile, the saturation nonlinearity of control input is also considered. The asymptotic stability of the closed-loop system is demonstrated theoretically. With the existence of fractional order, the presented controller can perform faster and more smooth tether deployment when compared with conventional ones. Finally, the effectiveness and superiority of the proposed control approach are validated by illustrative simulations.

Fractional-Order Fuzzy Sliding Mode Control for the Deployment of Tethered Satellite System Under Input Saturation

Fixed-time attitude tracking control for spacecraft without unwinding

Space debris is growing dramatically with the rapid pace of human exploration of space, which seriously threatens the safety of artificial spacecraft in orbit. Therefore, the active debris removal (ADR) is important. This review aims to review the ADR methods and to advance related research in the future. The current research and development status are clearly demonstrated by mapping knowledge domain and charts. In this paper, the latest research results are classified and summarized in detail from two aspects of space debris capture and removal. The scheme comparison and evaluation of all ADR methods are performed, and the applicable scopes of various methods are summarized. Each ADR method is scored using a cobweb evaluation model based on six indicators. Future development of ADR is discussed to promote further research interest.

Survey on research and development of on-orbit active debris removal methods

This paper investigates the anti-unwinding finite-time attitude synchronization control problem for Spacecraft formation flying with external disturbances. Two finite-time controllers are designed based on rotation matrix and terminal sliding mode method. By designing a novel sliding mode surface, the first controller is developed when the upper bound of the external disturbances can be exactly known. However, this value is not always available in reality. In addition, the direct use of the upper bound of the external disturbances can result in the chattering problem. For the purpose of overcoming the disadvantage of the first controller, a modified control law is proposed, in which the adaptive law is applied to estimate the unknown value online. Theoretical analysis and numerical simulations are presented to demonstrate the validity of the proposed controllers.

Rotation matrix based finite-time attitude synchronization control for spacecraft with external disturbances.

Tethered satellite systems (TSSs) have attracted significant attention due to their potential and valuable applications for scientific research. With the development of various launched on-orbit missions, the deployment of tethers is considered a crucial technology for operation of a TSS. Both past orbiting experiments and numerical results have shown that oscillations of the deployed tether due to the Coriolis force and environmental perturbations are inevitable and that the impact between the space tether and end-body at the end of the deployment process leads to complicated nonlinear phenomena. Hence, a set of suitable control methods plays a fundamental role in tether deployment. This review article summarizes previous work on aspects of the dynamics, control, and ground-based experiments of tether deployment. The relevant basic principles, analytical expressions, simulation cases, and experimental results are presented as well.

Review of deployment technology for tethered satellite systems

De-Spin of Massive Rotating Space Object by Tethered Space Tug

This paper focuses on the tethered satellite deployment control issue via tether tension control in a propellant-free manner. The tether deployment is a typical underactuated control problem when only the tension control was employed by actively accommodate tether length by mechanical device. Firstly, unlike most existing control methods, the energy-based view of feedback approaches are proposed in an analytical form with tension constraint. To regulate the dynamic behavior of tether deployment, an artificial potential energy function is introduced and combined with the system's Hamiltonian to construct the Lyapunov function. The asymptotic stability is shown by invoking the Lyapunov technique and LaSalle's invariance principle. Secondly, the proposed control approach is extended into an output feedback form without velocity measurement. Because the relative position can be easily measured rather than velocity from the practical perspective. In the controller, the term of tether length velocity is replaced by an approximate differentiation. Finally, numerical simulations are carried on to verify the effectiveness of the proposed control approaches. Performance of these proposed control approaches is investigated according to their dependency on control gains.

Energy-based Output Feedback Tension Control for Space Tether Deployment under Physical Constraint

This article investigates the attitude control and stability analysis of an electric solar wind sail (E-sail) by considering elastic deflection of tethers while assuming main spacecraft and remote units as point masses. The attitude and orbital motion of the E-sail is analyzed by a high-order high-fidelity E-sail model derived from the nodal position finite-element method, where the attitude angles are implicitly described via the nodal coordinates. To overcome the difficulty in handling the stability analysis of high-order model under the Lyapunov framework, the E-sail's attitude dynamics is approximated explicitly by a reduced order analytical model with only three attitude angles. A sliding mode control law is proposed for the E-sail attitude control based on the reduced order analytical E-sail model and its stability is proved by the Lyapunov theory. Finally, two schemes are derived to map the control torque to either the control thrust at remote units or the voltages of main tethers respectively, which are applied to the high-fidelity E-sail model for attitude control. Numerical simulation demonstrates that the proposed control law performs similarly with the high-fidelity and reduced order analytical E-sail models if proper control gains are selected. It shows that the control law developed from the reduced order analytical E-sail model can stably control the attitude of a real E-sail. The investigation also indicates that the high-order flexible E-sail model provides an effective virtual testbed to evaluate the E-sail attitude control strategy derived from the reduced order attitude dynamics.

Attitude Control and Stability Analysis of Electric Sail

DESCENT: Mission Architecture and Design Overview

A tethered towing system provides an effective method for capturing pieces of space debris and dragging them out of orbit. This paper focuses on the in-plane stability analysis and libration control of a two-segment tethered towing system. The first segment is the same as the traditional single-tether towing system. The second segment is similar to a simplified space tether net. The dynamic equations are established in the orbit frame. Considering the elasticity of the tethers, the equilibrium solutions are obtained and the stability of equilibrium solutions is proved. An in-plane libration controller based on the sliding mode control scheme is designed to ensure the safety of the towing mission and save fuel. The controller suppressed the librations of the in-plane angles in the desired state by applying two external torques. Finally, simulation results are provided to validate the effectiveness of the proposed controller.

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Junjie Kang

Papers

De-Spin of Massive Rotating Space Object by Tethered Space Tug

Energy-based Output Feedback Tension Control for Space Tether Deployment under Physical Constraint

Attitude Control and Stability Analysis of Electric Sail

DESCENT: Mission Architecture and Design Overview

In-Plane Libration Suppression of a Two-Segment Tethered Towing System