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The partial space elevator is a space transportation system that conveys cargo by a climber moving along the tether that connects the main satellite and the end body. This work proposed a novel prescribed performance based dual-loop control strategy for configuration keeping of the partial space elevator in cargo transportation. The control loop I controls the libration angle of the climber by a newly proposed prescribed performance control law to track the desired state with bounded performance. The Lyapunov stability of the control law is proved analytically. Control loop II stabilizes the overall configuration of the PSE by applying thrust and deploying/retrieving the tether simultaneously at the end body. To enforce the constraint that the total tether length is unchanged at the end of transportation, an event-triggered loaning control algorithm is proposed to further improve the Control loop II. Numerical simulations validate the prescribed performance based dual-loop control strategy. The results show that the stable configuration of the PSE is kept effectively with no libration motion in the period of cargo transportation.

Spacecraft formation maneuvering will inevitably induce flexible vibration from flexible appendages of spacecraft such as solar array appendages or antennae, which leads to complex disturbances with unknown fundamental frequencies. To achieve high performance of spacecraft formation flying, a novel adaptive iterative learning disturbance observer based on adaptive notch filter is designed to estimate and compensate unknown multi-frequency disturbances. Different from existing results on iterative learning disturbance observer, the newly proposed observer can estimate effectively both low-frequency disturbances and high-frequency periodic disturbances. Based on the proposed observer, an output feedback pose tracking law is derived by combining the proposed velocity observer and a feedback controller in dual quaternions description. The stability of the closed-loop system is approved based on the Lyapunov framework. Finally, the effectiveness and accuracy of the proposed observer and controller are demonstrated successfully by numerical simulations.

A novel concept of a looped tether transportation system with multiple rungs (L-TTS-R) is proposed for highly efficient payload transfer in space. In addition to two huge platforms connected by two parallel tethers with multiple moving climbers, some rigid rungs are evenly distributed between the two tethers in L-TTS-R to suppress the libration movement of the system and to reduce or avoid the risk of collision between climbers and tethers in the process of payload transportation. To establish an accurate model of L-TTS-R in the framework of multibody system dynamics, the gradient deficient beam elements of the absolute nodal coordinate formulation (ANCF) are used to mesh two tethers. The sliding joint based on ANCF is introduced to build up the contact interaction model between tethers and climbers. The generalized forces acting on the L-TTS-R, for example, the gravitational force and the elastic force, are derived in brief. The generalized-alpha method is used to solve the dynamics equations of the constrained flexible multibody systems. Some representative examples are given to validate the effectiveness of the proposed L-TTS-R model for space payload transfer missions and to assess the influence of rungs on the system libration suppression, the climber collision risk avoidance, the relative oscillation and pitching motion of platforms, and the tether tensions. The numerical results reveal that the L-TTS-R shows distinct effects on suppressing the overall libration of the system, reducing or even avoiding the risk of collision between climbers and tethers and decreasing significantly the oscillating magnitudes of the relative distances between two platforms, and these effects are more visible with increasing the number of rungs.

This paper describes the experimental validation of a CubeSat tether deployment design by air-bearing ground test and microgravity parabolic flight test. The tethered CubeSat mission includes two 1U CubeSats with a tape-type tether of 100 m. The tether will be deployed by pull with two CubeSats separating at a desired velocity. Various ground tests were performed to validate the designed separation velocity, estimate the internal friction force, and measure the deployed tether length. Finally, the engineering model of tether deployment system is validated by microgravity parabolic flight testing. The parabolic flight demonstrated the tether deployment system works as expected. By measuring the separation velocity of CubeSats in the parabolic flight, it reveals the internal friction is much less in the microgravity environment than the value measured on the ground.

This paper investigates the tracking and control problem of a spacecraft rendezvous with a non-cooperative and tumbling space target subject to parametric uncertainty and unknown external disturbances. The kinematics and dynamics of spacecraft position and attitude are described by dual quaternions. A novel adaptive sliding mode disturbance observer is proposed to track the pose of non-cooperative tumbling target without need for upper bounds of first and second derivatives of lumped disturbance. Based on the proposed observer, a finite time sliding mode control is developed in term of dual quaternion. Different from existing sliding mode control schemes, the conditions on the controller parameters bounds are relaxed. The stability and robustness of the overall closed-loop control is proved by the Lyapunov framework. The robustness and effectiveness of the proposed control scheme are validated by numerical simulations in comparison with existing approaches.

This paper explores a new control strategy to suppress the libration of a partial space elevator by applying torque control at the climber only. The control torque at the climber is generated by reaction wheels. A new dynamic model of the partial space elevator is developed by integrating the attitude dynamics of the climber into the classical two-piece dumbbell model. The influence of the climber attitude motion on the libration motion of the partial space elevator is analyzed with and without the control torque at the climber. Based on the characteristics of the system dynamics, a novel reaction wheel control strategy is proposed to suppress both the libration of the elevator and the climber attitude motion. Such a new control strategy is implemented by an optimal control scheme. The simulation results validate the effectiveness of the proposed control strategy, which provides a new alternative method to stabilize the libration of the partial space elevator for fast transfer of cargo with constant speeds. To avoid the adverse effect on the reaction wheel due to the frequent switch of rotation direction, a control strategy by two unidirectional reaction wheels is proposed to achieve the same control effect, where the reaction wheels rotate in only one direction.

This paper proposes a novel concept of looped tether transportation system with multiple climbers for highly efficient transportation of payloads. It is formed by connecting two parallel tether transportation systems or partial space elevators with multiple climbers per tether at upper and lower ends. A high-fidelity and accurate model for the system is built up to capture the high order flexural modes of tethers based on the nodal position finite element method in the arbitrary Lagrangian-Eulerian description. Numerical analysis is conducted to understand the dynamic characteristics of the looped tether transportation system compared to the tether transportation system with a single tether. The results show that the high-order flexural modes of tethers must be considered in the system's engineering analysis. The analysis also shows the interaction between two tethers caused by climbers on different tethers moving in different directions could be beneficial. It will reduce the overall libration of the system while keeping the magnitude of tether tension comparable to the tether transportation system with a single tether. In addition, the analysis of high order flexural modes of tether indicates that there exists a risk of tether collision in the payload transportation, which indicates again the necessity to include the high order flexural modes of tether in the analysis. Finally, the study shows the risk of tether collision could be avoided by optimizing the number of climbers per tether, the climber's moving profiles, and the distance between climbers using the optimal control methodology.

This paper investigates the dynamic characteristics of thrust-induced sail plane coning and attitude motion of an electric solar wind sail (E-sail) by considering high-order modes of flexible elastic tethers. The tethers of the E-sail are assumed elastic and discretized into inter-connected 2-noded tensile elements using the nodal position finite element method, while the central spacecraft and the remote units are simplified as lumped masses. The E-sail is assumed in the heliocentric ecliptic orbital plane at a distance of 1 au from the Sun. The influences of the propulsive force models and the initial E-sail orientation on the dynamic characteristics of the sail plane coning and attitude motion of E-sail are analyzed. The current work derives an analytic expression of the coning motion frequency under the assumption of small coning angle. Through parametric analyses, the current work shows that the magnitude of the propulsive force significantly influences the increment magnitude of the E-sail's orbital radius while has little effect on the angles of sail and thrust angles and the E-sail spin rate. The parametric analyses also show that the initial E-sail orientation significantly influences the thrust vector and the variation of sail angle. Finally, the relationships of the sail and thrust angles, as well as the dimensionless acceleration of the E-sail, are given in polynomial expressions by curve-fitting of simulation results of E-sails with the consideration of coning motion. The relationships are compared with the previous results of E-sails without including coning motion. It shows the coning motion has negligible effect on the macro dynamic behaviors of E-sail.

This paper studies the libration suppression of a moon-based partial space elevator in the Earth-Moon three-body system. The elevator is connected to the Moon surface by a tether and a space station is connected to the free end of tether as the end body. One or multiple climber(s) can move along the tether to transfer cargos between the Moon and the end body. A high-fidelity dynamic model is derived to describe the motion of the climber(s), the end body and the flexible tether by the combination of rigid body dynamics and nodal position finite element method. The validity of the proposed model and the effect of element discretization along the tether on the dynamic behaviour of the elevator are investigated through numerical simulations. To ensure the stability and satisfy the mission constraints in the cargo transfer period, an optimal control based on the high-fidelity model is employed to regulate the control input with limited magnitude. Case studies show that by adjusting the thrusts on the end body reasonably, the libration of the Moon-based partial space elevator can be suppressed with limited control input effectively.

This paper investigates spacecraft orbital boost maneuver by a fully insulated electrodynamic tether using a coupled multiphysics dynamic model that considers electric-magnetic-dynamic energy coupling. The current-potential characteristics of the electrodynamic tether is described by a simplified analytical model, where revised Parker-Murphy model is employed to evaluate electric current generation at plasma contactors together with libration dynamics of tether. The 13th-order Earth's magnetic field model is used to account influence of inhomogeneity of Earth's magnetic field on orbital parameters of electrodynamic tether system, especially in inclined orbits. Parametric analysis has been conducted for orbital boost maneuver from 400 km to 1,200 km at four different orbital inclinations. The results show that (i) the orbit of electrodynamic tether system will change from circular to elliptical orbits, especially in inclined orbits, (ii) the voltage of onboard power supply at the anode affect electric current generation, (iii) the coupled multiphysics model is necessary to characterize the interaction of electrodynamic tether with the surrounding space environment and the controllability of electric current in electrodynamic tether, (iv) the motion of orbital boost maneuver by electrodynamic tether is stable, which is different from the deorbit by electrodynamic tether.

This paper studies the dynamic characteristics of an electric solar wind sail (E-sail). A high-fidelity multiphysics model is developed by the nodal position finite element method to investigate the coupling effects of orbital and self-spinning motions of the E-sail, and the interaction between the axial/transverse elastic motions of tether and the Coulomb force. Furthermore, parametric study is conducted to better understand these coupling effects. The simulation results show that the coupling effects have a significant impact on the dynamic behavior of E-sail and the induced thrust. Furthermore, the analysis indicates a strong dependence of the thrust on sail and coning angles of E-sail even in the case of small sail angle. Finally, the influence of the initial self-spin rate and the sail angle on the dynamic behavior of a flexible E-sail is investigated. It shows that a high spin rate is needed to hold the geometrical configuration of the E-sail, and the difference in the orbital maneuvering is distinct when the E-sail inclines to the incident solar wind. It implies that a suitable control strategy should be employed to accomplish the thrust vectoring for the orbit maneuvering. The analysis provides an effective and robust way to design the E-sail in the mission planning phase.

This paper develops control laws for the deployment of tethered spacecraft systems with an explicit non-negative velocity constraint using invariance principle of control systems. It addresses a class of space tether deployment control problems where the tether is deployed out only. This implies the tether deployment velocity must be always positive and approaches to zero at the end of deployment. This non-negative velocity constraint is explicitly satisfied in the proposed tension control laws by transforming it into an invariance property of control system. Two control laws with nonlinear feedback are derived with two complementary manifolds. The Lyapunov stability of the control laws is proved and the controllability of the tethered spacecraft system with tension input is analyzed. Finally, the effectiveness of control laws is demonstrated by numerical simulation.

This paper investigates the stable orbital transfer of a climber in a partial space elevator system in circular orbits. The elevator includes a main satellite, an end body, and a climber, which are connected by two straight, inextensible, massless and variable length tethers. Derived from system dynamics, two closed-loop velocity control strategies are proposed to regulate the tethers' deploying and retrieving speeds directly to control the Coriolis forces acting on the climber and the end body directly. The stable region of the control strategies is analyzed, and the effectiveness of the proposed strategies is demonstrated by numerical simulation. Simulation results show that the newly proposed strategies effectively minimize the libration of a partial space elevator system during the orbital transfer of the climber and the system states successfully approach to the desired equilibrium by the end of the orbital transfer. Furthermore, the proposed deployment/retrieval control strategies can be converted to tension control laws easily.

This paper studies the control of spacecraft rendezvous with attitude stable or spinning targets in an elliptical orbit. The linearized Tschauner-Hempel equation is used to describe the motion of spacecraft and the problem is formulated by model predictive control. The control objective is to maximize control accuracy and smoothness simultaneously to avoid unexpected change or overshoot of trajectory for safe rendezvous. It is achieved by minimizing the weighted summations of control errors and increments. The effects of two sets of horizons (control and predictive horizons) in the model predictive control are examined in terms of fuel consumption, rendezvous time and computational effort. The numerical results show the proposed control strategy is effective.

This paper investigates the dynamic characteristics a three-body tethered satellite system in large elliptic orbits and the control strategy to suppress the libration of the system in orbital transfer process. The system is modeled by a two-piece dumbbell model in the domain of true anomaly. The model consists of one main satellite and two subsatellites connected with two straight, massless and inextensible tethers. Two control strategies based on the sliding mode control are developed to control the libration to the zero state and the steady state respectively. The results of numerical simulations show that the proposed control scheme has good performance in controlling the libration motion of a three-body tethered satellite system in an elliptic orbit with large eccentricity by limited control inputs. Furthermore, Hamiltonians in both states are examined and it shows that less control input is required to control the libration motion to the steady state than that of zero state.

This paper developed a new multiphysics finite element method for the elastodynamic analysis of space debris deorbit by a bare flexible electrodynamic tether. Orbital motion limited theory and dynamics of flexible electrodynamic tethers are discretized by the finite element method, where the motional electric field is variant along the tether and coupled with tether deflection and motion. Accordingly, the electrical current and potential bias profiles of tether are solved together with the tether dynamics by the nodal position finite element method. The newly proposed multiphysics finite element method is applied to analyze the deorbit dynamics of space debris by electrodynamic tethers with a two-stage energy control strategy to ensure an efficient and stable deorbit process. Numerical simulations are conducted to study the coupled effect between the motional electric field and the tether dynamics. The results reveal that the coupling effect has a significant influence on the tether stability and the deorbit performance. It cannot be ignored when the libration and deflection of the tether are significant.

This paper presents a real-time, vision-based algorithm for the pose and motion estimation of non-cooperative targets and its application in visual servo robotic manipulator to perform autonomous capture. A hybrid approach of adaptive extended Kalman filter and photogrammetry is developed for the real-time pose and motion estimation of non-cooperative targets. Based on the pose and motion estimates, the desired pose and trajectory of end-effector is defined and the corresponding desired joint angles of the robotic manipulator are derived by inverse kinematics. A close-loop visual servo control scheme is then developed for the robotic manipulator to track, approach and capture the target. Validating experiments are designed and performed on a custom-built six degrees of freedom robotic manipulator with an eye-in-hand configuration. The experimental results demonstrate the feasibility, effectiveness and robustness of the proposed adaptive extended Kalman filter enabled pose and motion estimation and visual servo strategy.

The paper presents a tension control law to stabilize the motions of a Tethered Space-Tug system during its deorbiting process by regulating the tension in the tether. The tension control law is designed on a basis of two straightforward ideas, i.e., the potential energy shaping and the damping injection. The law is expressed in an analytical feedback form in terms of only the tether length without the need of the feedback of full state information. Meanwhile, the requirements of measuring velocities are removed with the aid of a dynamic extension technique based on the feedback interconnection of Euler-Lagrange systems. The positive and bounded tension constraint is taken into consideration explicitly by including a pair of special saturation terms in the feedback control law. The relative motions of the space-tug and the debris are described with respect to a local non-inertial orbital frame of reference, whereas the orbital motion equations of the system are formulated in terms of the modified equinoctial elements of the orbit. Finally, the effectiveness of the proposed scheme is demonstrated via numerical case studies.

This paper concerns the position-based visual servo control of autonomous robotic manipulators in space. It focuses on the development of a real-time vision-based pose and motion estimation algorithm of a non-cooperative target by photogrammetry and extended Kalman filter for robotic manipulators to perform autonomous capture. Optical flow algorithm is adopted to track the target features in order to improve the image processing efficiency. Then, a close-loop position-based visual servo control strategy is devised to determine the desired pose of the end-effector at the rendezvous point based on the estimated pose and motion of the target. The corresponding desired joint angles of the robotic manipulator in the joint space are derived by the inverse kinematics of the robotic manipulator. The developed algorithm and position-based visual servo control strategy are validated experimentally by a custom built robotic manipulator with an eye-in-hand configuration. The experimental results demonstrate the proposed estimation algorithm and control scheme are feasible and effective.