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Space-based gravitational wave detection has gained attention in recent years due to its lower detection frequency. The long-term stability of configuration is critical for high-precision measurements, placing stringent demands on spacecraft orbit injection accuracy. However, during orbit transfer, uncertainty in the low thrust propulsion system’s parameters accumulate over time, which may cause the spacecraft to potentially deviate from its normal orbit. This paper proposes a low thrust transfer orbit design method considering uncertainty factors for heliocentric space-based gravitational wave observatory. First, an optimization model for low thrust transfer orbit is established, using global optimization algorithm to design the nominal transfer orbit. Then, considering uncertainty in navigation and thrust, an online low thrust trajectory replanning method is proposed, which can effectively reduce end-state errors through periodic replanning. Finally, the proposed method is applied to the Taiji program. Simulation results show that after online low thrust trajectory replanning, the fuel consumption of single spacecraft is approximately 30 kg, with end-position and velocity errors of less than 4 km and 2 mm/s, respectively. This research could provide valuable references for the transfer orbit design of future Taiji program and other high-precision space science missions.

The plume-surface interaction that occurs as a result of a variable-thrust engine exhaust plume impinging on soil during landings is critical for future lunar mission design. Unique lunar environmental properties, such as low gravity, high vacuum, and the regolith layer, make this study complex and challenging. In this paper, we build a reliable simulation model, with constraints based on landing photos, to characterize the erosion properties induced by a low-thrust engine plume. We focus on the low-thrust plume-surface erosion process and erosion properties during the Chang’E-5 mission, aiming to determine the erosion difference between high- and low-thrust conditions; this is a major concern, as the erosion process for a low-thrust lunar mission is rarely studied. First, to identify the entire erosion process and its relative effect on the flat lunar surface, a one-to-one rocket nozzle simulation model is built; ground experimental results are utilized to verify the simulated inlet parameters of the vacuum plume flow field. Following that, plume flow is considered using the finite volume method, and the Roberts erosion model, based on excess shear stress, is adopted to describe plume-surface interaction properties. Finally, a Lagrangian framework using the discrete phase model is selected to investigate the dynamic properties of lunar dust particles. Results show that erosion depth, total ejected mass, and the maximum particle incline angle during the Chang’E-5 landing period are approximately 0.2 cm, 335.95 kg, and 4.16°, respectively. These results are not only useful for the Chang’E-5 lunar sample analysis, but also for future lunar mission design.

This paper discusses the application of the homotopy approach to optimizing the free-flight-time low-thrust trajectory considering the performance characteristics. The trajectory optimization problem is formulated as an optimal control problem (two-point boundary value problem). The developed homotopy algorithm to solve the optimal control problem comprises three steps—orbital energy/acceleration matching, flight-time matching, and orbital reshaping. A comprehensive case study demonstrates the effectiveness of the proposed homotopy-based optimization algorithm for an optimal design of a low-thrust trajectory involving long mission time.

The present research performs numerical studies to search for the best maneuvers, from the point of view of minimum time, to make adjustments in the semi-major axis, eccentricity and inclination of a spacecraft traveling around the Earth. For those maneuvers, low thrust propulsion is used under optimal and sub-optimal assumptions, to verify the main differences in terms of transfer time. In addition, solar sail dynamics is used. The spacecraft is assumed to have a propulsion with a fixed magnitude and that the control is based on choosing the direction of the propulsion. It is found that optimal control gives the minimum transfer time, while sub-optimal control restricted the control to follow a predescribed function, which is assumed to be a constant or linear function in time. Finally, solar sails present themselves as an option where fuel is a critical factor, given their much longer maneuver duration, but with a zero fuel consumption. The numerical-analytical modeling of optimization methods developed in this study can break any type of symmetry in the solutions. In turn, they can increase their energetic efficiency. The present research compares those results in detail, in particular looking at the transfer time in all cases studied.

The reachability assessment of low-thrust spacecraft is of great significance for orbital transfer, because it can give a priori criteria for the challenging low-thrust trajectory design and optimization. This paper proposes an approximation method to obtain the variation maximum of each orbital element. Specifically, two steps organize the contribution of this study. First, combined with functional approximations, a set of analytical expressions for the variation maxima of orbital elements over one orbital revolution are derived. Second, the secular approximations for the variation maxima of the inclination and the right ascension of the ascending node are derived and expressed explicitly. An iterative algorithm is given to obtain the secular variation maxima of the other orbital elements the orbital elements other than the inclination and right ascension of the ascending node. Numerical simulations for approximating the variation maxima and a preliminary application in estimation of the velocity increment are given to demonstrate the efficiency and accuracy of the proposed method. Compared with the indirect method used alone for low-thrust trajectory optimization, the computation burden of the proposed method is reduced by over five orders of magnitude, and the computational accuracy is still high.

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill–Clohessy–Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Δv requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.

The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing ( $S$ ) and phasing ( $\\unicode[STIX]{x1D711}$ ) to be investigated over a range of non-dimensional frequencies (or Strouhal number, $St$ ). Results indicate that the hind foil can produce from no thrust to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flow fields indicates that high thrust occurs when the hind foil weaves between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the $S-\\unicode[STIX]{x1D711}$ parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered $(0.2\\leqslant St\\leqslant 0.5)$ . A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.

This paper presents the results of an experimental study of the jet thrust of ionized nitrogen flowing from the working chamber of an experimental sample of an accelerator ion thruster into a vacuum space. The resonant aerodynamic method (RAM-method) was chosen as the main research method. A method for determining low thrust and the design of a stand for implementing the RAM- method are proposed. The object of research is a prototype of an accelerator two-gap ion thruster with a solid-state microwave plasma generator and a toroidal resonator. The study showed that a 2.5 W microwave generator together with a 2.5 W accelerating potential difference voltage source at a nitrogen consumption of 0.1 mg/s creates an ion jet, the speed of which reaches 100 km/s. The current of the ion jet was 5.5-6 μA. The jet thrust was 0.141-0.188 μN.

The aeroacoustics of a boundary layer ingesting (BLI) ducted fan is investigated experimentally. The study examines a ducted fan immersed in an adverse streamwise pressure gradient turbulent boundary layer developed over a curved wall. Aeroacoustics measurements indicate that the noise from the BLI ducted fan results from a complex interaction among the fan, duct and the incoming boundary layer. The fundamental mechanisms of noise generation are explained using a general source separation strategy. A detailed noise comparison is made at varying fan rotational speeds and across a wide range of axial inflow velocities. In a low thrust regime, the noise is found to be driven by the fan loading, coupled with duct acoustics and the haystacking phenomenon. In a high thrust regime, the contribution from duct acoustics diminishes, and the noise is predominantly driven by the fan loading coupled with the haystacking phenomenon.