Track layout method of global illumination lunar device

Abstract

The invention discloses an orbit layout method for a global illumination lunar device, which is used for solving the problem that the lunar device cannot continuously obtain sun illumination when executing a task for a long time, and is directly related to stable energy supply and heat balance of a spacecraft. According to the method, a planar and three-dimensional long-distance retrograde orbit family is generated through a continuation and bifurcation method of an earth-moon space periodic orbit, the illumination condition of the orbit is obtained by utilizing a planetary shadow model, and a super sun-synchronous orbit is used as a lunar device orbit layout scheme. The relation among the sun, the lunar device, the moon and the earth is further analyzed, the illumination condition and shadow distribution are evaluated, and a reasonable orbit selection basis is provided. Besides, an attitude pointing scheme of the lunar device and a rotation control rule of the solar array are provided, so that the solar energy acquisition efficiency is improved, and sufficient sun illumination supply in a task is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft orbit design and attitude control, and more particularly to an orbit layout method for a global illumination lunar orbiter. Background Art

[0002] In recent years, the Moon, due to its unique energy advantages and resource value, has attracted widespread research interest. Consequently, while relevant countries are accelerating their forays into near-Earth space, they are also turning their attention to cislunar space. Against the backdrop of growing interest in cislunar space, a new wave of lunar exploration has begun, with major space powers worldwide competing to launch lunar orbiters to conduct lunar exploration missions or conduct preliminary research on manned lunar landings.

[0003] In the whole process of space mission design (such as Figure 1 (as shown in the figure), the lighting conditions of the spacecraft are crucial to the success of the mission. Sunlight is not only the main energy supply for the spacecraft, but is also directly related to the thermal balance and operational stability of the system. By optimizing the orbital design and lighting conditions, it is possible to ensure that the spacecraft is always in a good lighting state throughout the orbital cycle, thereby maintaining efficient energy utilization. Lighting conditions are crucial for tasks such as scientific experiments, data collection, and communications, because stable lighting conditions directly affect the accuracy of the experiments and the quality of the data. As a type of spacecraft, the lunar orbiter can operate stably in the complex environment between the moon and the earth through in-depth research and optimization of lighting conditions, providing a reliable foundation for scientific research and ensuring the successful completion of the mission.

[0004] In order to avoid shadowing during the operation of the lunar orbiter, the main methods can be roughly divided into two categories: real-time orbit maneuvers and orbit design optimization. Real-time adjustment of orbital parameters through orbital maneuvers is a flexible method that can respond to emergencies in a timely manner. When not performing a mission, the lunar orbiter can perform planned maneuvers through thrusters. However, this method will change the mission orbit. The most important problem is that it will consume a lot of propellant, thus shortening the mission life and affecting the execution of the mission. In addition, in constellation missions, the manipulation of a single satellite is very likely to destroy the configuration stability of the constellation, which is not conducive to the execution of the mission. Therefore, the method of real-time orbital maneuvers is usually only used in emergencies and is not often used under normal circumstances.

[0005] Orbital design optimization, which involves both orbital design and initial phase selection, is a commonly used method in space missions. By optimizing the orbital design and selecting appropriate orbital parameters, the design goal is to minimize shadows cast by the Earth and Moon, ensuring long-term or global illumination of the lunar orbiter. For example, in theory, a classic lunar sun-synchronous orbit can achieve global illumination when the initial values ​​are appropriately chosen. McCarthy and Howell utilized quasi-periodic orbits in cislunar space for mission design. They found that a cislunar resonant orbit in 2:1 resonance with the lunar period (29.5 days) can reduce potential shadows during spacecraft operation while maintaining a constant line of sight between the spacecraft and the Earth. By selecting an appropriate orbital insertion point (initial phase), global illumination of the orbit is possible. In the Tianqin space-based gravitational wave detection program, Ye et al. proposed two strategies for a high circular orbit to address the combined challenges of avoiding solar eclipses and stabilizing a near-equilateral triangle constellation. These strategies include selecting an appropriate initial phase and adjusting the orbit to a 1:8 resonant resonance with the Moon. The latter involves increasing the radius of Tianqin's initial orbit from 1×10 5 km is slightly increased to about 100900km, and its allowed initial phase range is about 15°. The final orbit design result can remain shadow-free within the "3+3" month observation window of the 5-year mission, while meeting the constellation stability requirements. In response to the mission requirements of the Chang'e-4 relay satellite, Gao Shan and others comprehensively considered the mission geometry and orbital illumination conditions, and studied the orbital shadow conditions near the Earth-Moon L2 point. In order to avoid the threat posed by excessive shadow time to the safety of the spacecraft, Gao Shan and others focused on the relationship between orbital parameters and illumination conditions, analyzed the impact of factors such as the Halo orbit amplitude and phase at the L2 point on orbital illumination, and finally determined that the mission orbit of the Chang'e-4 relay satellite is A Z Towards the southward Halo orbit of about 13,000 km, the corresponding A X The amplitude is about 12500km, A Y The directional amplitude is about 38,000 km, the orbital period is about 14 days, and the target orbit with the optimal lighting conditions under mission constraints is obtained.

[0006] Although orbital real-time maneuvers and orbital design optimization can achieve full-area illumination of the lunar orbiter's orbit to a certain extent, they both have certain defects. Orbital real-time maneuvers consume more propellant, which will shorten the mission's life, and large-scale orbital maneuvers are not conducive to orbit stability and control. Although orbital design optimization methods are effective in many missions, they also have some potential disadvantages and challenges. First, orbital design optimization usually requires complex calculations and numerical simulations, especially when considering multi-body gravitational perturbations and other nonlinear effects, which may require a lot of computing resources and time, especially in the highly dynamic near-lunar space environment. In addition, the optimization method may be very sensitive to the initial conditions, and even small changes may lead to completely different orbit optimization results, which may make the designed orbit very sensitive to small changes or external disturbances in the actual mission, thereby causing complexity in practical applications. Therefore, focusing on the long-term illumination conditions of the lunar orbiter, the present invention proposes an orbit layout method for a full-area illumination lunar orbiter. Summary of the Invention

[0007] The purpose of the present invention is to propose an orbital layout method for a lunar orbiter by combining methods such as periodic orbit design in Earth-Moon space and satellite attitude control to address the problem that shadow areas that may be encountered during the operation of the lunar orbiter may affect the thermal balance of the lunar orbiter itself or the execution of its mission, so as to achieve long-term or global illumination of the lunar orbiter.

[0008] Considering that sunlight is not only the main energy source for the lunar orbiter, but also directly related to its thermal balance and operational stability, this paper proposes a global illumination lunar orbiter orbit layout method based on periodic orbit design in Earth-Moon space and satellite attitude control. Through this layout, it can be ensured that the lunar orbiter can continuously obtain long-term or global sunlight during its operating cycle, supporting the successful completion of the lunar orbiter mission. Specifically, it is divided into the following four mechanisms:

[0009] First, based on the continuation and bifurcation methods of Earth-Moon space orbits, we study the distant retrograde orbits (DROs) in the Earth-Moon space plane and extend and bifurcate them to obtain the planar and three-dimensional DRO orbit families.

[0010] Second, the orbital lighting conditions were simulated using a planetary shadow model, and a super sun-synchronous orbit was defined as the orbital layout of the lunar orbiter.

[0011] Third, by studying the relationship between the Sun, the lunar orbiter, and the Moon / Earth, and analyzing the orbital lighting conditions and shadow distribution, we can provide a basis for selecting the lunar orbiter's layout and orbit.

[0012] Fourth, the attitude pointing scheme of the lunar orbiter and the rotation control law of the solar array are given to improve the solar illumination conditions of the lunar orbiter.

[0013] The present invention provides a method for arranging a track for a global illumination lunar orbiter, and the track layout is completed by performing the following steps:

[0014] Step 1: Modeling the double-circle four-body problem in Earth-Moon space;

[0015] Step 2: DRO orbit extension and bifurcation in Earth-Moon space;

[0016] Step 3: trajectory correction based on multiple shooting method;

[0017] Step 4: Analyze the long-term illumination conditions of the DRO lunar orbiter;

[0018] Step 5: Analyze the lighting conditions based on the relationship between the Sun, the lunar orbiter, the Moon, and the Earth.

[0019] Step 6: Global lighting track layout plan;

[0020] Step 7: lunar orbiter attitude pointing plan;

[0021] Step 8: Control law of the lunar orbiter's zero-incident-angle solar array.

[0022] The technical effects of the method of the present invention are:

[0023] ① The orbital layout method of the lunar orbiter based on three-dimensional DRO proposed in the present invention can achieve long-term good lighting conditions, which is beneficial to the energy supply and operation stability of the lunar orbiter.

[0024] ② The present invention takes into account various factors affecting lighting conditions, fully utilizes the relationship between the Sun-lunar orbiter-Earth / Moon, analyzes the effects of various influencing factors, and provides a basis for the orbital layout of the lunar orbiter, which is conducive to the layout of the lunar orbiter according to mission requirements.

[0025] ③ The present invention takes into account the impact of the sun's incident direction on the lighting conditions of the lunar orbiter, designs an attitude pointing scheme based on the mission requirements, and then combines the solar cell array drive component to control the solar array, designs a control law, and realizes the tracking of the sun's direction, so that the lighting conditions of the lunar orbiter are further optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a design structure diagram of a space mission.

[0027] Figure 2 This is the flow chart of the orbital layout of the global illumination lunar orbiter of the present invention.

[0028] Figure 3 This is a diagram of the two-circle four-body problem.

[0029] Figure 4 This is an example of a 3D DRO orbital. A Z =0.03 schematic diagram.

[0030] Figure 5 This is a schematic diagram of the DRO orbital family.

[0031] Figure 6 It is the simulation result of segmented multiple shooting method.

[0032] Figure 7 is the total illumination proportion of all DROs η S Lighting parameters.

[0033] Figure 8 is the longest continuous shadow duration of all DROs S Lighting parameters.

[0034] Figure 9 It is a single Super-SSO on the moon orbiter within three years SSM Angle change diagram.

[0035] Figure 10 Is a single Super-SSO (A Z =0.015LU) on the lunar orbiter α SSE Angle change diagram.

[0036] Figure 11 Velocity distribution of Super-SSO: a) main branch; b) secondary branch.

[0037] Figure 12 It is a global illumination orbit: a) orbit image; b) α of Super-SSO in three years SSM (green curve) and α SSE (blue curve).

[0038] Figure 13 This is a schematic diagram of the attitude pointing scheme of the lunar orbiter.

[0039] Figure 14 It is the solar cell array control effect. DETAILED DESCRIPTION

[0040] The present invention will be further described in detail below with reference to the accompanying drawings. The parameters listed are merely exemplary embodiments of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention.

[0041] See also Figure 2As shown, the orbital layout method of a global illumination lunar orbiter of the present invention includes the following steps:

[0042] Step 1: Modeling the double-circle four-body problem in Earth-Moon space;

[0043] See also Figure 3 As shown in Figure 1, the Bicircular Restricted Four-Body Problem (BR4BP) takes into account the influence of the sun's gravity on the basis of the Circular Restricted Three-Body Problem (CR3BP). The dynamic equation of the fourth celestial body (spacecraft) is:

[0044]

[0045] x is the coordinate component of the spacecraft in the x direction.

[0046] y is the coordinate component of the spacecraft in the y direction.

[0047] z is the coordinate component of the spacecraft in the z direction.

[0048] is the first derivative of the spacecraft's coordinate component in the x-direction with respect to time t.

[0049] is the first derivative of the spacecraft's coordinate component in the y direction with respect to time t.

[0050] is the first derivative of the spacecraft's coordinate component in the z direction with respect to time t.

[0051] is the second-order derivative of the spacecraft's coordinate component in the x-direction with respect to time t.

[0052] is the second-order derivative of the spacecraft's coordinate component in the y direction with respect to time t.

[0053] is the second-order derivative of the spacecraft's coordinate component in the z direction with respect to time t.

[0054] is the partial derivative in the x direction.

[0055] is the partial derivative in the y direction.

[0056] is the partial derivative in the z direction.

[0057] U 4BPis the pseudo-gravitational potential energy of BR4BP.

[0058] Among them U 4BP and U 3BP Expressed as:

[0059]

[0060] U 3BP is the pseudo-gravitational potential energy of CR3BP.

[0061] m S is the mass of the Sun.

[0062] a S is the distance from the Sun to the center of mass of the Earth and the Moon.

[0063] μ is the ratio of the mass of the Moon to the sum of the masses of the Earth and the Moon.

[0064] r1 is the distance between the spacecraft and the Earth.

[0065] r2 is the distance between the spacecraft and the moon.

[0066] r3 is the distance between the spacecraft and the sun.

[0067] θ S is the phase angle of the sun.

[0068] where r1, r2 and r3 are expressed as:

[0069]

[0070] For lunar orbiters, the non-spherical gravitational perturbation of the moon and the perturbation caused by the tilt of the moon's rotation axis also need to be considered. This can be achieved by improving the pseudo-gravitational potential energy in equation (3). Considering the J2 term of the moon's gravity, equation (3) is transformed into:

[0071]

[0072] Where, is the angular velocity of the Earth-Moon system, and A2 is the oblateness coefficient of the Moon. The tilt of the Moon's rotation axis can be achieved by coordinate transformation using Equation (8).

[0073]

[0074] ε is the tilt of the Moon's axis of rotation.

[0075] x ε is the coordinate component of the spacecraft in the x direction after rotating by angle ε.

[0076] y ε is the coordinate component of the spacecraft in the y direction after rotating by angle ε.

[0077] z ε is the coordinate component of the spacecraft in the z direction after rotating by angle ε.

[0078] Substituting the rotated coordinates into formula (7) we can obtain the pseudo-gravitational potential energy of CR3BP that takes into account both the non-spherical gravitational perturbation of the moon and the tilt of the moon's rotation axis.

[0079] Step 2: DRO orbit extension and bifurcation in Earth-Moon space;

[0080] The various periodic and quasi-periodic orbital families in cis-lunar space are fundamental to cis-lunar space exploration and provide a rich set of candidate orbits for lunar orbiter deployment. The DRO orbit was chosen as the lunar orbiter's layout orbit. Given that the analysis results for a single DRO are not universal and it is difficult to obtain the optimal solution for the lunar orbiter's layout orbit, it is necessary to extend the orbital family using a single DRO as a "seed" to obtain the complete data for this DRO family and facilitate orbital comparison.

[0081] The pseudo arc length extension algorithm is used to extend the planar DRO family. Considering the symmetry of the DRO orbit about the xz plane, the initial value of the orbit is set to The Poincare section is set to {Σ:y=0}. The DRO orbit needs to vertically cross the Poincare section. Therefore, in order to obtain a periodic orbit, the initial value needs to satisfy formula (9):

[0082]

[0083] f is the mapping function that maps the initial state of the spacecraft to the velocity after half a period.

[0084] x0 is the initial coordinate component of the spacecraft in the x direction.

[0085] z0 is the initial coordinate component of the spacecraft in the z direction.

[0086] is the initial velocity component of the spacecraft in the y direction.

[0087] is the velocity component of the spacecraft in the x direction after half a period.

[0088] is the velocity component of the spacecraft in the z direction after half a period.

[0089] T is the period of DRO.

[0090] In the present invention, the DRO solution obtained by extending the initial solution is numbered as m, and the next solution after m is numbered as m+1.

[0091] If X mis the current solution of the DRO family, then the initial value iteration of the next solution m+1 satisfies:

[0092]

[0093] It is the initial value of the iteration of the next feasible solution of the DRO family.

[0094] Δs is the pseudo arc length.

[0095] i s is the identity matrix in the null space direction of the Jacobian matrix G of f.

[0096] With the introduction of Δs, the simultaneous equation (9) is obtained:

[0097]

[0098] are simultaneous functions.

[0099] In the present invention, the DRO orbit is the solution of equation (11). By using the pseudo-arc length extension method, a family of planar DRO orbits can be obtained.

[0100] In this paper, studying bifurcations in the DRO orbit can fundamentally change the dynamic characteristics of periodic orbits. For example, using period-doubling bifurcations, a planar DRO can acquire out-of-plane amplitudes, resulting in a three-dimensional DRO, providing new insights into the orbital layout of the lunar orbiter. The state transition matrix of the orbit is calculated based on the dynamic equations of the CR3BP. The state transition matrix over a period is the orbital single-value matrix. The DRO orbital stability factor is calculated based on the eigenvalues ​​of the single-value matrix:

[0101]

[0102] ν is the stability factor of the periodic orbit.

[0103] λ j is an eigenvalue of the jth reciprocal eigenvalue pair of a single-valued matrix.

[0104] If |ν|>1, the orbit is unstable; if |ν|≤1, the orbit is stable. j = cosθ + isinθ and i is the imaginary unit, and θ is the Euler angle corresponding to the imaginary eigenvalue. The eigenvectors corresponding to the two eigenvalues ​​are e1±ie2. After one cycle, we get:

[0105]

[0106] e1 is the eigenvector in the direction of the real axis

[0107] e2 is the eigenvector in the direction of the imaginary axis.

[0108] θ is the Euler angle corresponding to the imaginary eigenvalue.

[0109] R(θ) is the rotation matrix.

[0110] This indicates that a small displacement in the characteristic space rotates by an angle θ per cycle. To form a periodic orbit, the cumulative phase difference should be 2kπ, where k is a positive integer. Therefore, the ratio of the number of orbital rotations n to k is:

[0111]

[0112] n is the number of revolutions of the orbit.

[0113] k is the approximate resonance between the orbital period of the bifurcation point and the rotation of the coordinate system.

[0114] When the eigenvectors contain out-of-plane components, a three-dimensional Period-doubling DRO orbit. Figure 4 Shown is the resonance ratio An example of a 3D DRO orbit with an amplitude in the z direction (out-of-plane) of 0.03 LU (1 LU is the average Earth-Moon distance). Figure 5 are all the DRO orbits obtained by extension and bifurcation. Each point in the figure corresponds to a DRO orbit, and the initial value of the orbit is Define the characteristic parameter of the DRO orbit as A x =1-μ-x0, A z = z0. The color of the dot represents the stability factor characteristic of the orbit. Each period-doubling orbital family contains two branches, named primary branches and secondary branches.

[0115] Step 3: trajectory correction based on multiple shooting method;

[0116] Since the lunar orbiter on the DRO orbit is affected by various perturbations in the Earth-Moon space, long-term operation without correction may cause orbital deviation or even divergence. Therefore, it is necessary to extend the DRO orbit generated by the extension and bifurcation in CR3BP to the perturbed BR4BP model. This process requires the use of a multiple-targeting method. N ] is divided into several time periods [t i ,t i+1 ](i=1,…N-1), N is the total number of time periods, t=t i The state quantity at the moment is defined as i=1,2,...N, for CR3BP system, Q iis the initial value, integral t i+1 -t i Time can get Q i+1 , the mapping process is φ(Q i )=Q i+1 When considering multiple perturbations, the integral will produce deviations, making the integration process become The multi-targeting method ensures the continuity between time periods through the following constraints:

[0117]

[0118] F is the deviation function between the mapping of the CR3BP system and the mapping result after considering the perturbation.

[0119] φ is the mapping of the CR3BP system.

[0120] is the mapping of the CR3BP system after perturbation.

[0121] The Newton iteration method is used to optimize the orbit state at each moment so that the constraints meet the tolerance of 1×10 -10 . Assume the initial state is Q (0) , after the jth iteration, the corrected result can be obtained:

[0122] DF(Q (j) )(Q (j+1) -Q (j) )=-F(Q (j) ) (16)

[0123] j is the number of iterations.

[0124] DF is the differential matrix of F.

[0125] The structure of DF is:

[0126]

[0127] I is the identity matrix.

[0128] Φ i is the state transition matrix of DRO, and i=1,2,...,N-1.

[0129] In this invention, it is necessary to study the long-term illumination condition of the DRO orbit. However, a long simulation time may cause the deviation of the orbit terminal state estimated by the state transfer matrix to become larger. Therefore, the total simulation time is divided into segments, and multiple shooting is performed respectively. The terminal state of the previous segment is regarded as the initial state of the next segment, and finally a quasi-periodic DRO orbit is obtained. One of the corrected simulation results is as follows: Figure 6 As shown, Figure 6 (b) Yes Figure 6(a) A top-down view of each trajectory segment represents the result of a multi-targeting approach, with each segment lasting approximately 1.5 months, for a total of three years of simulation. The results demonstrate that the segmented targeting approach can effectively converge the perturbed DRO and maintain it within a certain range of the trajectory of the original CR3BP system over the long term.

[0130] Step 4: Analyze the long-term illumination conditions of the DRO lunar orbiter;

[0131] The cylindrical shadow model is used to simulate the orbital lighting conditions. This model assumes that the sun is far enough away from the earth and the moon so that the sunlight is considered parallel. The following function can be used to determine whether the lunar orbiter is in the shadow:

[0132]

[0133] r is the vector pointing from the shadow-causing planet to the spacecraft.

[0134] γ is a constant coefficient that can be adjusted according to the required accuracy and is taken as 1×10 9 .

[0135]

[0136] r S is the vector pointing from the shadow-causing planet to the Sun.

[0137] R is the radius of the planet causing the shadow.

[0138] The shadow situation of the DRO (Dro) after multiple target shooting corrections was simulated within three years, and the total illumination ratio η within three years was calculated. S and the longest continuous shadow duration d S A DRO orbit with an orbital illumination percentage exceeding 98.5% and a maximum shadow duration of no more than 550 minutes over three years is defined as a Super-Sun-Sychronous Orbit (Super-SSO) around the Moon. This Super-SSO is the orbital layout for the lunar orbiter in this invention. The lower limit of the illumination percentage is based on the illumination percentage of the Chang'e-4 relay satellite mission, while the upper limit of the maximum shadow duration is based on the shadow duration of the classic lunar sun-synchronous orbit.

[0139] A three-year illumination simulation of all DRO tracks revealed that most 3D DROs meet the definition of Super-SSO, and there are DRO tracks with global illumination. The total illumination of all DROs accounts for η S and the longest continuous shadow duration d S like Figure 7 and Figure 8 shown.

[0140] Step 5: Analyze the lighting conditions based on the relationship between the Sun, the lunar orbiter, the Moon, and the Earth.

[0141] Due to the large number of Super-SSOs, the lunar orbiter needs to comprehensively consider the mission requirements and orbital lighting conditions when selecting the orbital layout scheme. The key factors affecting the orbital lighting conditions and their influencing effects are given. The influencing factors include: the out-of-plane amplitude A of the Super-SSO z , orbital resonance ratio and the initial solar phase angle (the angle between the sun and the line connecting the earth and the moon). The main purpose is to provide a reference basis for the orbital layout plan of the lunar orbiter.

[0142] The shadow of the lunar orbiter may be caused by two celestial bodies, namely the Earth and the Moon. The appearance of the shadow depends on the position of the lunar orbiter relative to the Sun. Studies have found that the angle α between the Sun, lunar orbiter and Earth SSE and the angle α between the Sun, the lunar orbiter, and the Moon SSM It can well reflect the distribution and variation of orbital shadows. When the angle is less than a certain threshold, the Earth's shadow (α SSE <α SSE-阈值 ) or the lunar shadow (α SSM <α SSM-阈值 The angle threshold of the Sun-Moon Orbiter-Earth is α SSE-阈值 , the angle threshold of the Sun-lunar orbiter-Moon is α SSM-阈值 .like Figure 9 As shown in the figure, the blue dots are the moments when the lunar orbiter experiences the moon's shadow within three years, and the light green line is the α SSM The evolution law of the angle is that it oscillates according to a certain period.

[0143] Step 51, out-of-plane amplitude and illumination conditions;

[0144] α for Super-SSO SSM A long-term simulation was conducted on the angle and the analysis found that A z A larger (higher out-of-plane amplitude) Super-SSO will have a concentrated lunar shadow area on the time axis (e.g. Figure 9 The blue dots appear in the cluster. And, as A z As the value of A increases, the duration of the concentrated shadow area will become shorter, while the intervals between the concentrated shadow areas will also be extended, that is, the duration of the period without the moon's shadow will be longer. z The improvement will significantly shorten the duration of the lunar shadow, and the lunar orbiter can be placed on a DRO orbit as high as possible while meeting the mission requirements.

[0145] Therefore, the out-of-plane amplitude A is analyzed z When the lighting conditions are right, the lunar orbiter will be placed on the highest DRO orbit.

[0146] Step 52, orbital resonance ratio and illumination conditions;

[0147] In addition to the out-of-plane amplitude, the characteristics of the Super-SSO, such as the shape and period, also depend on the resonance ratio This affects the lighting conditions of Super-SSO. and A z The impact on Super-SSO is uncoupled and can be discussed separately. Studies have found that an increase in the resonance ratio of Super-SSO will lead to a longer duration of concentrated lunar shadow areas. However, the continuous moon-free time between concentrated lunar shadow areas will also be extended, which is beneficial to the lighting conditions of the lunar orbiter. Therefore, when selecting a suitable lunar orbiter orbit according to the mission, the required orbital height, resonance ratio and the time taken into account should be considered. The relatively high Super-SSO is more conducive to avoiding the lunar shadow for a longer period of time, but when performing the mission, care should be taken to avoid the concentrated lunar shadow area. Otherwise, the lunar orbiter will need to undergo frequent light-shadow switching in the longer concentrated shadow area, which is very unfavorable for the thermal control system and component operation of the lunar orbiter.

[0148] Therefore, analyzing the orbital resonance ratio The lunar orbiter will be placed on the DRO orbit with the highest resonance ratio when meeting the lighting conditions, while avoiding the concentrated lunar shadow area.

[0149] Step 53, solar phase angle and lighting conditions;

[0150] The definition of solar phase angle is as follows Figure 1 θ in S As shown, the initial solar phase angle θ S0 The initial operation time of the lunar orbiter can be determined. From the perspective of spatial position, it determines the configuration formed by the lunar orbiter, the Earth, and the Moon, and thus greatly affects the formation of the orbital shadow. The study found that although the change of the initial phase angle of the sun does not affect the long-term illumination condition index (η S and d S ) has a substantial impact, but it can shift the distribution of the lunar shadow along the time axis, effectively adjusting the temporal distribution of the shadow. If this change is considered in conjunction with the Earth's shadow, it will affect the duration of the lunar orbiter's completely shadow-free period. In actual missions, the initial solar phase angle corresponds to the epoch of the Super-SSO initial position, which means the selection of the launch window. Therefore, choosing the appropriate mission launch window ensures that the lunar orbiter receives global illumination throughout the mission.

[0151] Similarly, the shadow of the Earth on the lunar orbiter can be expressed by the angle α SSE Reflect. Figure 10 As shown, the α of the lunar orbiter SSE The oscillation period of the α angle is roughly the same as the rotation period of the sun in the Earth-Moon rotation system (29.53 days). The period of the lunar orbiter on the Super-SSO will only make the α SSE The angle changes slightly during one solar rotation period. z For Super-SSOs with a value smaller than the Earth radius (0.016LU), no matter how the orbital radius is, it is impossible to skip the Earth's concentrated shadow area in each period (29.53 days), e.g. Figure 10 shown.

[0152] Therefore, analyzing the solar phase angle θ S0 The selected θ is related to the lighting conditions S0 This ensures that the spacecraft experiences the least amount of concentrated Earth shadow during the mission period.

[0153] Step 6: Global lighting track layout plan;

[0154] In actual missions, full-area illumination of the track is a major goal of track design optimization. Figure 11 Shown are the velocity distributions of two three-dimensional DRO tracks with the same out-of-plane amplitude and resonance ratio, belonging to the main branch and the secondary branch, respectively.

[0155] According to the above conclusions, when the spacecraft is closer to the moon, it is more likely to be blocked by the earth or the moon, and the duration of the shadow is related to the arc length of the trajectory of the intersection of the cylindrical shadow. Therefore, if the spacecraft moves faster when approaching the lunar surface, it may produce global illumination. Figure 11 (a) shows that the Super-SSO velocity on the main branch is almost uniformly distributed and symmetric about the xy plane, so it is difficult for its trajectory to remain outside the shadow of the Earth or the Moon for a long time, thus achieving global illumination, which is also confirmed by numerical results. Figure 11 The Super-SSO in the secondary branch (b) has an asymmetric orbital shape, and the spacecraft is faster when approaching the lunar surface, but its speed decreases significantly when moving away from the moon (from 0.59VU to 0.40VU, 1VU is about 1.0232km / s). Therefore, the lighting conditions of the Super-SSO in the secondary branch can be significantly improved, and the fully illuminated orbit can only appear on the secondary branch. Figure 10 The figure shows a three-year global illumination trajectory, with a resonance ratio of Out-of-plane amplitude A Z =0.04LU, LU is the average distance between the earth and the moon.

[0156] Step 7: lunar orbiter attitude pointing plan;

[0157] The purpose of designing an attitude pointing scheme for the lunar orbiter is to determine the lunar orbiter's attitude for subsequent acquisition of the zero-incidence angle solar array. The lunar orbiter is usually used for observation, imaging and lunar surface communication. Therefore, the lunar orbiter attitude pointing scheme for such missions is as follows: Figure 13 shown.

[0158] The attitude pointing scheme of the lunar orbiter involves two coordinate systems: the orbital system and the lunar orbiter system. The origin of the orbital system is located at the center of mass of the lunar orbiter, with x0 pointing to the moon, the y0 axis perpendicular to the sun-lunar orbiter-moon plane, and the z0 axis following the right-hand rule. This system is fixed to the lunar orbiter. According to the mission requirements, when performing remote sensing and imaging of the lunar surface, it is necessary to keep the camera or sensor equipment constantly pointed at the moon. Therefore, the equipment on the lunar orbiter, such as the CCD camera, is aligned along the x axis. b The two branches of the solar array are mounted on the ±y axis to ensure that it always points to the moon. b The orbital coordinate system determines the nominal lunar orbiter attitude and pointing scheme, which can be achieved by keeping the Euler angle between the orbital system and the local system zero.

[0159] Step 8: Control law of the lunar orbiter's zero-incident-angle solar array;

[0160] In order to receive sufficient solar energy, a one-dimensional solar array is designed to orbit ±y b The purpose of the solar array's rotation is to ensure that the array can always track the sun, maintaining a perpendicular incidence of sunlight on the solar array, i.e., achieving a zero-incident-angle solar array. The solar array is driven by the Solar Array Drive Assembly (SADA). Therefore, a control law for the solar array on the lunar orbiter will be designed to further optimize the lighting conditions on the Super-SSO lunar orbiter.

[0161] The optimal incident direction of sunlight requires that the normal of the solar array be parallel to the sunlight. b The angle between the axis and the lunar orbiter-sun vector is the angle between the expected normal direction of the solar array and the x b The angle β between the axes is marked on Figure 13 The expected angle is exactly the angle α between the Sun, the lunar orbiter and the Moon. SSM The control law of the solar array needs to be designed to make the β angle track the α SSM Since the mass of the lunar orbiter's rigid platform greatly exceeds that of the solar array, the lunar orbiter can be assumed to be stationary when the solar array is running at a low speed. The driving torque of the SADA is output from the shaft to the load (solar array) and is expressed as angular acceleration. Ignoring the friction effect, it is expressed as:

[0162]

[0163] is the second-order derivative of the angle β with respect to time t.

[0164] T is the torque consumed by the load.

[0165] I a is the moment of inertia of the solar cell array.

[0166] The present invention designs a proportional-derivative (PD) controller to track α SSM :

[0167]

[0168] u is the control law.

[0169] e is the control error.

[0170] is the first-order derivative of the control error with respect to time t.

[0171] k p is the proportional gain of the controller.

[0172] k d is the controller's derivative gain.

[0173] For different lunar orbiters on Super-SSO, in order to improve the tracking performance of the solar array to the sun, it is necessary to design k according to the characteristics of Super-SSO. p and k d With the Super-SSO resonance ratio The increase of z-axis amplitude A Z Smaller Super-SSOs require larger k p To track high frequency signals. In the same situation, A Z The smaller Super-SSO is more likely to enter the shadow, so a larger k is required to ensure that the tracking error caused by passing through the shadow is quickly eliminated. d To achieve rapid control of zero-angle solar cell arrays.

[0174] A simulation example is used to demonstrate the effectiveness of the PD control law for a zero-angle solar cell array. Table 1 lists the relevant simulation parameters. The present invention sets the control to start when the initial error is less than 5° and sets the target tracking accuracy to 0.1°. The control results are shown in Figure 1. Figure 14The results show that the solar array achieved angular tracking in approximately 12 seconds (e < 0.1°), and subsequently maintained tracking with only a few control pulses. The maximum torque required was only 0.0784 Nm. Compared with the increase in power generation from maintaining the solar array at zero declination, the power consumption of this control process is almost negligible. Furthermore, this torque is much smaller than the torque required for attitude control of the lunar orbiter (approximately 25 Nm), indicating that controlling the solar array on the lunar orbiter on the Super-SSO does not incur significant additional power consumption. Therefore, this control strategy can be used as a solar array control scheme for the orbital layout of a global illumination lunar orbiter.

[0175] Table 1 Solar cell array control law simulation parameters

[0176]

Claims

1. A method for orbital layout of a global illumination lunar orbiter is based on periodic orbital design in Earth-Moon space and satellite attitude control, and is used to support the successful completion of the lunar orbiter mission; it is characterized by: Track layout includes the following steps; Step 1: Modeling the double-circle four-body problem in the Earth-Moon space; The double-circle four-body model takes into account the influence of the sun's gravity on the basis of the circular restricted three-body problem. The dynamic equation of the fourth celestial body is: x is the coordinate component of the spacecraft in the x direction; y is the coordinate component of the spacecraft in the y direction; z is the coordinate component of the spacecraft in the z direction; is the first derivative of the spacecraft's coordinate component in the x direction with respect to time t; is the first derivative of the spacecraft's coordinate component in the y direction with respect to time t; is the first derivative of the coordinate component of the spacecraft in the z direction with respect to time t; is the second-order derivative of the spacecraft's coordinate component in the x direction with respect to time t; is the second-order derivative of the spacecraft's coordinate component in the y direction with respect to time t; is the second-order derivative of the coordinate component of the spacecraft in the z direction with respect to time t; is the partial derivative in the x direction; is the partial derivative in the y direction; is the partial derivative in the z direction; U 4BP is the pseudo-gravitational potential energy of BR4BP; Among them U 4BP and U 3BP It is expressed as: U 3BP is the pseudo-gravitational potential energy of CR3BP; m S is the mass of the Sun; a S is the distance from the Sun to the center of mass of the Earth and the Moon; μ is the ratio of the mass of the Moon to the sum of the masses of the Earth and the Moon; r1 is the distance between the spacecraft and the Earth; r2 is the distance between the spacecraft and the moon; r3 is the distance between the spacecraft and the sun; θ S is the phase angle of the sun; Where r1, r2 and r3 are expressed as: By improving the pseudo-gravitational potential energy in equation (3), considering the J2 term of the lunar gravity, equation (3) is transformed into: In the formula, is the angular velocity of the Earth-Moon system, A2 is the oblateness coefficient of the Moon; the inclination of the Moon's rotation axis can be realized by coordinate transformation using equation (8); ε is the tilt angle of the moon's rotation axis; x ε is the coordinate component of the spacecraft in the x direction after rotating by angle ε; y ε is the coordinate component of the spacecraft in the y direction after rotating by angle ε; z ε is the coordinate component of the spacecraft in the z direction after rotating by angle ε; Substituting the rotated coordinates into formula (7), we can obtain the pseudo-gravitational potential energy of CR3BP that takes into account both the non-spherical gravitational perturbation of the moon and the tilt of the moon's rotation axis; Step 2: DRO orbit extension and bifurcation in Earth-Moon space; The pseudo arc length extension algorithm is used to extend the planar DRO family; considering the symmetry of DRO about the xz plane, the initial value of the orbit is set to Set the Poincare section to {Σ:y=0}. The DRO orbit needs to cross the Poincare section vertically. Therefore, in order to obtain a periodic orbit, the initial value needs to satisfy: f is the mapping function that maps the initial state of the spacecraft to the velocity after half a period; x0 is the initial coordinate component of the spacecraft in the x direction; z0 is the initial coordinate component of the spacecraft in the z direction; is the initial velocity component of the spacecraft in the y direction; is the velocity component of the spacecraft in the x direction after half a period; is the velocity component of the spacecraft in the z direction after half a period; T is the period of DRO; If X m is the current solution of the DRO family, then the initial value iteration of the next solution m+1 satisfies: It is the initial value of the iteration of the next feasible solution of the DRO family; Δs is the pseudo arc length; i s is the identity matrix in the null space direction of the Jacobian matrix G of f; With the introduction of Δs, the combined formula (9) is obtained: are simultaneous functions; The state transfer matrix of the orbit is calculated according to the dynamic equation of CR3BP. The state transfer matrix over a period is the orbital single-value matrix. The orbital stability factor is calculated according to the eigenvalue of the single-value matrix: ν is the stability factor of the periodic orbit; λ j and is an eigenvalue of the jth reciprocal eigenvalue pair of the single-valued matrix; If |ν|>1, the orbit is unstable; if |ν|≤1, the orbit is stable; let λ j = cosθ + isinθ and i is the imaginary unit, θ is the Euler angle corresponding to the imaginary eigenvalue; the eigenvectors corresponding to the two eigenvalues ​​are e1±ie2; after one cycle, we get: e1 is the vector of the eigenvector in the direction of the real axis e2 is the vector of the eigenvector in the direction of the imaginary axis; θ is the Euler angle corresponding to the imaginary eigenvalue; R(θ) is the rotation matrix; The ratio of the number of orbital revolutions n and k is: n is the number of revolutions of the orbit; k is the approximate resonance relationship between the orbital period of the bifurcation point and the rotation of the coordinate system; Step 3: trajectory correction based on multiple shooting method; The multiple-targeting method ensures the continuity between time periods by using the following constraints: F is the deviation function between the mapping of the CR3BP system and the mapping result after considering the perturbation; φ is the mapping of the CR3BP system; It is the mapping of the CR3BP system after considering the perturbation; The Newton iteration method is used to optimize the orbit state at each moment so that the constraints meet the tolerance of 1×10 -10 ; Set the initial state to Q (0) , after the jth iteration, the corrected result can be obtained: DF(Q (j) )(Q (j+1) -Q (j) )=-F(Q (j) ) (16) j is the number of iterations; DF is the differential matrix of F; The structure of DF is: I is the identity matrix; Φ i is the state transition matrix of DRO, and i=1,2,...,N-1; Step 4: Analysis of long-term illumination conditions of the DRO lunar orbiter; The cylindrical shadow model is used to simulate the orbital lighting conditions, and the calculation function is used to determine whether the lunar orbiter is in the shadow: r is the vector pointing from the shadow-causing planet to the spacecraft; γ is a constant coefficient that can be adjusted according to the required accuracy and is taken as 1×10 9 ; r S is the vector pointing from the planet causing the shadow to the Sun; R is the radius of the planet causing the shadow; Step 5: Analysis of lighting conditions based on the relationship between the sun, lunar orbiter, moon / Earth; Out-of-plane amplitude A z Place the lunar orbiter on the highest DRO orbit when the lighting conditions are right; Orbital resonance ratio Place the lunar orbiter on the DRO orbit with the highest resonance ratio when the lighting conditions are right, while avoiding the concentrated lunar shadow area; Solar phase angle θ S0 The selected θ is related to the lighting conditions S0 Minimize the Earth's concentrated shadow during the mission period; Step 6: Global lighting track layout plan; The global illumination track is the velocity distribution of two three-dimensional DRO tracks with the same out-of-plane amplitude and resonance ratio, belonging to the main branch and the secondary branch, respectively; Step 7: Attitude pointing plan of the lunar orbiter; The attitude pointing scheme of the lunar orbiter involves two coordinate systems: the orbital system and the lunar orbiter system. The origin of the orbital system is located at the center of mass of the lunar orbiter, with x0 pointing to the moon, y0 axis perpendicular to the sun-lunar orbiter-moon plane, and z0 axis following the right-hand rule. The system is fixed to the lunar orbiter. According to the mission requirements, the camera or sensor equipment needs to be continuously pointed at the moon when performing remote sensing and imaging of the lunar surface. Therefore, the equipment on the lunar orbiter, such as the CCD camera, etc., are aligned along the x axis. b axis to ensure that it always points to the moon; in addition, the two branches of the solar array are mounted on ±y b On the plane; the orbital coordinate system determines the nominal attitude pointing scheme of the lunar orbiter, which can be achieved as long as the Euler angle between the orbital system and the local system is kept zero; Step 8, control law of solar array of lunar orbiter with zero incidence angle; Moon Ring Device x b The angle between the axis and the lunar orbiter-sun vector is the angle between the expected normal direction of the solar array and the x b The angle β between the sun, the lunar orbiter and the moon is exactly the angle α between the sun, the lunar orbiter and the moon. SSM ; It is necessary to design the control law of the solar array to make the β angle track the α SSM The driving torque of the solar cell array drive assembly is output from the shaft to the solar cell array and is expressed as angular acceleration: is the second derivative of the angle β with respect to time t; T is the torque consumed by the load; I a is the moment of inertia of the solar array; Tracking α with a proportional-derivative controller SSM : u is the control law; e is the control error; is the first-order derivative of the control error with respect to time t; k p is the proportional gain of the controller; k d is the differential gain of the controller; For different lunar orbiters on Super-SSOs, in order to improve the tracking performance of the solar array to the sun, it is necessary to design k according to the characteristics of Super-SSO. p and k d ; With the Super-SSO resonance ratio The increase of z-axis amplitude A Z Smaller Super-SSOs require larger k p To track high frequency signals; In the same situation, A Z The smaller Super-SSO is more likely to enter the shadow, so a larger k is required to ensure that the tracking error caused by passing through the shadow is quickly eliminated. d To achieve rapid control of zero-angle solar cell arrays.

2. The orbital layout method of the global illumination lunar orbiter according to claim 1, characterized in that: In step six, the spacecraft moves faster when approaching the lunar surface, resulting in global illumination.

3. The orbital layout method of the global illumination lunar orbiter according to claim 1, characterized in that: In step eight, the effectiveness of the PD control law for the zero-declination solar cell array begins when the initial error is less than 5°, and the target tracking accuracy is set to 0.1°; it shows that the solar cell array achieves angle tracking in about 12 seconds and when e<0.1°, and only a few control pulses are needed to maintain tracking subsequently, and the maximum torque required is only 0.0784Nm; compared with the torque of 25Nm required for the attitude control of the lunar orbiter, this control strategy serves as a better solar cell array control scheme for the orbital layout of the global illumination lunar orbiter.

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