Design feasibility via ascent optimality for next-generation spacecraft

This paper deals with the optimization of the ascent trajectories for single-stage-sub-orbit (SSSO), single-stage-to-orbit (SSTO), and two-stage-to-orbit (TSTO) rocket-powered spacecraft. The maximum payload weight problem is studied for different values of the engine specific impulse and spacecraft structural factor.The main conclusions are that: feasibility of SSSO spacecraft is guaranteed for all the parameter combinations considered; feasibility of SSTO spacecraft depends strongly on the parameter combination chosen; not only feasibility of TSTO spacecraft is guaranteed for all the parameter combinations considered, but the TSTO payload is several times the SSTO payload.Improvements in engine specific impulse and spacecraft structural factor are desirable and crucial for SSTO feasibility; indeed, aerodynamic improvements do not yield significant improvements in payload.For SSSO, SSTO, and TSTO spacecraft, simple engineering approximations are developed connecting the maximum payload weight to the engine specific impulse and spacecraft structural factor. With reference to the specific impulse/structural factor domain, these engineering approximations lead to the construction of zero-payload lines separating the feasibility region (positive payload) from the unfeasibility region (negative payload).     

Design of optimal earth pole-sitter transfers using low-thrust propulsion

Recent studies have shown the feasibility of an Earth pole-sitter mission using low-thrust propulsion. This mission concept involves a spacecraft following the Earth's polar axis to have a continuous, hemispherical view of one of the Earth's poles. Such a view will enhance future Earth observation and telecommunications for high latitude and polar regions. To assess the accessibility of the pole-sitter orbit, this paper investigates optimum Earth pole-sitter transfers employing low-thrust propulsion. A launch from low Earth orbit (LEO) by a Soyuz Fregat upper stage is assumed after which solar electric propulsion is used to transfer the spacecraft to the pole-sitter orbit. The objective is to minimize the mass in LEO for a given spacecraft mass to be inserted into the pole-sitter orbit. The results are compared with a ballistic transfer that exploits manifold-like trajectories that wind onto the pole-sitter orbit. It is shown that, with respect to the ballistic case, low-thrust propulsion can achieve significant mass savings in excess of 200 kg for a pole-sitter spacecraft of 1000 kg upon insertion. To finally obtain a full low-thrust transfer from LEO up to the pole-sitter orbit, the Fregat launch is replaced by a low-thrust, minimum time spiral, which provides further mass savings, but at the cost of an increased time of flight.     

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.     

Spacecraft Injection into a Heliocentric Terrestrial Orbit

We consider the problem of injection of a spacecraft into the heliocentric Earth's orbit ahead and/or behind the Earth by 60° and 120° in heliographic longitude. The range of solar and astrophysical problems for which these orbits are necessary is reviewed. The variants of injection into heliocentric orbits work from a low around-Earth orbit with one turn-on of the engine in this orbit and one turn-on at the end of the injection trajectory. In this case, it turns out to be more profitable to put spacecraft into orbit for three or even four revolutions of the Earth about the Sun. The velocities necessary for the start from a low around-Earth orbit, the velocities at the final point of injection, and the fuel mass (relative to the spacecraft mass) necessary for injection are estimated. The problems for which injection to similar orbits is executed, using the low-thrust engine and with a combined regime of injection, are also considered.     

Ballistics, navigation, and motion control for a spacecraft during its landing on the surface of Phobos

Basic concepts and algorithms laid as foundations of the scheme of landing on the Martian moon Phobos (developed for the Phobos-Grunt project) are presented. The conditions ensuring the landing are discussed. Algorithms of onboard navigation and control are described. The equations of spacecraft motion with respect to Phobos are considered, as well as their use for correction of the spacecraft motion. The algorithm of estimation of the spacecraft’s state vector using measurements with a laser altimeter and Doppler meter of velocity and distance is presented. A system for modeling the landing with a firmware complex including a prototype of the onboard computer is described.     

Electric transfer optimization for mars sample return mission

The aim of this paper is to analyse an alternative scenario for Mars Sample Return Orbiter mission, where electric propulsion is used for Earth-Mars and Mars-Earth heliocentric cruises and for Mars orbit insertion / escape transfers, whereas chemical propulsion is used for final Mars rendezvous. The problem consists in minimizing the initial vehicle mass to obtain a specific final dry mass in reasonable time. The planetocentric phases correspond to continuous low-thrust trajectories, spiraling around Mars between a low orbit and the influence sphere altitude. The heliocentric phases consist of a succession of low-thrust and coasting arcs with specific departure and arrival conditions at the Earth. For these two types of transfer, efficient optimal control tools exist based on Pontryagin's maximum principle. Thanks to the coordination between planetocentric and heliocentric phases, the solution obtained with these two separate tools gives a good upper bound of the optimal solution in terms of propellant consumption and duration. This optimization procedure is described and finally applied to the proposed mission. The numerical results are presented and compared with the baseline chemical mission solution. The electric option could allow to decrease the spacecraft departure mass but may lead to rather long mission duration.     

The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: II

As examples of application of the technique suggested in the first part of this work, the problems of optimizing the trajectories of spacecraft transfers between circular coplanar orbits are considered in this second part. During the transfer the spacecraft is controlled by the vector of thrust of a limited-thrust jet engine. The mass consumption is minimized for a limited time of transfer. Extreme trajectories with two and three powered sections (Homan-type and bi-elliptic transfer trajectories) are numerically determined. The solution of these well-studied problems allows one to compare the results of applying the suggested technique with the results of application of other previously used techniques.     

About one problem of trajectory optimization

The optimization problem for trajectories of spacecraft flight from the Earth to an asteroid is considered in this paper. The flight is realized in the central Newtonian gravitational field of the Sun with a possibility of gravitational maneuvers near planets. Perturbation maneuvers are taken into account using the method of point area of action with a limitation on the flyby altitude. The spacecraft is controlled by changing the value and direction of the engine thrust. The problem is solved taking into account constraints on the launch time, flight duration, and minimum distance to the Sun.     

The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I

In this first part of our paper, it is suggested to use solutions to boundary value problems in the optimization problems (in impulse formulation) for spacecraft trajectories in order to obtain the initial approximation, when boundary value problems of the maximum principle are solved numerically by the shooting method. The technique suggested is applied to the problems of optimal control over motion of the center of mass of a spacecraft controlled by the thrust vector of jet engine with limited thrust in an arbitrary gravitational field in a vacuum. The method is based on a modified (in comparison to the classic scheme) shooting method computation together with the method of continuation along a parameter (maximum reactive acceleration, initial thrust-to-weight ratio, or any other parameter equivalent to them). This technique allows one to obtain the initial approximation with a high precision, and it is applicable to a wide range of optimal control problems solved using the maximum principle, if the impulse formulation makes sense for these problems.     

The Use of a Solar Electrojet Propulsion System for Jupiter Satellite Injection

The problem of optimization of the interplanetary trajectory of flight for a multistage spacecraft with high- and low-thrust engines into the Jupiter satellite orbit is considered. Low-thrust engines (stationary plasma engines) are used on a heliocentric flight segment. Their operation is maintained with electric power supply from solar batteries. The principal feasibility of the realization of such a project is shown, and estimations of the mass of a spacecraft placed into Jupiter's satellite orbit are presented.     

Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method

The problem of optimization of interplanetary trajectories is considered for spacecraft with a small-thrust ideally regulated engine. When the maximum principle is used, determination of the optimal trajectory is reduced to solution of a two-point boundary value problem for a system of ordinary differential equations. In order to solve this boundary value problem, the method of continuation in parameter is used, and with the help of it the formal reduction of the boundary value problem to a Cauchy problem is performed. Different variants of the continuation method are considered, including the method of continuation in the gravitational parameter which allows one to find extreme trajectories with a preset angular distance. The issues of numerical realization of the continuation method are discussed, and numerical examples of its use for solving the problems of optimization of interplanetary trajectories are presented.     

Solving Optimization Problems for the Flight Trajectories of a Spacecraft with a High-Thrust Jet Engine in Pulse Formulation for an Arbitrary Gravitational Field in a Vacuum

A mathematically well-posed technique is suggested to obtain first-order necessary conditions of local optimality for the problems of optimization to be solved in a pulse formulation for flight trajectories of a spacecraft with a high-thrust jet engine (HTJE) in an arbitrary gravitational field in vacuum. The technique is based on the Lagrange principle of derestriction for conditional extremum problems in a function space. It allows one to formalize an algorithm of change from the problems of optimization to a boundary-value problem for a system of ordinary differential equations in the case of any optimization problem for which the pulse formulation makes sense. In this work, such a change is made for the case of optimizing the flight trajectories of a spacecraft with a HTJE when terminal and intermediate conditions (like equalities, inequalities, and the terminal functional of minimization) are taken in a general form. As an example of the application of the suggested technique, we consider in this work, within the framework of a bounded circular three-point problem in pulse formulation, the problem of constructing the flight trajectories of a spacecraft with a HTJE through one or several libration points (including the case of going through all libration points) of the Earth–Moon system. The spacecraft is launched from a circular orbit of an Earth's artificial satellite and, upon passing through a point (or points) of libration, returns to the initial orbit. The expenditure of mass (characteristic velocity) is minimized at a restricted time of transfer.     

Very high delta-V missions to the edge of the solar system and beyond enabled by the dual-stage 4-grid ion thruster concept

A new and innovative type of gridded ion thruster, the “Dual-Stage 4-Grid” or DS4G concept, has been proposed and its predicted high performance validated under an ESA research, development and test programme. The DS4G concept is able to operate at very high specific impulse and thrust density values well in excess of conventional 3-grid ion thrusters at the expense of a higher power-to-thrust ratio. This makes it a possible candidate for ambitious missions requiring very high delta-V capability and high power. Such missions include 100 kW-level multi-ton probes based on nuclear and solar electric propulsion (SEP) to distant Kuiper Belt Object and inner Oort cloud objects, and to the Local Interstellar medium. In this paper, the DS4G concept is introduced and its application to this mission class is investigated. Benefits of using the DS4G over conventional thrusters include reduced transfer time and increased payload mass, if suitably advanced lightweight power system technologies are developed.A mission-level optimisation is performed (launch, spacecraft system design and low-thrust trajectory combined) in order to find design solutions with minimum transfer time, maximum scientific payload mass, and to explore the influence of power system specific mass. It is found that the DS4G enables an 8-ton spacecraft with a payload mass of 400 kg, equipped with a 65 kW nuclear reactor with specific mass 25 kg/kW (e.g. Topaz-type with Brayton cycle conversion) to reach 200 AU in 23 years after an Earth escape launch by Ariane 5. In this scenario, the optimum specific impulse for the mission is over 10,000 s, which is well within the capabilities of a single 65 kW DS4G thruster. It is also found that an interstellar probe mission to 200 AU could be accomplished in 25 years using a “medium-term” SEP system with a lightweight 155 kW solar array (2 kg/kW specific mass) and thruster PPU (3.7 kg/kW) and an Earth escape launch on Ariane 5. In this case, the optimum specific impulse is lower at 3500 s which is well within conventional gridded ion thruster capability.     

Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.     

Fuel optimum low-thrust elliptic transfer using numerical averaging

Low-thrust electric propulsion is increasingly being used for spacecraft missions primarily due to its high propellant efficiency. As a result, a simple and fast method for low-thrust trajectory optimization is of great value for preliminary mission planning. However, few low-thrust trajectory tools are appropriate for preliminary mission design studies. The method presented in this paper provides quick and accurate solutions for a wide range of transfers by using numerical orbital averaging to improve solution convergence and include orbital perturbations. Thus, preliminary trajectories can be obtained for transfers which involve many revolutions about the primary body. This method considers minimum fuel transfers using first-order averaging to obtain the fuel optimum rates of change of the equinoctial orbital elements in terms of each other and the Lagrange multipliers. Constraints on thrust and power, as well as minimum periapsis, are implemented and the equations are averaged numerically using a Gausian quadrature. The use of numerical averaging allows for more complex orbital perturbations to be added in the future without great difficulty. The effects of zonal gravity harmonics, solar radiation pressure, and thrust limitations due to shadowing are included in this study. The solution to a transfer which minimizes the square of the thrust magnitude is used as a preliminary guess for the minimum fuel problem, thus allowing for faster convergence to a wider range of problems. Results from this model are shown to provide a reduction in propellant mass required over previous minimum fuel solutions.     

MERLIN: Mars-Moon Exploration,Reconnaissance and Landed Investigation

Mars' moons Phobos and Deimos are low-albedo, D-type bodies that may preserve samples of outer solar system material that contributed organics and volatiles to the accreting terrestrial planets. A Discovery-class mission concept described in this paper, the Mars-Moon Exploration, Reconnaissance and Landed Investigation (MERLIN), will obtain in situ measurements from Deimos to test models for the moon's origin. The measurement objectives of MERLIN are to determine Deimos' elemental and mineralogical composition, to investigate its volatile and organic content, and to characterize processes that have modified its surface. To achieve these objectives, a landed payload will provide stereo imaging and measurements of elemental and mineralogical composition and interior structure. An orbital payload will acquire global high-resolution and color imaging, putting the landing site in context by characterizing Deimos' geology. Following MOI the spacecraft flies in formation with Deimos, and uses small changes in its orbit around Mars to investigate Deimos from a range of altitudes and illuminations over 4 months. Data taken during 1- to 2-km altitude flyovers will certify a landing site. The spacecraft will be delivered to a point several kilometers above Deimos, and will navigate to landing on a fresh exposure of regolith using onboard imaging. 90 days of baseline landed operations will provide a complete set of measurements, with schedule reserve, and there is sufficient propellant to repeat the measurements at a second site.     

有效载荷机柜结构优化设计

有效载荷机柜是载人航天器密封舱内安装有效载荷的重要结构,在设计上既要具备一定的刚度保证,以满足发射力学环境要求,又要通过减轻自身重量来提高有效载荷发射能力。文章根据载人航天器密封舱的基本结构设计要求,完成了有效载荷机柜结构的基线设计,进行了有效载荷机柜的有限元建模和模态分析,以减重为目标,刚度为约束条件,完成了有效载荷机柜结构优化设计,并基于敏感度分析得到了有效载荷机柜结构设计参数对其刚度的影响关系。文章的分析思路和研究结果对工程设计具有指导意义。     

Optimization of low-thrust orbit transfers with constraints

Approximate numerical methods of optimization are presented for multi-orbit noncoplanar orbit transfers of low-thrust spacecraft. The linear representation of derivatives of boundary parameters is used in the vicinity of a reference trajectory with its discretization into small segments. For each segment a set of pseudo-impulses is introduced, representing possible directions of the thrust vector. In order to solve essentially nonlinear problems, the iterative process of upgrading the reference trajectory is used. At each iteration the linear programming problem of high dimensionality is solved, its boundary conditions being represented in the form of a linear matrix equation. Interval constraints are considered in the form of blocking the propulsion system operation on shadow segments of the orbit, as well as cycling constraints, and constraints on total duration of maneuvers at certain trajectory segments. The results of comparison with solutions obtained by other methods are presented together with examples illustrating the convergence of iterative processes. Optimizations of the trajectories for launching geosynchronous satellites to their orbits and of the trajectories of a noncoplanar transfer from low to high-elliptic Molniya orbit are considered under these constraints.     

Missions to the asteroid anteros and the space of true anomalies

Three opportunities for missions to rendezvous ballistically with the Earth-crossing asteroid Anteros are studied to illustrate the requirements for a trip to a near-Earth minor planet. The rationale, sample payload, spacecraft requirements and trajectory characteristics of these opportunities are typical of a rendezvous mission to an accessible near-Earth object. Round trip ballistic trajectories to return small samples of the asteroid with launch dates between 1985 and 2000 are also presented. Contours of minimum total ΔV drawn in the space of launch and arrival true anomalies, given the designation Prime Rib curves, are introduced as a useful tool for mission design.