Orbit Design Method Research Articles

Relative orbit design of CubeSats for on-orbit visual inspection of China space station

This paper presents a novel relative orbit design method for CubeSats flying around the space station to perform visual inspection considering the Field-Of-View (FOV) constraints and occlusion effect. Firstly, a parametric model for Periodic Relative Orbits (PROs) is established by using the well-known Clohessy-Wiltshire equations. Based on this model, the relative orbit design problem for orbital target inspection is successfully integrated into a problem of two-parameters determination, one of which is the correlation coefficient and the other is the orbital amplitude. Secondly, by categorically evaluating the range of design variables, the design method for generating feasible solutions of PROs to satisfy the FOV constraints is proposed. Thirdly, considering the existence of the occlusion effect of large space structure, this paper presents an efficient calculating method to evaluate the degree of occlusion based on the analysis of line-of-sight blockage. Then, to avoid the occlusion effect, an improved relative orbit design method is developed. Finally, the designed algorithms are testified by carrying out some typical simulations with the China Space Station as the observed object and a small CubeSat assumed to perform the required inspection mission. The results illustrate well the validity and practicability of the proposed method.

Redefining low Earth orbit as a parking orbit for flexible and economical Earth departure in deep space missions

There are a number of deep space probes that are currently in operation with diverse destinations and objectives. For example, the Japanese Hayabusa2 and the U.S. OSIRIS-REx missions are both sample returns, targeting different near-Earth asteroids. Europe’s ExoMars and the U.S. Perseverance are orbiting and roving Mars as precursors of future manned explorations. Conventionally, deep space missions require dedicated launch vehicles for each mission. The interplanetary Earth departure trajectory from the low Earth orbit (LEO) usually lacks flexibility and efficiency. Furthermore, innovative and reusable launch systems have been researched and developed by multiple organizations including private sector organizations such as SpaceX and Blue Origin. It is expected that the unit cost per launch weight to LEO be significantly reduced by rideshare mass transportation executed by using reusable mega launchers in the near future. This study aims to fill the transportation gap between LEO and deep space by realizing a flexible and economical interplanetary Earth departure without sacrificing the arbitrariness of LEO, target V-infinity vector, and target Earth departure epoch. Thus, the one-revolution Earth free-return orbit (1rEFRO) and the consequent Earth gravity assist (EGA) are introduced to separate the velocity increment and direction adjustment. The planetary free-return and EGAs are common in interplanetary missions; however, a comprehensive study on the flexibility, economic efficiency, and arbitrariness of the sequence (1rEFRO + EGA) originating from LEO was not explicitly found. After describing the necessary coordinate frames, LEO’s orbital elements, 1rEFRO, and the terms ‘flexibility’ and ‘economic efficiency’ are defined in Section 2. Then in Section 3, the two-body-based preliminary orbit design method is proposed and formulated. Section 4 aims to reveal LEO’s comprehensiveness as efficient parking orbits when adopting the 1rEFRO + EGA sequence, using the newly proposed “ΣVEt LEO i-Ω diagram”. Section 5 describes a detailed orbit design constructed based on multi-body propagation and optimization to confirm the feasibility, flexibility, and economics of the solution and the usefulness of the initial solution given by the preliminary design method formulated in Section 3.

Repeat Ground-Track Orbit Design Using Objective Dimensionality Reduction and Decoupling Optimization

It is important for China's Land Observing Satellite-1 to run in a repeat ground-track orbit with almost constant altitude over the same geographical area, so the satellite can have a high-precision deformation monitoring capability. The strong continuity of reference trajectory and high computational efficiency of the algorithm are required in the satellite orbit design stage. To fulfill those requirements, we first propose a fast orbit design method based on objective dimensionality reduction and decoupling optimization, which makes the satellites drift naturally without additional propellant consumption. Besides, a completely different convergence standard for the orbit design is introduced, which greatly reduces the complexity of the optimization process by decreasing the optimization objective dimension. Meanwhile, an optimal strategy keeping the argument of latitude constant is proposed, which reduces the coupling characteristics among optimization objectives. In addition, the optimization model of the repeat ground-track orbit is established. Then, the steepest descent method is introduced to solve this optimization problem. Simulation results in the high-order gravity force reveal that the position accuracy and velocity accuracy of the reference trajectory are up to millimeters and centimeters per second respectively. The calculation efficiency of our method is about 56 times faster than that of the NSGA-II method.

The Modular Relative Orbit Design Method for Spacecraft Proximity Motion

Abstract This paper presents a modular relative motion trajectory design tool for proximity operation of on-orbit service spacecrafts. First, a series of commonly used relative motion trajectories are defined. The dynamics are solved such that each type of trajectory is encapsulated into different modules. The input parameters of each module include the key geometrical features, such as the initial position, desired final position, and flying time. Different modules are connected via the same position and velocity. The modular orbit design tool is able to cover most of the typical proximity operation scenarios. Following that, two notational on-orbit service missions are given as examples to describe the specific usage process of the tool. It includes three major steps, namely, determining the appropriate module sequence according to the mission requirements, designing the pending input parameters of each module by taking consideration of constraints, and computing the details of module sequence to generate relative trajectories. Compared with the traditional maneuver-optimized orbit design approach, the modular method has fewer parameters to solve. Additionally, the modular application tool is versatile and can be used for a variety of different on-orbit service missions. This tool is of great importance in standardizing the space operations.

Design and Analysis of Direct Abort Orbits in the Earth-Moon Transfer Phase of Crewed Lunar Exploration Missions

A direct abort orbit design method is presented for direct abort missions in the Earth-Moon transfer phase of crewed lunar exploration missions. First, according to the demand of an emergency rescue in the Earth-Moon transfer phase, two direct abort orbit schemes are introduced. Then, a serial orbit design method is proposed for a high-fidelity direct abort orbit. An analytical model is established for the calculation of initial values, and the optimization design is performed in the high-fidelity orbit model to determine a single-impulse abort orbit. A hybrid optimization design process is proposed to generate a two-impulse abort orbit. The results of simulation examples verify the validity and feasibility of the proposed direct abort orbit design method. Finally, extensive simulations are carried out to analyze the characteristics of abort impulse and abort return time and reveal the general rules of direct abort orbits. The research conclusions can provide a reference for the design of emergency rescue schemes in future crewed lunar exploration missions.

Satellite Orbit Design and Analysis Based on STK

The design and analysis of satellite orbits has always been a hot topic in the aerospace field. Through the selection and optimization of orbital parameters, the satellite can meet the corresponding performance indicators and work requirements. However, there are often various constraints in actual scenes, so the orbital parameters cannot be set arbitrarily. Therefore, how to design the orbit under the constraints to make the satellite in optimum condition is very important. Based on STK, this paper proposes a satellite orbit design method, and realizes the optimization of the orbit through the simulated annealing algorithm. The simulation results show that this method can achieve satisfactory results and has certain practical value.

Three-impulse point return orbit design for the manned lunar high-latitude exploration mission

A three-impulse point return orbit design method is proposed for the manned lunar high-latitude exploration mission. First, considering the restrictions of the reentry corridor and the landing point simultaneously, the constraint conditions of the point return orbit are analyzed. Second, a serial orbit design strategy is presented. In the initial calculation, by decoupling the three-impulse transfer and the lunar escape, a two-segment patched method based on the pseudo-perilune parameters is proposed to determine the three-impulse point return orbit. The three-impulse transfer segment is backward designed by combining maneuvering at the special points with the Lambert problem in the hybrid orbit model, while the lunar escape segment is forward solved by introducing a comprehensive conic method. In the accurate solution, the result of the initial calculation serves as the initial value to perform the backward and forward integration for two segments in the high-fidelity model, respectively. The simulation examples verify the effectiveness and feasibility of this strategy, and show the advantages of high accuracy of the initial calculation and low velocity increment consumption. Finally, a large amount of simulations are conducted by applying this strategy, and the orbit characteristics are discussed. The research conclusions can provide a reference for the design of the point return orbit scheme for the manned lunar exploration mission.

Adaptive LEO-Phase Free-Return Orbit Design Method for Manned Lunar Mission Based on LEO Rendezvous

To design a free-return orbit for manned lunar mission based on low earth orbit (LEO) rendezvous, an adaptive LEO-phase free-return orbit design method based on high-precision dynamics model is proposed. First, the radius of perilune and the absolute value of perilune velocity are decoupled using a coordinate system rotation, which is derived from moon-centric local vertical and local horizontal instantaneous coordinate system at the time of perilune. The two Euler rotation angles and the absolute value of perilune velocity are used as independent design variables because their initial values are easy to guess. Next, a two-segment numerical integration strategy is proposed to calculate orbital elements at the moments of trans-lunar injection and free-return vacuum perigee. Subsequently, an optimization algorithm software package for solving large-scale nonlinear sequential quadratic programming problems (SQP_snopt) is employed to search the objective free-return orbit with a fixed trans-lunar injection inclination and the other two constraints on radiuses of perigee at the times of trans-lunar injection and vacuum perigee. After that, an iteration algorithm is devised to adjust trans-lunar injection window for adaptive LEO-phase. Finally, numerical results show a fast and accurate performance of the direct optimization method, which can provide valuable references to manned lunar missions based on LEO rendezvous.

Fixed-thrust Earth–Moon free return orbit design based on a hybrid multi-conic method of pseudo-perilune parameters

This study proposes a high-precision fixed-thrust free return orbit design method for a manned lunar mission centred on the rendezvous and docking with the lunar space station. Future manned lunar landing missions based on the lunar space station will require different spacecraft to achieve rendezvous and docking with it in different mission stages. Adopting the perilune parameters to design the Earth–Moon flight trajectory would be more convenient for decoupling in this kind of series missions. Thus, a new set of pseudo-parameters representing the perilune motion states is defined, and based on these, a hybrid multi-conic method is then proposed to design the free return orbit for manned spacecraft. The new method is more accurate than the traditional four-phase patched-conic method, and can produce initial values with a higher converging speed for a high-precision trajectory iteration design. Then, a fast and high-precision continuation method for the fixed-thrust trajectory is proposed based on the impulse-based solutions, and the gravity loss of the impulse-thrust transfer is analysed. Finally, the general characteristics and launch window of the free return orbit, as well as the reachable domain of the pseudo-perilune parameters, are analysed using the hybrid multi-conic method. The results will provide a theoretical basis for future missions planning.

Mission design for multi-target and multi-mode rendezvous missions to small bodies

Multi-target exploration to small bodies has the advantages of reducing mission cost and increasing scientific return. It will be widely used in the future small body exploration missions. This paper investigates the problem of perturbation sensitivity, complicated constraints and changeable thrust, which may be faced in the multi-target exploration mission. The Earth quasi-satellite sampling return and main-belt comet rendezvous missions are studied. First, based on the mission constraints, the mission design schedule and relevant constraints are given. Then, the multi-impulse asteroid sampling return trajectory is investigated in the elliptical three body model. Considering the gravitational perturbation of Earth, the integral trajectory design consist of Earth escape phase, interplanetary transfer phase, and Earth reentry phase is proposed. The trajectory design is divided into two parts. The optimal preliminary transfer opportunity is firstly searched in two-body problem and is transferred to the elliptical three body model. The differential correction scheme is applied to correct the error caused by Earth gravity perturbation. The trajectory for the Earth quasi-satellite 2016HO3 is designed. Finally, considering the engineering constraints, the first-order necessary condition of the changeable low-thrust trajectory are derived, where both the thrust and special impulse change with the distance to Sun. By introducing the B-plane parameters, the initial states determination under the constraint of the gravity assist is developed. Based on the homotopy method, the low-thrust optimal trajectory after Mars gravity assist to the main belt comet 133P are designed and compared with constant low thrust trajectory. The proposed multi-target exploration scheme and the orbit design method can provide a reference for future small bodies exploration missions in China.

Orbit design and control method for satellite clusters and its applications to NetSat project

In this paper, an optimal orbit design and control method for satellite clusters is presented and the method is applied to the four pico/nano-satellite system NetSat. Firstly, the relative motion based on relative eccentricity/inclination vectors is reviewed. Then, an optimal orbit design method for the cluster flight is developed, and the initial states of satellites in the cluster are derived using a graphical representation of the relative eccentricity/inclination vectors combined with a constrained nonlinear programming method. Next, a novel satellite cluster feedback control method is designed, and an optimal three-maneuver strategy is proposed, which could maintain the satellites in a bounded relative motion, satisfying the tight fuel consumption constraints and fuel balance for a long operational lifetime. Finally, the feasibility and effectiveness of the optimal orbit design and control for satellites cluster and its application to NetSat project are verified through numerical simulations.

Interplanetary parking method and its applications

In this study, we propose a flexible orbit design method that enables anytime launch of a deep-space explorer. Based on the Electric Delta-V Earth Gravity Assist (EDV-EGA) scheme, (Kawaguchi, 2001, 2002) [1,2] the proposed interplanetary parking method enables the explorer to make an Earth return orbit at an arbitrary time-of-flight by connecting to the minimum energy transfer orbit to destination. While the time-of-flight of the transfer orbit is fixed, the Earth return orbit with the arbitrary time-of-flight significantly alleviates the severe launch window constraint in interplanetary missions. We offer two case examples of applications of this method. The first is the dual launch of a Mars explorer with a geostationary transfer orbit (GTO) mission payload. The second is a dual launch of Mars and Venus explorers by a single launch vehicle. In the first case, we assume that a small Mars explorer is dual launched into a GTO for a secondary payload. With this assumption, the secondary payload cannot choose a desirable launch epoch for itself because the launch window to Mars is very narrow and opens only every 2 years. Moreover, the GTO, whose orbital period is approximately 10h, repeatedly passes through the Van Allen belt wherein the radiation level is very high. Hence, the explorer has to escape from the GTO as soon as possible. However, our proposed interplanetary parking method enables the explorer to reach the destination within the limits of a practical mass resource, regardless of the Earth departure epoch. In the second case, the explorers traveling to different destinations, i.e., Mars and Venus, are dual launched by a single launch vehicle, and they fly to each destination via an interplanetary parking orbit. Our proposed method will widen the scope of opportunity for interplanetary missions.

임무기반 태양동기궤도 운영궤도 설계에 관한 연구

This paper presents a mission orbit design method for spacecraft which use the sun-synchronous and ground repeat orbits. In this work, we have proposed a new design procedure, “Nonlinear simulation-based numerical optimization technique” using the commercial S/W’s such as STK (Satellite Tool kit) and Matlab, which are widely adopted S/W’s in the area of orbital mechanics and engineering analysis. Inclusion of all the perturbation effects on the spacecraft not only can more precisely satisfy the mission requirements for sun-synchronicity and repeated ground track, and also operational requirements such as minimum change in the S/C local time, maximization of the contact time with a specified ground station, etc. can be appropriately considered. Design examples for LEO sun-synchronous mission are presented to demonstrate the usefulness of the proposed method in this paper.

Cluster flight orbit design method for fractionated spacecraft

PurposeThe purpose of this paper is to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.Design/methodology/approachBased on the concept of fractionated spacecraft, orbit design requirements for cluster flight in the case of fractionated spacecraft are proposed, and categorized into three requirements: stabilization requirement, passive safety requirement, and the maximum inter‐satellite distance requirement. These design requirements are then reformulated in terms of relative eccentricity and inclination vectors (E/I vectors) using a relative motion model based on relative orbital elements (ROEs). By using ROEs theory, the cluster flight orbit design issue is modelled as the distribution of relative E/I vectors for each member satellite in the cluster, and solved by combining three different heuristic search methods and one nonlinear programming (NLP) method.FindingsThe simulation results show that the NLP method is valid and efficient in solving the cluster flight orbit design problem and that for some cluster flight scenarios, the heuristic search methods can be adopted to give feasible solutions without the NLP method.Research limitations/implicationsThe cluster flight scenario in this paper is limited because the cluster should be in the near‐circular low earth orbit (LEO), and the relative distance between the member satellites should be small enough to satisfy the relative motion linearization assumption.Practical implicationsThe cluster flight orbit design method proposed in this paper can be applied by fractionated spacecraft mission designers to propose potential cluster flight orbit solutions.Originality/valueIn this paper, the relative E/I vectors method is adopted to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

Transfer Orbit Design and Control Based on Forbes' Assumption

In order to meet the requirements of space operation, the spacecrafts must maneuver agilely with the artifical propulsion. The orbit under artificial control is termed as Non-Keplerian orbit which does not follow Kepler’s Laws. The transfer orbit design under the continuous thrust is one of the most important topics in this new field. Shape-based method for Non-Keplerian orbit design is developed in this paper. Firstly, the equations of motion are established in polar coordinates system. And then the nondimensional variables are introduced for computation accuracy and speed, which give rise to nondimensional equations of motion. The general equation is derived with which common curves could be utilized in orbit design. In addition, the orbit design method is described based on Forbes’ velocity assumption and the formulation of the radius r with respect to time t, which is a sinusoidal function. The determination of the coefficients causes the orbit design problem to translate into an orbit control problem. The requisite thrust magnitude and direction are available via the simplified nondimensional equations of motion. In the end, an example of the transfer orbit is given. The result demonstrates that the shape-based method is feasible for the transfer orbit design or control problem under the continuous thrust, and the fuel expenditure is practicable.

スウィングバイ軌道における高精度軌道設計方式の提案

スウィングバイ軌道における高精度軌道設計方式の提案