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.     

Detection and Prediction of Absorbed Radiation Doses from Solar Proton Fluxes onboard Orbital Stations

We consider cases of simultaneous detection of the absorbed doses produced by proton fluxes of powerful solar events onboard the Mir and ISS orbital stations and the Ekspress A3 geosynchronous satellite. Experimental data are analyzed using a software package that takes into account the energy spectra of protons at the Earth's orbit depending on the time of event evolution, as well as their penetration to near-earth orbits and through the protective shields of spacecraft. Based on a comparison of the experimental data of dosimeters with the calculation of absorbed doses under the action of solar proton events, we developed a method of estimating the effective thickness of the shielding of dosimeters and made some estimates. A possibility is considered for predicting the radiation hazard onboard orbital stations upon the appearance of solar proton events using dosimeter data from a geosynchronous orbit.     

A preliminary study of pulse-laser powered orbital launcher

An air-breathing pulse-laser powered orbital launcher has been proposed as an alternative to conventional chemical launch systems. The aim of the present study is to assess its feasibility through the estimation of its achievable payload mass per unit beam power and launch cost. A transfer trajectory from the ground to a geosynchronous Earth orbit (GEO) is proposed, and the launch trajectory to its geosynchronous transfer orbit (GTO) is computed using the realistic performance modeled in the pulsejet, ramjet, and rocket flight modes of the launcher. Results show that the launcher can transfer 0.084 kg of payload per 1 MW beam power to a geosynchronous earth orbit. The cost becomes a quarter of existing systems if one can divide a single launch into 24,000 multiple launches.     

Determination of parameters of attitude motion of a small communication satellite using the data of measurements of current of solar panels

A communication satellite (small spacecraft) injected into a geosynchronous orbit is considered. Flywheel engines are used to control the rotational spacecraft motion. The spacecraft after the emergency situation has passed into a state of uncontrolled rotation. In this case, no direct telemetric information about parameters of its rotational motion was accessible. As a result, the problem arose to determine the rotational satellite motion according to the available indirect information: current taken from the solar panels. Telemetric measurements of solar panel current obtained on the time interval of a few hours were simultaneously processed by the least squares method integrating the equations of rotational satellite motion. We present the results of processing 10 intervals of the measurement data allowing one to determine the real rotational spacecraft motion and to estimate the total angular momentum of flywheel engines.     

Overcoming Genesis mission design challenges

Genesis is the fifth mission selected as part of NASA's Discovery Program. The objective of Genesis is to collect solar wind samples for a period of approximately 2 years while in a halo orbit about the Sun–Earth colinear libration point, L1, located between the Sun and Earth. At the end of this period, the spacecraft follows a free-return trajectory with the samples delivered to a specific recovery point on the Earth for subsequent analysis. This type of sample return has never been attempted before and presents a formidable challenge, particularly with regard to planning and execution of propulsive maneuvers. Moreover, since the original inception, additional challenges have arisen as a result of emerging spacecraft design concerns and operational constraints. This paper will describe how these challenges have been met to date in the context of the better-faster-cheaper paradigm. [This paper addresses an earlier mission design, as of May 2000.]     

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.     

Mapping orbits with low station keeping costs for constellations of satellites based on the integral over the time of the perturbing forces

The present paper is concerned with the search for orbits that have potential to require low fuel consumption for station-keeping maneuvers for constellations of satellites. The method used to study this problem is based on the integral over the time of the undesired perturbing forces. This integral measures the change of velocity caused by the perturbation forces acting on the satellite, so mapping orbits that are less perturbed, which generates good candidates for orbits that requires low fuel consumption for station-keeping maneuvers. The integral over the time depends only on the orbit of the spacecraft and the dynamical system considered. The type of engine and the control technique applied to the spacecraft are not considered to search for those orbits. It can be a good strategy to be applied for a first mapping of orbits. For this search, it is analyzed the integral of orbits with different values of the Keplerian elements in order to find the best ones with respect to this criterion. The perturbations considered are the ones caused by the third body, which includes the Sun and the Moon, and the J₂ term of the geopotential. The results presented here show numerical simulations to obtain the integral of those perturbing forces for different orbits. The GPS and the Molniya constellations are used as examples for those calculations.     

Locally Optimal Laws of Control of a Spacecraft Motion with an Electrodynamic Engine at Circumterrestrial Orbits

The motion of a spacecraft under the action of Ampére force is investigated. This force arises as a result of the interaction of the current in a rigid rod, at whose ends the devices which close the electric circuit through the circumterrestrial plasma are located, with the magnetic field of the Earth. The locally optimal laws of control by this rod orientation are found, when one of the elements of the orbit gains the maximum increment under the action of this engine. Numerical estimates of the gained increments are obtained, and it is demonstrated that this engine is a promising tool for the execution of light spacecraft maneuvers at low circumterrestrial orbits.     

基于紫外敏感器的航天器自主导航

对基于紫外敏感器的卫星自主导航方法进行了研究 ,给出了自主轨道确定的滤波算法。对基于紫外敏感器的导航在地球中低轨道、大椭圆轨道和同步轨道上的应用进行了数学仿真验证。仿真结果表明 ,导航误差主要取决于地心方向的测量误差 ,而地心距测量误差的影响要小得多。在已知卫星惯性姿态的条件下 ,仅以地心方向为观测量 ,滤波器同样能够收敛 ,并能获得较高的定轨精度。     

Decentralized coordinated control for multiple spacecraft formation maneuvers

We investigate the decentralized coordinated control problem by looking into local information exchange among formation flying spacecraft regarding formation maneuvers. The nonlinear dynamics that describes the motion of formation flying spacecraft relative to a reference spacecraft is considered for the general case, in which the reference spacecraft is in an ideal elliptical orbit. With the novel use of consensus algorithms combined with behavior-based control, coordinated formation controllers are proposed for three schemes: (i) with full state feedback; (ii) without velocity measurements; (iii) and with external disturbances and parametric uncertainty. The three algorithms used in the schemes can achieve both formation maneuvering and formation keeping, as well as consider actuator saturation. Numerous simulations demonstrate the effectiveness of the proposed control schemes.     

Analytical solutions for the relative motion of spacecraft subject to Lorentz-force perturbations

A spacecraft capable of producing higher-than-natural electrostatic charges may achieve propellantless orbital maneuvering via the Lorentz-force interaction with a planetary magnetic field. Development of maneuver strategies for these propellantless vehicles is complicated by the fact that the perturbative Lorentz force acts along only a single line of action at any instant. Relative-motion dynamical models are developed that lead to approximate analytical solutions for the motion of charged spacecraft subject to the Lorentz force. These solutions indicate that the principal effects of the Lorentz force on a spacecraft in a circular orbit are to change the intrack position and to change the orbit plane. A rendezvous example is presented in which a spacecraft with a specific charge of ?3.81 $\times$ 10^?4 C/kg reaches a target vehicle initially 10 km away (on the same equatorial low-Earth orbit) in 1 day. Fly-around maneuvers may be achieved in low-Earth orbit with specific charges on the order of 0.001 C/kg.     

A new generation of space engines

A primary method of launching future spacecraft will be the Space Transportation System (STS). Studies have identified minimum length stages capable of lifting heavy and deployed payloads from the STS low-Earth orbit to geosynchronous Earth orbit using storage or cryogenic propulsion systems.

Aerojet TechSystems is presently developing two engines suitable for these stages, a storable engine in the few thousand pound thrust range, and a cryogenic engine with a thrust of only a few hundred pounds. The stringent life and performance requirements of these engines offer new technical challenges which can only be met through the consequent employment of novel materials and processes for the storable engine and through innovative design concepts for the cryogenic engine. The storable engine breadboard testing has been accomplished, and the flightweight development program will be complete by the end of this decade. A qualified engine is anticipated for service in the early 1990 time frame. The low thrust cryogenic engine lags this storable engine by approximately three years in development and availability.

This paper discusses the technical issues, their solutions, and the development status of these two engines.     

Potential effects of cosmic dust and rocket exhaust particles on spacecraft charging

Attention is called to the importance of including the roles of cosmic dust particles and rocket exhaust particles in the detailed analysis of spacecraft charging effects, arcing and power drains due to leakage currents. Aspects of the problem pertaining to both low and high (geosynchronous) Earth orbit are discussed. Recommendations are made to assessing the long-term effects of hypervelocity impacts of these particles.     

Use of Optical Characteristics to Identify Orbiting Material

Knowledge of the observable properties of orbital debris is necessary to validate debris models for both the low Earth orbit (LEO) and the geosynchronous Earth orbit (GEO). Current methods determine the size and mass of orbital debris based on knowledge or assumption of the material type of the piece. Improvement in the knowledge of material is the goal of the research described herein. The process of using spectral absorption features to determine the material type is explored. A review of the optical measurements of orbital debris as well as current research in the area is discussed. Reflectances of common spacecraft materials are compared. The need for, and advances made possible by obtaining real data are explored. The prospects of the venture are investigated.     

Longitude-dependent effects of fragmentation events in the geosynchronous orbit regime

The effects of on-orbit fragmentation events on localized debris congestion in each of the longitude slots of the geosynchronous orbit (GEO) regime are evaluated by simulating explosions and collisions of uncontrolled rocket bodies in multiple orbit configurations, including libration about one or both of the gravitational wells located at 75°E and 105°W. Fragmentation distributions are generated with the NASA Standard Breakup Model, which samples fragment area-to-mass ratio and delta-velocity as a function of effective diameter. Simulation results indicate that the long-term severity and consequence of a GEO fragmentation event is strongly dependent upon parent body longitude at the epoch of fragmentation, which can spawn bi-annual “fragment storms” in high-risk longitude slots, driven by lower-energy fragments that have been captured and have started librating around the nearby gravitational well.     

Optimum low thrust transfer to geosynchronous orbit

The low thrust transfer for geosynchronous mission has been studied by many investigators from the viewpoint of optimization in case of continuous thrust. This paper discusses the possibility of fuel saving to attain a geosynchronous orbit by introducing coast phases during each revolution. In advance of optimizing the whole transfer mission, optimization during a single revolution is treated, and it is shown that the entrance and the exit of optimal coasting arcs are expressed by a sixth order equation, which, in case of coplanar transfer, degenerates into a cubic equation, with respect to the cosine of true longitude. Then an optimum transfer to a geosynchronous orbit, including coast phases in each revolution, is simulated. Computational results for typical initial conditions are shown to be compared with those for all-propulsion cases.     

Geosynchronous magnetopause crossings on October 29–31, 2003

During the period October 29–31, 2003, geosynchronous magnetopause crossings (GMC) have been identified based on the magnetic data of the GOES series spacecraft and plasma data of the LANL series spacecraft. It is shown that most of the time the size of the dayside magnetosphere was highly decreased under the effect of very high pressure associated with high velocities and densities of the solar wind plasma, as well as high negative values of the B_z component of the interplanetary magnetic field (IMF). For tens of hours the subsolar magnetopause was deep inside the geosynchronous orbit. During the main phase and at the maximum of the strong geomagnetic storms that occurred in the period under consideration, the dayside magnetosphere was characterized by a strong dawn-dusk asymmetry, so that its size in the postnoon sector considerably exceeded the size in the pre-noon sector. The geomagnetic disturbances in the morning on October 30 and 31, 2003 were accompanied by global magnetospheric pulsations with periods of 5–10 min and high amplitude (up to 0.8 R_E).Translated from Kosmicheskie Issledovaniya, Vol. 42, No. 6, 2004, pp. 574–584.Original Russian Text Copyright © 2004 by Dmitriev, Suvorova.     

Large and sharp changes of solar wind dynamic pressure and disturbances of the magnetospheric magnetic field at geosynchronous orbit caused by these variations

The large and sharp changes of solar wind dynamic pressure, found from the INTERBALL-1 satellite and WIND spacecraft data, are compared with simultaneous magnetic field disturbances in the magnetosphere measured by geosynchronous GOES-8, GOES-9, and GOES-10 satellites. For this purpose, about 200 events in the solar wind, associated with sharp changes of the dynamic pressure, were selected from the INTERBALL-1 satellite data obtained during 1996–1999. The large and sharp changes of the solar wind dynamic pressure were shown to result in rapid variations of the magnetic field strength in the outer magnetosphere, the increase (drop) of the solar wind dynamic pressure always lead to an increase (drop) of the geosynchronous magnetic field magnitude. The value of the geomagnetic field variation strongly depends on the local time of the observation point, reaching a maximum value near the noon meridian. It is shown that the direction of the B _z component of the interplanetary magnetic field has virtually no effect on the geomagnetic field variation because of a sharp jump of pressure. The time shift between an event in the solar wind and its response in the magnetosphere at a geosynchronous orbit essentially depends on the inclination of the front of a solar wind disturbance to the Sun-Earth line.     

Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer

This paper considers minimax problems of optimal control arising in the study of aeroassisted orbital transfer. The maneuver considered involves the coplanar transfer from a high planetary orbit to a low planetary orbit. An example is the HEO-to-LEO transfer of a spacecraft, where HEO denotes high Earth orbit and LEO denotes low Earth orbit. In particular, HEO can be GEO, a geosynchronous Earth orbit.The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. Hence, this type of flight is also called synergetic space flight. With reference to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The presence of upper and lower bounds on the lift coefficient is considered.The following minimax problems of optimal control are investigated: (i) minimize the peak heating rate, problem P1; and (ii) minimize the peak dynamic pressure, problem P2. It is shown that problems P1 and P2 are approximately equivalent to the following minimax problem of optimal control: (iii) minimize the peak altitude drop occurring in the atmospheric portion of the trajectory, problem P3.Problems P1–P3 are Chebyshev problems of optimal control, which can be converted into Bolza problems by suitable transformations. However, the need for these transformations can be bypassed if one reformulates problem P3 as a two-subarc problem of optimal control, in which the first subarc connects the initial point and the point where the path inclination is zero, and the second subarc connects the point where the path inclination is zero and the final point: (iv) minimize the altitude drop achieved at the point of junction between the first subarc and the second subarc, problem P4. Note that problem P4 is a Bolza problem of optimal control.Numerical solutions for problems P1–P4 are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Numerical examples are presented, and their engineering implications are discussed. In particular, it is shown that, from an engineering point of view, it is desirable to solve problem P3 or P4, rather than problems P1 and P2.     

电推进羽流与航天器相互作用的研究现状与建议

电推进与传统的化学推进相比可以节约大量推进剂质量,被广泛用作地球同步轨道卫星南北位置保持和深空探测等任务的主推进系统。电推进器工作时产生的羽流与传统的化学推进器羽流有显著区别,电推进羽流对航天器的影响是进行卫星电推进器系统设计时需要重点关注的问题。文章讨论了电推进羽流对航天器的主要影响,介绍了国外在地面模拟试验、空间飞行验证和软件仿真技术等方面的研究现状,同时对国内开展羽流与航天器相互作用研究提出了建议。