Low-thrust Engines Research Articles

Parametric study on the performance of an expander bleed engine

Expander bleed cycles have a rather simple configuration when compared to other engine cycles, making them appealing when a new low-thrust engine must be designed. This type of cycles can only operate with light fuels that can be pumped in the liquid state and then properly expanded as a gas in the turbines. As a consequence of the limited amount of power provided by the coolant, expander cycles are characterized by a maximum thrust level of a few hundreds of kilonewtons. The present study focuses on the analysis of a liquid oxygen/liquid hydrogen expander bleed engine cycle dedicated to upper stage applications. A basic selection of all the key parameters defining the engine and its subsystems is carried out to obtain a specific configuration able to work at a prescribed working point. Starting from this configuration, a parametric analyses is performed to study the effect of single component properties and modelling on the expected overall engine performance.

The Design of Low Thrust Engine Spacecraft for Near-earth Asteroid Exploration

This paper discusses the application of computer-assisted design systems to development of low thrust spacecraft intended to take an exploratory flight to potentially hazardous asteroids. The design model of the low thrust spacecraft that is created with computer-aided design systems is described. The mathematical motion model within the heliocentric system of coordinates for such type of spacecraft is considered and used for a motion simulation session. The simulation of flight to the potentially hazardous asteroid is performed with the aid of special complex software that is developed for the purpose of the work. The results of the paper consist of a detailed three-dimensional model of the low thrust spacecraft, heliocentric trajectory of the spacecraft, the values of flight duration and propellant consumption during exploratory flight.

Optimization of Design Parameters of Spacecraft Equipped with Electro Rocket Low-thrust Engine and Calculation its Applying Area at Low Earth Orbit

The problem of electro rocket engine type and its main design parameters optimization for spacecraft located at low circular Earth orbit is studied. The efficiency of chemical (impulse) and electro rocket engine of low-thrust is analyzed. Introduced criteria of efficiency – payload mass maximization, introduced assumption that engine exhaust velocity is constant. In accordance with criteria and assumption, the analytical solution for spacecraft design parameters of spacecraft is obtained. Also, analytical solution for area of efficiency of electro rocket low-thrust engine is obtained. Calculation of spacecraft design parameters equipped with electro rocket low-thrust engine and area of its efficiency applying is carried out.

Shape-based analytic safe trajectory design for spacecraft equipped with low-thrust engines

To rapidly design three dimensional low-thrust safe trajectories for spacecraft orbit transfer and rendezvous problems, an analytic shape-based approach is proposed. Unlike some existing analytic methods, in which a fixed shape of the trajectory is assumed, the proposed trajectory model in this paper is based on the initial and target orbit elements, through which the fitting ability for the trajectory shape is effectively improved. Additionally, the trajectory safety is guaranteed by using the shaping function. Moreover, the proposed approach can avoid computationally intensive numerical integration of the motion equations. The low-thrust trajectories designed by the proposed method can be also used to provide initial guess for more-accurate numerical trajectory optimization. Extensive numerical simulations are presented to show the effectiveness of the proposed approach.

Autonomous navigation during the final ascent of a spacecraft into the geostationary orbit. II. Simulation of operation of an integrated autonomous SC navigation and control system

This study continues the series of papers devoted to the approach to solving the problem of autonomous navigation of a spacecraft (SC) in a geostationary orbit at all stages of its lifecycle: final ascent, transfer to the operating longitude, remaining at the operating longitude, removal from the orbit, and burial. In [1], we formulated the concept of autonomous navigation of a spacecraft at the stage of its final ascent to a geostationary orbit. This stage is most complicated from the technical point of view, taking into account the nonlinearity of the applied mathematical models, the influence of uncontrollable factors of various physical nature, and the necessity of the application of promising hardware (electric low-thrust engine, onboard receiver of signals from global navigation satellite systems, intersatellite communication channels, etc.). Taking this into account, the only constructive method for proving the viability and efficiency (taking into account the requirements formulated by the customer who placed the order) of the developed concept of the autonomous navigation at the final ascent stage in the mathematical simulation of this process. The subject of this study is to demonstrate the capabilities of the developed concept of autonomous navigation from the point of view of achieving the required level of reliability and accuracy in solving the navigation problem at the final ascent stage. This demonstration is based on the analysis of the results of imitating the simulation of the process of a spacecraft's final ascent to a geostationary orbit obtained using the specially developed software complex.

Conjunction challenges of low-thrust geosynchronous debris removal maneuvers

The conjunction challenges of low-thrust engines for continuous thrust re-orbiting of geosynchronous (GEO) objects to super-synchronous disposal orbits are investigated, with applications to end-of-life mitigation and active debris removal (ADR) technologies. In particular, the low maneuverability of low-thrust systems renders collision avoidance a challenging task. This study investigates the number of conjunction events a low-thrust system could encounter with the current GEO debris population during a typical re-orbit to 300km above the GEO ring. Sensitivities to thrust level and initial longitude and inclination are evaluated, and the impact of delaying the start time for a re-orbiting maneuver is assessed. Results demonstrate that the mean number of conjunctions increases hyperbolically as thrust level decreases, but timing the start of the maneuver appropriately can reduce the average conjunction rate when lower thrust levels are applied.

The norm of the position shift of a celestial body upon variation of its orbit

A precise estimate of the variation of the position of a celestial body in the case of small variations of the elements of its orbit is obtained using an Euclidean (mean-square) norm for the deviation in the position. A relatively simple expression for the mean-square deviation of the radius vector dr in terms of the deviations of the elements is derived. These are taken to be first-order small quantitites, with second-order quantities neglected. This relation is applied to estimate the norm ||dr|| in two problems. In the first one, small and constant differences between six orbital elements (including the mean anomaly) are considered for two orbits. In the second one, a zero-mass point moves under the gravitation of a central body and a small perturbing acceleration F. The vector F is taken to be constant in a co-moving coordinate system with axes directed along the radius vector, the transversal, and the binormal vector. In this latter problem, dr is the difference between the position vectors in the osculating and mean orbit. The norm ||dr||2 is the weighted sum of the squares of the components of F, neglecting higher-order small quantities. The coefficients of the quadratic form depend only on the semi-major axis and the eccentricity of the mean orbit. The results are applied to the motion of a small asteroid under the action of a low-thrust engine imparting a small force.

Fault-Tolerant Low-Thrust Trajectory Design with Backups for Multiple Targets

This paper presents a method to design robust trajectories against the possible faults of low-thrust engines. Recently, increasing number of space probes with low-thrust engines have been developed. Due to the insufficient reliability of low-thrust propulsion system, almost all probes with ion engines have experienced the failure of engines. Conventional methods to design the low-thrust trajectory have pursued fuel minimum solution to only one target celestial body which does not necessarily mean the maximization of mission achievement. In other words, it can enhance the mission accomplishment to intelligently change the trajectory when engine failures occur. In this research, the objective function is defined as expected scientific gain, and the optimal solution is searched by a proposed method. Resulting method, Bellman Rapidly-exploring Random Trees (Bellman RRT) are efficiently extended by applying the Bellman equation. Finally, the numerical simulation demonstrated that the Bellman RRT improved the mission achievement using real deep space exploration scenario.

Stabilizing the coupled orbit–attitude dynamics of a rigid body in a J2 gravity field using Hamiltonian structure

The gravitationally coupled orbit–attitude dynamics of a rigid body in a J2 gravity field is a high-precision model for the spacecraft in the close proximity of a small spheroid celestial body, since the gravitational orbit–attitude coupling of the spacecraft is naturally taken into account in this model. A Hamiltonian structure-based feedback control law is proposed to stabilize relative equilibria of the rigid body in the J2 gravity field. The proposed stabilization control law is consisted of three parts: potential shaping, momentum control, and energy control. The potential shaping is used to modify the gravitational potential artificially so that the relative equilibrium is a minimum of the modified Hamiltonian. It is shown that the unstable relative equilibrium can always be stabilized in the Lyapunov sense by the potential shaping with sufficiently large feedback gains. Then the momentum control leads the motion to the same invariant manifold with the relative equilibrium, which is actually a momentum level set. The energy control introduces energy dissipation into the system and the motion will asymptotically converge to the minimum of the modified Hamiltonian on the invariant manifold, i.e., the relative equilibrium. The feasibility of the proposed stabilization control law is validated through numerical simulations. The control law can be implemented by the attitude control system and low-thrust engines onboard and the fuel consumption is reasonable. This Hamiltonian structure-based stabilization approach is applicable to non-canonical Hamiltonian systems commonly existing in the astrodynamics. Since the natural dynamical behaviors of the system is fully utilized, the proposed control law is very simple and is easy to implement autonomously with little computation in the space applications.

Оптимальное удержание космического аппарата с двигателями малой тяги на солнечно-синхронной орбите

Оптимальное удержание космического аппарата с двигателями малой тяги на солнечно-синхронной орбите

A solution of the navigation problem for autonomous insertion of payload into a geostationary orbit using a low-thrust engine

An onboard navigation system for a space vehicle (satellite) as it is inserted into a geostationary orbit using a low-thrust engine is considered. The navigation system uses optoelectronic Earth, Sun, and star sensors and a multichannel GNSS signal receiver. The purpose of the study is to form a general design of the integrated navigation system, including the justification of its architecture and operation algorithms, based on requirements for the accuracy of the navigation problem solution. To integrate various measurements, a quasilinear Kalman filter and its special "scalar" modification are used. The vector to be estimated onboard the spacecraft consists of the coordinate and velocity components, the attitude of its body axis, and the attitude and actual thrust of its main thruster. Instrument sensor errors are considered as uncontrollable factors. The main tool for the analysis of the navigation system error is simulation, which is performed using dedicated software developed using the object-oriented paradigm.

Software for planning and processing the test results for low-thrust liquid rocket engines

In this paper, we developed software for planning and subsequent statistical processing of the test results for low-thrust liquid rocket engines (LRE).

Spectral-tomographic methods and means of studying propellant flows of ion and plasma low-thrust engines

Methods of spectral-tomographic diagnostics of ion and plasma jets in ion-plasma low-thrust engines are described. Methods that I have developed of 2D and 3D reconstruction of local values of temperature, concentration and absolute intensity in the ion-plasma jet are analyzed. Experimental setups of laboratory type for studying parameters of propellants of ion and plasma propulsion engines are described.

Construction of optimum controls and trajectories of motion of the center of masses of a spacecraft equipped with the solar sail and low-thrust engine, using quaternions and Kustaanheimo-Stiefel variables

The problem of optimum rendezvous of a controllable spacecraft (SC) with an uncontrollable spacecraft, moving over a Keplerian elliptic orbit in the gravitational field of the Sun, is considered. Control of the SC is performed using a solar sail and low-thrust engine. For solving the problem, the regular quaternion equations of the two-body problem with the Kustaanheimo-Stiefel variables and the Pontryagin maximum principle are used. The combined integral quality functional, which characterizes energy consumption for controllable SC transition from an initial to final state and the time spent for this transition, is used as a minimized functional. The differential boundary-value optimization problems are formulated, and their first integrals are found. Examples of numerical solution of problems are presented. The paper develops the application [1–6] of quaternion regular equations with the Kustaanheimo-Stiefel variables in the space flight mechanics.

Analytical guidance for spacecraft relative motion under constant thrust using relative orbit elements

Proximity control of modern nano-spacecraft often relies on low and discrete thrust engines that are characterized by low consumption, and generate on-off force profiles. New guidance solutions must take into account the nature of this type of orbital engines. This paper introduces novel analytical guidance solutions for spacecraft relative motion considering continuous, on-off thrust, and using relative orbit elements as a geometrical representation of the dynamics. The solutions provide the relative state vector at any given time, accommodating any thrust magnitude along the three directions of the relative frame, as well as generic activation times and durations. Relative orbit elements geometrically interpret key aspects of the relative motion, including for example, the relative ellipse size, and the evolution of its center in time. The new solutions provide the guidance designer with a direct visualization of the thrust effects on the relative motion geometry, offering new possibilities for analytical guidance in the presence of continuous thrust engines, such as low thrust engines on nano-spacecraft. The paper presents the analytical solutions, and tests their effectiveness using a sample thrust profile based on input-shaping, previously developed by one of the authors using classical Cartesian coordinates. The use of relative orbit elements shows substantial benefits and added simplicity with respect to Cartesian-based approaches, holding the promise for straightforward onboard spacecraft implementation. The software developed for this research will be available open source11〈http://www.riccardobevilacqua.com/links.html〉., to be used by spacecraft guidance designers as trajectory design tool.

Automated Design of Propellant-Optimal, Low-Thrust Trajectories for Trojan Asteroid Tours

The sun–Jupiter Trojan asteroid swarms are targets of interest for robotic spacecraft missions, where low-thrust propulsion systems offer a viable approach for realizing tours of these asteroids. This investigation introduces a novel scheme for the automated creation of prospective tours under the natural dynamics of a multibody regime with thrust supplied by a variable-specific-impulse engine. The procedure approximates tours by combining independently generated fuel-optimal rendezvous arcs between asteroid pairs into a series of trajectory legs. Propellant costs as well as departure and arrival times are estimated from the performance of the individual thrust arcs. Tours of interest are readily constructed in higher-fidelity models, and options for the end-to-end trajectories are easily assessed. In this investigation, scenarios where constant and varying-power sources are available to the low-thrust engine are explored. In general, the automation procedure rapidly generates a large number of potential tours and supplies reasonable cost estimates for preliminary baseline mission design. Computational aspects of the design procedure are automated such that end-to-end trajectories are generated with a minimum of human interaction after key elements associated with a proposed mission concept are specified.

Optimization of transfer trajectories to the Apophis asteroid for spacecraft with high and low thrust

The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid’s satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft’s hyperbolic velocity “at infinity” during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft’s final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.

Trajectory control around non-spherical bodies modelled by parallelepipeds

This work is a study of the dynamics around bodies with non-spherical shapes. The gravitational field of a body with non-uniform mass distribution is not central, resulting on orbits around this body that behave different from a keplerian orbit, generating a perturbation on the gravitational field. Irregular objects can be modelled by combining several geometric figures like parallelepipeds. This model can be applied to asteroids, which are objects with non-spherical shapes. The disturbing force generated by these bodies can then be obtained as the sum of the force on each cube. The present paper makes a first study in this problem by showing the evolution of the keplerian elements of orbits around a cube. It also considers a closed loop control system for the trajectory, required to compensate the perturbations due to the irregular shape of the body with the use of a low thrust engine. The main goal is to show that it is possible to use this type of control to keep the orbit keplerian all the time and the details on how to do that.

Optimal trajectories for solar bow shock mission

This paper deals a Solar Bow Shock mission, a phenomenon of interaction between the solar wind and the interstellar medium, due to the relative motion of our star with respect to the enormous interstellar matter cloud that contains it. This phenomenon occurs at boundary of the solar system (200 AU), and it is preferable a mission in situ that could examine in detail what actually happens on-the-spot, to understand its effect on the planets of the solar system. Voyager 1 & 2 reached the area where the phenomenon takes place after 30 years. The target is to arrive there optimizing both the transfer time, and the propellant mass consumption. Therefore, the trajectory will be optimized using different propulsion systems and appropriate flyby sequences.. The approach techniques that will be used foresee executions of impulsive or ballistic gravity assists with the utilisation of high thrust engine only, or low thrust engine only, or both engines in two different phases of the mission. By comparing all the solutions obtained imposing different initial conditions the optimal trajectory to arrive at Solar Bow Shock is presented.

Finite-Burn Linear Targeting Algorithm for Autonomous Path Planning and Guidance

In path planning and guidance applications, linear targeting through differential corrections is a classical approach for identifying feasible solutions that meet specified mission and trajectory constraints. However, to date, these methods relied on the assumption that the associated correction maneuvers were impulsive in nature. This impulsive assumption is generally reasonable when the duration of the engine burn is small. However, this approximation breaks down when lower thrust engines are employed as the duration of the burn becomes more significant. In these cases, an impulsive linear targeting algorithm is inadequate. Often times, low-thrust problems of this type are solved from the perspective of optimal trajectory design and depend on numerical methods like nonlinear programming. These methods, however, are generally considered prohibitive for autonomous flight applications, where computational resources are limited and optimality is not always as important as feasibility. The present study focuses on the theoretical development and numerical validation of a linear targeting algorithm capable of accommodating finite burn maneuvers. Examples are presented to contrast the performance of this new targeting process against more classical impulsive targeting methods. The examples presented focus largely on precision entry applications, but the finite burn targeting process itself is applicable across a broad set of scenarios and fields.