Low-thrust Control Research Articles

Faster-Than-Natural Satellite Circumnavigation via Continuous Control

The design of a continuous control architecture for faster-than-natural satellite circumnavigation missions, where the desired relative orbital period is shorter than the natural orbital period, is investigated. In such cases, satellites must complete orbits around a target faster than would be possible through natural motion alone, requiring advanced control systems. This paper considers the case of continuous low-thrust control because of its low fuel expenditure. One challenge of continuous control for faster-than-natural relative motion is its susceptibility to noise due to the large nominal thrust that is required. The deleterious effect of noise has not been addressed in the literature for this problem. This work develops a feedforward control that helps to eliminate unnecessary control effort and jitter in the actuation due to noise. When implemented in conjunction with existing feedback control schemes, the resulting control system is shown to perform well and shows promise as an implementable option with current technology.

Relative E/I vector-based optimal and suboptimal control for continuous low thrust formation reconfiguration in circular orbits

This paper addresses the fuel-optimal satellite formation reconfiguration problem with continuous low-thrust control. Based on the relative eccentricity and inclination (E/I) theory, a comprehensive approach to optimal continuous low-thrust reconfiguration in circular or near-circular orbits is proposed. By analyzing the feasible fuel cost lower bound, the reconfiguration scenarios are categorized into four types, and the corresponding optimal or suboptimal control schemes are derived. More specifically, for suboptimal continuous control schemes, the relation between user-defined variables with fuel-cost is derived, providing a clear direction for better fuel cost. Compared with previous work that gives only feasible analytical solutions or obtains optimal solutions with numerical methods, the proposed method provides an efficient approach to optimal continuous low thrust reconfiguration for feasible scenarios and adjustable sub-optimal schemes for unfeasible scenarios. The proposed framework contributes to the practical application in engineering, enabling the design and analysis of more cost-effective space missions. The analysis of fuel cost reveals that the optimal continuous low thrust reconfiguration is limited with scenarios. The overall solutions are simulated and validated in four reconfiguration scenarios.

Distributed satellite system autonomous orbital control with recursive filtering

In this article, we propose a recursive orbital elements filter for autonomous control of Distributed Satellite Systems (DSS) that significantly reduces the variance of relative orbital elements between the observed and the desired satellite orbits. Leveraging satellite kinematics and control inputs data, combined with a model of relative dynamics, the filter provides smooth and continuous orbital control, while minimizing propellant consumption. In conjunction with Precise Point Positioning (PPP) navigation, the proposed filter enables onboard continuous low-thrust control compatible with high-performance electric propulsion. We also propose a restricted transverse/normal control law that simplifies the thruster's configurations and/or attitude manoeuvres required for propulsion pointing. The applicability and validity of our proposed techniques are verified by numerical simulations with two case studies: a constellation for Differential Interferometric Synthetic Aperture Radar (DInSAR) for global infrastructure monitoring; and a maritime domain awareness mission based on along-track interferometric synthetic aperture radar which requires single-pass interferometry for responsive ship traffic surveillance, and the coverage of a very large maritime zone with high revisit rates.

Robustness analysis and station-keeping control of an interferometer formation flying mission in low Earth orbit

The impact of formation flying on interferometry is growing over the years for the potential performance it could offer. However, it is still an open field, and many studies are still required. This article presents the basic principles behind interferometry focusing first on a single array and secondly on a formation of satellites. A sensitivity analysis is carried out to evaluate how the performance of the interferometry is affected by an error in the relative position in the formation geometry. This is estimated by computing the loss of the performance in terms of percentage deviation due to a non-nominal relative trajectory, including two-dimensional errors and defining a payload index. The main goal of this study is to estimate whether some errors in the relative state are more impacting than others. The final objective is to compute the link between a position error and a specific loss of performance, to foresee the origin of the the error. Furthermore, a dynamical model is developed to describe the relative motion in the Low Earth Orbit environment, considering both the unperturbed and the J2 and drag contributions. A Proportional, Integral and Derivative controller is implemented for the position control of a multiple satellite formation flying, considering a low thrust control profile. The Formation Flying L-band Aperture Synthesis study is taken as the case scenario, analysing both nominal and non-nominal configurations. This study serves as a starting point for the development of a combined tool to assess the performance of the interferometry and the control on the relative state for future remote sensing studies involving relative motion.

A filter for tracking non-cooperative low-thrust satellites using surveillance radar data

Numerous satellites with electric propulsion perform long duration maneuvers during their orbit acquisition phase. This poses a challenge to space object cataloging activities if no information regarding the maneuver plan is known a priori. Various works have been devoted to maneuver detection and tracking of space objects using radar and optical surveillance data, but the special case of unknown dynamics, analogous to a maneuver spanning several days or months, has received less attention. Herein, we propose a methodology to maintain custody of uncooperative low-thrust spacecraft under the special characteristics of surveillance radar observations. Based on the stochastic hybrid systems framework, a multi-hypothesis algorithm leverages information derived from measurements and the dynamical characteristics of the object. The latter is accomplished in an efficient manner by means of a low-thrust control metric that relies on the Thrust Fourier Coefficients approximation. To improve filter robustness, the maneuver transition density is assumed to be uniform within the set of reachable states, whose outer bound is approximated via the proposed control measure. The algorithm is applied to the orbit acquisition phase of a LEO satellite using synthetic data from a simulated surveillance radar network, and its shown to be capable of maintaining custody throughout the entire three-month transfer.

End-to-end trajectory concept for close exploration of Saturn’s Inner Large Moons

We present a trajectory concept for a small mission to the four inner large satellites of Saturn. Leveraging the high efficiency of electric propulsion, the concept enables orbit insertion around each of the moons, for arbitrarily long close observation periods. The mission starts with a EVVES interplanetary segment, where a combination of multiple gravity assists and deep space low thrust enables reduced relative arrival velocity at Saturn, followed by an unpowered capture via a sequence of resonant flybys with Titan. The transfers between moons use a low-thrust control law that connects unstable and stable branches of the invariant manifolds of planar Lyapunov orbits from the circular restricted three-body problem of each moon and Saturn. The exploration of the moons relies on homoclinic and heteroclinic connections of the Lyapunov orbits around the L1 and L2 equilibrium points. These science orbits can be extended for arbitrary lengths of time with negligible propellant usage. The strategy enables a comprehensive scientific exploration of the Inner Large Moons, located deeply inside the gravitational well of Saturn, which is unfeasible with conventional impulsive maneuvers due to excessive fuel consumption.

A satellite formation to display pixel images from the sky: Mission design and control algorithms

A concept of deploying spacecraft formations to display advertisement images from space is considered. The spacecraft are equipped with sunlight reflectors, which under certain lighting conditions and given the right attitude can be observed from Earth as bright stars in the sky. When deployed into appropriately selected orbits the spacecraft can be grouped into a pixel image. The problem of formation deployment and maintenance to demonstrate two particular images over a chosen point of interest is addressed in this study. The images visibility conditions in terms of reflector size and proper lighting are formalized and relative orbits of the formation spacecraft are chosen. This brings the study to a fully formulated set of problems: formation deployment after launch, formation keeping to maintain the image geometry and formation reconfiguration to change the demonstrated images. The problem is solved by a hybrid control strategy comprising impulsive maneuvers and low-thrust control taking into account fuel consumption and collision avoidance. The proposed approach can be used in design studies of space advertising missions to evaluate the number of images to be displayed along the selected orbit, the amount of fuel required for formation maintenance and reconfiguration, and the mission lifetime.

Design of optimal low-thrust manoeuvres for remote sensing multi-satellite formation flying in low Earth orbit

This paper presents a strategy for optimal manoeuvre design of multi-satellite formation flying in low Earth orbit environment, with the aim of providing a tool for mission operation design. The proposed methodology for formation flying manoeuvres foresees a continuous low-thrust control profile, to enable the operational phases. The design is performed starting from the dynamic representation described in the relative orbital elements, including the main orbital perturbations effects. It also exploits an interface with the classical radial-transversal-normal description to include the maximum delta-v limitation and the safety condition requirements. The methodology is applied to a remote sensing mission study, Formation Flying L-band Aperture Synthesis, for land and ocean application, such as a potential high-resolution Soil Moisture and Ocean Salinity (SMOS) follow-on mission, as part of a European Space Agency mission concept study. Moreover, the results are applicable to a wide range of low Earth orbit missions, exploiting a distributed system, and in particular to Formation Flying L-band Aperture Synthesis (FFLAS) as a follow-on concept to SMOS.

Optimal Trajectory Synthesis for Spacecraft Asteroid Rendezvous

Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters.

Теоретичні дослідження з аерогазодинаміки об’єктів ракетно-космічної те-хніки

This paper presents the results of theoretical studies on rocket/space hardware aerogas dynamics obtained from 2016 to 2020 at the Department of Aerogas Dynamics and Technical Systems Dynamics of the Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine along the following lines: rocket aerodynamics, mathematical simulation of the aerogas thermodynamics of a supersonic ramjet vehicle, jet flows, and the hydraulic gas dynamics of low-thrust control jet engines. As to rocket aerodynamics, computational methods and programs (CMPs) were developed to calculate supersonic flow past finned rockets. The chief advantage of the CMPs developed is computational promptness and ease of adding wings and control and stabilization elements to rocket configurations. A mathematical simulation of the aerogas thermodynamics of a supersonic ramjet vehicle yielded new results, which made it possible to develop a prompt technique for a comprehensive calculation of ramjet duct flows and generalize it to 3D flow past a ramjet vehicle. Based on marching methods, CMPs were developed to simulate ramjet duct flows with account for flow past the airframe upstream of the air inlet, the effect of the combustion product jet on the airframe tail part, and its interaction with a disturbed incident flow. The CMPs developed were recommended for use at the preliminary stage of ramjet component shape selection. For jet flows, CMPs were developed for the marching calculation of turbulent jets of rocket engine combustion products with water injection into the jet body. This made it possible to elucidate the basic mechanisms of the effect of water injection, jet–air mixing, and high-temperature rocket engine jet afterburning in atmospheric oxygen on the flow pattern and the thermogas dynamic and thermalphysic jet parameters. CMPs were developed to simulate the operation of liquid-propellant low-thrust engine systems. They were used in supporting the development and ground firing tryout of Yuzhnoye State Design Office’s radically new system of control jet engines fed from the sustainer engine pipelines of the Cyclone-4M launch vehicle upper stage. The computed results made it possible to increase the informativity of firing test data in flight simulation. The CMPs developed were transferred to Yuzhnoye State Design Office for use in design calculations.

Autonomous closed-loop guidance using reinforcement learning in a low-thrust, multi-body dynamical environment

Onboard autonomy is an essential component in enabling increasingly complex missions into deep space. In nonlinear dynamical environments, computationally efficient guidance strategies are challenging. Many traditional approaches rely on either simplifying assumptions in the dynamical model or on abundant computational resources. This research effort employs reinforcement learning, a subset of machine learning, to produce a ‘lightweight’ closed-loop controller that is potentially suitable for onboard low-thrust guidance in challenging dynamical regions of space. The results demonstrate the controller’s ability to directly guide a spacecraft despite large initial deviations and to augment a traditional targeting guidance approach. The proposed controller functions without direct knowledge of the dynamical model; direct interaction with the nonlinear equations of motion creates a flexible learning scheme that is not limited to a single force model, mission scenario, or spacecraft. The learning process leverages high-performance computing to train a closed-loop neural network controller. This controller may be employed onboard to autonomously generate low-thrust control profiles in real-time without imposing a heavy workload on a flight computer. Control feasibility is demonstrated through sample transfers between Lyapunov orbits in the Earth–Moon system. The sample low-thrust controller exhibits remarkable robustness to perturbations and generalizes effectively to nearby motion. Finally, the flexibility of the learning framework is demonstrated across a range of mission scenarios and low-thrust engine types.

Correction to: Autonomous Low-Thrust Control of Long-Distance Satellite Clusters Using Artificial Potential Function

Correction to: Autonomous Low-Thrust Control of Long-Distance Satellite Clusters Using Artificial Potential Function

Autonomous Low-Thrust Control of Long-Distance Satellite Clusters Using Artificial Potential Function

Thispaper investigates the micro-satellite cluster long-distance gathering control problem including initialization, orbit maintenance and collision avoidance operations. This problem is formulated using absolute orbital elements and newly developed quadratic artificial potential function based on these elements. Incorporating with the artificial potential function, a distributed autonomous low-thrust control method is proposed to solve the cluster gathering problem. Comparing with the fuel-optimal control problem formulated by equations established in Cartesian coordinates, the proposed method demonstrates geometrical intuition and possesses a low-cost computation burden. These advantages make the proposed method more suitable for controlling micro-satellite clusters. The stability of the autonomous low-thrust control method is proved using the Lyapunov method. Additionally, a Monte Carlo analysis is applied to demonstrate both the effectiveness and the collision avoidance ability of the presented algorithm.

Linearization method for constant thrust control

Low-thrust control technologies display advantages in space missions. In this study, a linearization method for constant-thrust control is proposed. Based on elliptic integrals, the constant-thrust linear equations are introduced. Furthermore, an analytical two-section linear equations are derived. In addition, for considering J 2 perturbation, semi-analytical linear equations are also presented. Numerical simulations are conducted to demonstrate the validation of the proposed method, which proves to be a practical choice for engineering.

Loosely displaced formation-keeping control for satellite swarm with continuous low-thrust

Aiming at a long-term formation-keeping problem for the satellite swarm, the concept of a loosely displaced formation is proposed in this article. On this basis, a continuous low-thrust control strategy for maintaining the loosely displaced formation is designed. The control objective is to reduce more fuel consumption during the formation-keeping. For achieving that, we proposed a forward-feedback control strategy by using pseudo-spectral method and sliding mode theory. To be specific, the control strategy includes two parts: a forward control and a feedback control. For the forward control, a numerical optimization with the Legendre pseudo-spectral method is attempted to convert the optimal control problem into a nonlinear programming problem and fuel consumption is selected as the optimization index. For stability issue, the feedback control via adaptive finite-time sliding mode theory is introduced as an additional control component. Finally, the numerical results demonstrate that propellant mass is effectively saved as well as the formation can be tracked accurately with this control strategy proposed in this article.

Recent progress in research on micro-cathode arc thrusters

Micro-cathode arc thrusters have been widely used in micro-nanosatellites owing to their high specific impact, long lifetime, repeatable startup, low thrust and high control precision. Micro-cathode arc thrusters and their derivatives are currently being developed and optimized. The micro-cathode arc thruster can generate plasma stably and efficiently, and form a thrust force under a magnetic field with very low power in pulsed operation mode. This paper reviews the last 20 years of literature on micro-cathode arc thrusters, with a focus on papers published in this field in the last 5 years. In light of the development of the micro-cathode arc thruster and the latest research, the direction of future development and the application of key technologies are reviewed. Future micro-cathode arc propulsion systems are expected to exhibit higher reliability, longer lifetimes, higher specific impact, greater integration and higher thrust and to be operated in various modes.

Orbit-Attitude Coupled Tracking and Landing Control for an Asteroid

Recent research on asteroid exploration has shown tremendous potential to provide humankind detailed views of unexplored worlds in the inner solar system. A potential market of asteroid mining has aroused interest from commercial companies gradually. Asteroid exploration has the potential to offer the possibility to revolutionize the supply of many resources which are vital but exorbitant for human. A typical asteroid exploration mission is composed of remote asteroid detecting, approaching, hovering, landing and sampling, take-off and return, re-entry stage. Among these stages the tracking and landing control of the asteroid is crucial for the exploration. Rendezvous, approaching, fly-around and landing problem of an asteroid is investigated in this paper. The expected motion of the tracking spacecraft determined by the asteroid’ orbital and attitude status is presented firstly. According to the design of the OSIRIS-REx project, several constant thrusters are used for spacecraft to track the asteroid. Different control strategies like pulse control, saturated nonlinear control, limit cycle control and PWM based low-thrust control are developed to fulfil the asteroid’s tracking mission of different stages. Numerical simulations demonstrate the effectiveness of the tracking control.

Optimization of Satellite Orbits with Resonant Cross-Track Control

This paper is dedicated to developing a new approach for solving the low-thrust trajectory optimization problem of spacecraft in low Earth orbits. The unknown control function is parameterized by its Fourier coefficients up to a given order, thus transforming the optimal control problem into a nonlinear parameter optimization problem. An adequate choice of the period and the maximum degree of the truncated Fourier expansion leads to the creation of a resonance between the natural frequency of the orbital dynamics and the control function. Resonance is a well-known phenomenon; however, the novelty of the presented approach is to create the resonance artificially, in order to increase the effect of the control acceleration on the satellite trajectory evolution. This artificial resonance contributes to creating a rapid change of the cross-track orbital elements, using the low-thrust control acceleration. The proposed technique is applied to low Earth orbits constellation optimization, involving the minimization of the geometric dilution of precision of an Earth coverage problem.

Design of Artificial Sun-Synchronous Orbits with Main Zonal Harmonics and Solar Radiation Pressure Using Continuous Low-Thrust Control Strategies

Abstract Artificial sun-synchronous orbits are suitable for remote sensing satellites and useful in giving accurate surface mapping. To design such orbits accurately with arbitrary orbital elements, three control strategies are provided with the consideration of main zonal harmonics up to J 4 and solar radiation pressure (SRP). In this paper, the continuous variable low-thrust control is used as a way to achieve these artificial orbits and given by electric propulsions rather than chemical engines to enlarge lifespan of the spacecraft. The normal continuous low-thrust control is used to illustrate the control strategies. Furthermore, formulas for refinement of normal control thrusts are applied to overcome errors due to approximations. The results of the simulation show that the control strategies explained in this paper can realize sun-synchronous orbits with arbitrary orbital parameters without side effects and the effect of solar radiation pressure is very small relative to main zonal harmonics. A new technique is suggested, ASSOT-3, to minimize fuel consumption within one orbital period more than others. This technique is based on computing the root mean square of the rate of ascending node longitude instead of the average.

Construction of Frozen Orbits Using Continuous Thrust Control Theories Considering Earth Oblateness and Solar Radiation Pressure Perturbations

The problem of the artificial frozen orbits around the Earth is investigated. To design such orbits with arbitrary orbital parameters, six control strategies are discussed taking into account the main zonal harmonics up to J4 and solar radiation pressure (SRP). The effect in the argument of periapsis due to the main zonal harmonics is revealed to be about three orders of magnitude greater than that of SRP. Two comparisons are given. To obtain longer lifespan of the spacecraft, continuous variable low-thrust control is implemented. Radial and/or transverse thrusts are used to achieve these orbits. Furthermore, explicit formulas for refinement of the control thrusts are given in order to overcome errors due to approximations arising from long and short periodic variations of a and e. Some concluding remarks can be inferred from the presented simulation; e.g. the energy consumed is saved efficiently when using the root mean squares rather than using averages, also when using coupled radial and transverse thrusts instead of using single radial or transverse thrust. To minimize the fuel consumption more efficiently, three new techniques are suggested. The calculations illustrated that AFOT-F Technique, where the transverse control thrust is constant, has the minimum control thrust required.