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• Derived new coupling-free analytical speed function (CASF) for in-plane libration-free transportation. • Proposed hierarchical sliding mode control for out-of-plane libration based on CASF. • Proved asymptotic stability of proposed control strategy by Lyapunov framework. This study presents an original analysis of out-of-plane libration dynamics and its control in partial space elevator cargo transportation. A comprehensive three-dimensional dynamic model of the partial space elevator has been derived to examine the effects of out-of-plane libration. To ensure a stable in-plane configuration, a coupling-free analytical speed function is developed that cancels out the coupling effects stemming from out-of-plane libration. A novel approach is developed to introduce a thrust control strategy for the elimination of out-of-plane libration using a virtual dynamic-based hierarchical sliding mode control law. By employing a new combined channel implementation mode, it is demonstrated that in and out-of-plane libration can be controlled with a single thruster, resulting in reduced fuel consumption. The stability of the proposed control strategy is proven within the Lyapunov framework. Numerical simulations validate the effectiveness of the control strategy and highlight its significance. Results show that out-of-plane libration increases the magnitude of in-plane libration, while climber movement amplifies out-of-plane libration. The control strategy successfully eliminates out-of-plane libration using limited control input, ensuring stable cargo transportation in the partial space elevator. [ABSTRACT FROM AUTHOR]

To meet the growing demand for the surveillance of resident space objects, the Shanghai Astronomical Observatory has developed a new observation method for monitoring resident space objects using a high frame rate astronomical CMOS camera, called the short-exposure stacking mode. This method can be used to observe objects of various orbit types with high observation accuracy. This paper describes the implementation of this new method of RSO observation, and the observation experiment of one MEO satellite and two GEO satellites using this method with a 40 cm telescope, the observation system has a 0.5 ° × 0.5 ° field of view. The observation results show that the accuracy of the sensor calibration is 0.3 - 0.4 arc-second. Compared with the external precision ephemeris, the standard deviation of the residual differences is better than 0.5 arc-second, which means that the precise orbit of space objects can be obtained with enough observation. And compared with the method that uses drift scan CCD, the observation time efficiency of the short-exposure stacking mode is better. [ABSTRACT FROM AUTHOR]

• The tether tension's estimation issue of the PSE has been solved. • A speed function has been derived to plan the climber speed at desired state. • A novel observer-based control scheme has been proposed for multiple actuators. This work proposes a novel hybrid control scheme to stabilize a partial space elevator with unknown tether tensions in cargo transportation. The tether tensions are first estimated by a new observing method. The control scheme contains two controllers. With the estimated tensions, Controller I predicts the optimal reference climber speed implemented by the actuator on the climber. When the climber is moving at the reference speed, a novel observer-based super twisting sliding mode control law is proposed for Controller II to eliminates possible disturbances and further stabilises the system in real-time. Simulation results reveal that with the observed tensions, the proposed hybrid control scheme is very effective and accurate in stabilizing the partial space elevator actuated by multiple actuators in the cargo transfer period. [ABSTRACT FROM AUTHOR]

• Finite element Kalman filter to estimate unmeasurable state of tether by measures at tether ends. • Novel measurement model combining real measures at boundary and virtual measures in tether by FEM. • Singularity of reconstruct unmeasurable state by boundary state is eliminated by Kalman filter. This paper proposes a novel finite element Kalman filter to estimate the unmeasurable state of space tether systems based on the measured state at its ends only. The finite element method calculates the unmeasurable internal state as the virtual measurement based on the dynamic model of the system by imposing the input of measured state at the boundary to the model using the Lagrange multiplier method in the spatial space. Combining the real and virtual measurement into a hybrid measurement model of the system, the full state is reconstructed and propagated in the temporal space by the extended Kalman filter. Two state-space system models, the dynamics-based and kinematics-based state models, in the Kalman filter are explored. The observability and stability of the newly proposed finite element Kalman filter are examined and proved. The advantages of the proposed state estimator are (i) the singularity in the virtual measurement of state caused by the number of internal state greater than the number of state measured at the boundary is eliminated in the statistic meaning by the Kalman filter, and (ii) the effects of noises of the observation data and the uncertainties of model discretization are considered and minimized. The correctness and effectiveness of the proposed state estimator is demonstrated by the numerical analysis of a space tether system orbiting around the Earth. The results show the proposed state estimator with only measured state at the ends of the tether successfully provides an accurate time history estimation of geometric configuration and motion of the entire tether. Moreover, the results also show the difference caused by the dynamics-based and kinematics-based system models in the state estimator is negligible. The kinematics-based system model should be used in the state estimator due to its significantly low computational load. Finally, the proposed method can be easily applied for the state estimation process for other space tethered spacecraft systems. [ABSTRACT FROM AUTHOR]

This paper investigates the deployment control problem of tethered space systems subject to an explicit constraint of maximum libration angle and disturbance of tether tension. A two-stage control procedure is developed to design a simple and effective tension control law that is capable of limiting the magnitude of libration angle and suppressing the tension disturbance in the tether deployment process. First, the deployment reference trajectory is designed by a modified barrier Lyapunov function with an explicit constraint on the maximum libration angle. Then, a disturbance observer-based tension control law is developed to track the reference trajectory with the consideration of tension disturbance. Stability analysis of the controller shows that the estimate and tracking errors are bounded to desired ranges. Simulation results demonstrate the proposed simple tension control law is effective and robust in restricting the maximum amplitude of libration angle and suppressing tension disturbance, while guaranteeing a stable deployment without tether slack. [ABSTRACT FROM AUTHOR]

This paper develops a method to estimate the relative pose, motion, and center of mass of an unknown tumbling target using stereoscopic vision. First, the positions and velocities of detected feature points on the spacecraft are tracked and estimated by the measurements of optical flow and photogrammetry. Random observation noises are included in the process. Second, the angular velocity and attitude of the target are estimated by the least square method and q-method, respectively. Finally, the position and velocity of the center of mass of the spacecraft are recovered based on the relative kinematics of the target by successive images over a predefined observation period. Numerical simulations are conducted to demonstrate the effectiveness and precision of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a fractional order sliding mode control for the deployment of tethered space systems with the consideration of uncertainty of external disturbances and unmodeled system dynamics. The proposed fractional order sliding mode control consists of two sub-sliding manifolds that are defined separately for the actuated and unactuated states. This, in turn, generates a control scheme to make all states move toward to the desired states. The stability analysis of the proposed control law indicates not only all states converge to the desired states at equilibrium but also disturbances caused by the uncertainty can be suppressed satisfactorily. Parametric studies are conducted to investigate the influences of fractional order and sub-sliding manifold of unactuated states on the performance of the proposed control law. The performance is compared with the sliding mode, PD and fractional order PD control laws for a baseline scenario of tether deployment. The proposed control law performs better than others in the settling time and the maximum pitch angle control in the presence of unwanted disturbances. Effectiveness and robustness of the proposed control law are demonstrated by computer simulations. [ABSTRACT FROM AUTHOR]

This paper studies the pulse-width pulse-frequency modulation based trajectory planning for orbital rendezvous and proximity maneuvering near a non-cooperative spacecraft in an elliptical orbit. The problem is formulated by converting the continuous control input, output from the state dependent model predictive control, into a sequence of pulses of constant magnitude by controlling firing frequency and duration of constant-magnitude thrusters. The state dependent model predictive control is derived by minimizing the control error of states and control roughness of control input for a safe, smooth and fuel efficient approaching trajectory. The resulting nonlinear programming problem is converted into a series of quadratic programming problem and solved by numerical iteration using the receding horizon strategy. The numerical results show that the proposed state dependent model predictive control with the pulse-width pulse-frequency modulation is able to effectively generate optimized trajectories using equivalent control pulses for the proximity maneuvering with less energy consumption. [ABSTRACT FROM AUTHOR]

The paper presents how to stabilize the deployment and retrieval processes of a space tether system via the tension control, where the model predictive control is exploited to optimize the control performance while the nonlinear dynamics and tension constraint are explicitly taken into account. A new scheme of online quasi-linearization iteration is proposed to transfer the nonlinear optimal control problem into a series of linear optimal control problems that can be solved in sequence at a series of sampling instants. Consequently, it avoids the complete solution of the nonlinear optimal control problem at each sampling interval such that the computational load can be greatly alleviated. Furthermore, the scheme extends the conventional quasi-linearization schemes by distributing the iterative process across sampling instants and online updating the initial condition of the linear optimal control problem. The problems of linear optimal control are discretized using a pseudo-spectral algorithm and then solved by a solver of linear quadratic programming. Numerical case studies indicate that successful deployment and retrieval of the system can be achieved using the proposed control scheme without violating the positive tension constraint. The time cost for each online optimization in the proposed scheme is on the order of 10 ms and far below the sampling interval under consideration. [ABSTRACT FROM AUTHOR]

• Nonlinear dynamic modeling of multi-body hub-spoke tethered satellite formation. • Tether deployment controllers by adaptive sliding mode tension control without thrust. • Adaptive law estimates the upper bound of perturbation for the anti-entanglement of tethers. This work develops a tension control strategy for deploying an underactuated spin-stable tethered satellite formation in the hub-spoke configuration. First, the Lagrange equation is used to model the spin-deployment dynamics of the tethered satellite formation. The central spacecraft is modeled as a rigid body, and the tethered subsatellites are simplified as lumped masses. Second, a pure tension controller has been proposed to suppress the tether libration motion in the deployment without thrusting at the subsatellites. A nonlinear sliding mode control is introduced in the tension controller for the underactuated system to suppress the periodic gravitational perturbations caused by the spinning hub-spoke tethered satellite formation. The unknown upper bounds of the perturbations are estimated by adaptive control law. The bounded stability of the closed-loop tension controller has been proved by the Lyapunov theory. Finally, numerical simulations validate the effectiveness and robustness of the proposed controller, i.e., tethers are fully deployed stably to the desired hub-spoke configuration. [ABSTRACT FROM AUTHOR]

Abstract This work studies the dynamics and optimal stabilization method of a partial space elevator (PSE) system with multiple climbers. All satellites and climbers are assumed as lumped masses that are connected by straight, massless, and inextensible tethers. A general dynamic model is derived for the PSE with multiple climbers. It is found different climber moving patterns of climbers have major influence of dynamic behavior of PSE. Optimal control is used to develop optimal operation modes to suppress the libration of PSE with multiple climbers. Moreover, a new operation mode is proposed to approach the desired mission objectives. It is found that all libration angles can be suppressed to zero by the end of the transfer period if two climbers can be kept at a constant speed. At the same time, the magnitudes of libration angles can be kept bounded by regulating the speed of the middle climber relative to other two climbers. [ABSTRACT FROM AUTHOR]