On-satellite autonomous controllable transverse side-by-side multi-satellite formation method

Abstract

The invention provides an on-satellite autonomous controllable transverse side-by-side multi-satellite formation method. The method comprises the following steps: establishing a multi-satellite relative motion model under a circular orbit; taking any group of satellites as master and slave satellites, and obtaining a direct corresponding relation between a formation system baseline requirement and an orbit parameter; preliminary design of formation configuration is carried out according to inter-satellite baseline requirements of a formation system; establishing an expression of a baseline angle between the master and slave satellites and satellite orbit parameters by using a mathematical expression of a relationship between baseline vectors and orbit six elements, and taking the expression as a constraint condition of non-common-view shielding of formation configuration design; and designing orbit parameters of a plurality of satellites of the formation satellite system according to the latitude distribution requirement of the base line required by the task, and forming the formation system meeting the task requirement.

Description

Technical Field

[0001] This invention relates to an autonomous and controllable method for horizontally arranged multi-satellite formation on a satellite, belonging to the field of space technology. Background Technology

[0002] Distributed satellite formation flying requires designing reasonable and feasible formation configurations for different observation tasks, ensuring the stability and controllability of the configuration and the simultaneous measurability of inter-satellite baselines. For missions involving imaging moving ground targets, distributed formation satellites flying side-by-side laterally need to provide multiple stable baselines along the track in the latitude region of interest to ensure effective payload operation, and the length of these baselines can be flexibly adjusted in orbit according to mission requirements. Furthermore, real-time, unobstructed, high-precision measurements between multiple satellites are also a crucial aspect of formation design during actual in-orbit operation.

[0003] The most successful examples of current in-orbit applications of satellite constellations are the TamDEM heterogeneous binary system and macro satellites. Figure 1 The four-satellite formation on the same plane, including the TamDEM two-satellite formation method, employs the double-helix Helix formation method, which can design the baseline along the track according to the mission. However, its baseline along the track can only provide a fixed baseline for each orbit change, which cannot meet the baseline requirements of multiple satellites and multiple missions on the ground. Figure 1 While the spatial baseline designed by the four-satellite coplanar formation method can provide a baseline along the flight path, this baseline is coupled with the vertical baseline, failing to meet the need for flexible design of multiple baselines along the flight path. Therefore, there is an urgent need for a formation method with strong engineering feasibility, capable of flexibly designing a formation along the flight path baseline length to meet imaging tasks in different latitude regions, while also satisfying the requirement for unobstructed real-time relative measurements on-board and autonomous maintenance of the on-board formation configuration. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose an on-board autonomous and controllable lateral multi-satellite formation method. By establishing a baseline vector model through the theory of relative motion of multiple satellites, the mathematical relationship between the baseline and the orbital parameters of the formation satellites is obtained. Based on this mathematical relationship, the design of lateral multi-satellite formation satellites that meet the requirement of providing a specified length along the track baseline is completed. At the same time, the constraint condition of non-co-visual obstruction between multiple satellites is introduced to realize the on-board autonomous maintenance and control design of distributed formation satellites.

[0005] The technical solution of this invention is: an on-board autonomous and controllable method for horizontally arranged multi-satellite formation, comprising:

[0006] Based on orbital kinematics theory, a mathematical model of the relative motion of multiple satellites in a formation is established, and it is simplified to obtain a model of the relative motion of multiple satellites in a circular orbit. Taking any group of satellites as master and slave satellites, the simplified model of the relative motion of multiple satellites is used to establish mathematical expressions for the baseline vector and the six orbital roots in the RTN coordinate system, thereby obtaining the direct correspondence between the baseline requirements of the formation system and the orbital parameters.

[0007] Based on the inter-satellite baseline requirements of the formation system, a preliminary design of the formation configuration is carried out;

[0008] Under the obtained formation configuration, the mathematical expression of the relationship between the baseline vector and the orbital six roots is used to establish the expression of the inter-satellite baseline angle and satellite orbital parameters of the master and slave satellites, which serves as the constraint condition for non-co-existent occlusion in the formation configuration design.

[0009] Based on the constraints of formation configuration design and non-co-existing occlusion in formation configuration design, and according to the latitudinal distribution requirements of the baseline for mission requirements, the orbital parameters of multiple satellites in the formation satellite system are designed to form a formation system that meets mission requirements.

[0010] Based on orbital kinematics theory, a mathematical model of the relative motion of multiple satellites in a formation is established, and simplified to obtain a model of the relative motion of multiple satellites in a circular orbit. Taking any group of satellites as master and slave satellites, the simplified model of the relative motion of multiple satellites is used to establish mathematical expressions for the baseline vector and the six orbital roots in the RTN coordinate system, thereby obtaining the direct correspondence between the baseline requirements of the formation system and the orbital parameters, including:

[0011] Establish the RTN coordinates of the slave star relative to the master star, then the expression for the relative motion of the slave star relative to the master star is Δr. R For the relative motion of the formation satellite system in the radial R direction, Δr T For the relative motion of the formation satellite system along the track T direction, Δr N For the relative motion of the formation satellite system in the normal N direction:

[0012] Δr R =a a -a c +a c [-(e a cosω a -e c cosω c cosu c -(e a sinω a -e c sinω c )sinu c ]

[0013]

[0014] Δr N =a c [-(Ω a -Ω c )sini c cosu c +(i a -i c )sinu c ]

[0015] Where u c It is the mean latitude argument of the primary star, u c =ω c +M c ω c M is the perigee argument. c It is the angle of approach, Ω c (h c ) and r c These are the right ascension of the ascending node and the geocentric distance of the primary star, i c It is the inclination of the primary star, e c It is the eccentricity of the primary star, a c It is the semi-major axis of the primary star; a a e a u a M a Ω a i a r a For the orbital variables of the secondary star, its physical meaning is the same as that of the primary star mentioned above;

[0016] The relative motion Δr of the formation satellite system in the radial R direction R The relative motion Δr of the formation satellite system along the track T direction T The relative motion Δr in the normal N direction of the satellite formation system N Simplify the three mathematical expressions, let a a -a c =0, the primary star has a circular orbit, e c =0, then simplifying to:

[0017] Δr R =-a c e a cos(u c -ω a )

[0018] Δr T =a c (u a -u c )+2a c e a sin(u c -ω a)

[0019]

[0020] in,

[0021] Δr in the RTN coordinate system R , Δr T , Δr N The baselines are defined as the radial R-direction baseline, the trajectory T-direction baseline, and the normal N-direction baseline of the formation satellites, respectively, thereby establishing a mathematical expression for the relationship between the formation satellite baseline vector and the orbital six roots.

[0022] The preliminary design of the formation configuration based on the inter-satellite baseline requirements of the formation system includes: using the mathematical expression of the relationship between the baseline vector and the orbital six roots in the RTN coordinate system, the inter-satellite baseline required by the mission is decomposed into the baseline requirements in the R direction, T direction, and N direction for preliminary design of the formation configuration.

[0023] The mathematical expression relating baseline vectors and orbital root numbers in the RTN coordinate system is used to decompose the inter-satellite baseline requirements of the mission into baseline requirements in the R, T, and N directions for preliminary formation configuration design, including:

[0024] According to the formula for relative motion in the radial (R) direction of a satellite formation system, the mission requires the baseline in the radial (R) direction to be zero. This necessitates that the eccentricity of both satellites be zero, and that their semi-major axes be equal, i.e., e. c =e a =0, a c =a a ;

[0025] According to the formula for relative motion of the formation satellite system along the track T, the mission requires the satellites to maintain normal parallel flight, and the inter-satellite baseline in the T direction needs to be stable and basically not change periodically with time. At this time, the phase difference between the two satellites is needed to form the baseline in the T direction.

[0026] According to the formula for relative motion in the normal N direction of the formation satellite system, the mission requires the construction of a normal direction baseline, which requires designing the difference in right ascension ΔΩ and inclination Δi between the ascending nodes of the primary and secondary stars. Due to the influence of the different orbits of the primary and secondary stars, compensation needs to be made in the indicator phase.

[0027] Establish the mathematical relationship between the space baseline and the orbital parameters to obtain the baseline Δr in the radial R direction. R , baseline Δr along track T T Baseline Δr in the normal N direction N They are respectively:

[0028] Δr R =0

[0029] Δr T =a c (u a -u c )+a c (Ω a -Ω c cosi c

[0030]

[0031] The baseline length Δr in the T direction T =a c (u a -u c )+a c (Ω a -Ω c cosi c As a design constraint for safe collision avoidance distance, assuming the minimum safe distance between the formation satellites is ΔR, then the safe collision avoidance requirement is Δr. T >ΔR, which serves as a safety collision avoidance design constraint between satellites in the formation.

[0032] Under the obtained formation configuration, the mathematical expression relating the baseline vector and the orbital root numbers is used to establish expressions for the inter-satellite baseline angles and satellite orbital parameters of the master and slave satellites. These expressions serve as constraints for non-co-existent occlusion in the formation configuration design, including:

[0033] Let the expressions for the inter-satellite baseline angle between the master and slave satellites and the satellite orbital parameters be:

[0034]

[0035] When the number of satellites arranged in a horizontal row is even, let's assume it's m satellites, where m > 3 and is a natural number. We select the middle point O as a virtual star. Satellites M1 and M2 located on either side of point O form one group, and satellites M(m-1) and Mm located on either side of point O form another group. To ensure that M1, O, M2...M(m-1), O, and Mm are all on a straight line, the following conditions must be met:

[0036] (u a1 -u c0 )+(Ω a1 -Ω c0 cosi c0 =(-u a2 +u c0 )+(-Ω a2 +Ω c0 cosi c0

[0037]

[0038] (u a(m-1) -u c0 )+(Ω a(m-1) -Ω c0 cosi c0 =(-u am +u c0 )+(-Ω am +Ω c0 cosi c0

[0039]

[0040] When the number of satellites arranged in a horizontal row is odd, let's say (m+1) satellites, where m is even, we select the middle satellite as the center point O. Satellites M1 and M2 located on either side of point O form one group, and satellites M(m-1) and Mm located on either side of point O form another group. Satellites M1, M2, ..., M(m-1) and Mm also need to satisfy the following conditions:

[0041] (u a1 -u c0 )+(Ω a1 -Ω c0 cosi c0 =(-u a2 +u c0 )+(-Ω a2 +Ω c0 cosi c0

[0042]

[0043] (u a(m-1) -u c0 )+(Ω a(m-1) -Ω c0 cosi c0 =(-u am +u c0 )+(-Ω am +Ω c0 cosi c0

[0044]

[0045] Simplifying the conditions yields

[0046] u a1 -u c0 =-u a2 +u c0 ,Ω a1 -Ω c0 =-Ω a2 +Ω c0 ia1 -i c0 =-i a2 +i c0

[0047] u a(m-1) -u c0 =-u am +u c0 ,Ω a(m-1) -Ω c0 =-Ω am +Ω c0 i a(m-1) -i c0 =-i am +i c0

[0048] and

[0049] The expression for the difference in baseline inclination between the two sets of satellites is as follows:

[0050]

[0051] Based on the constraint of multi-star non-co-view occlusion, the constraint of non-co-view occlusion in formation configuration design is obtained.

[0052] The constraint condition for multi-satellite non-co-viewing obstruction is that the baseline tilt angle α formed by any two satellites must be different, and the angle difference Δα must not be less than the field of view angle θ of the baseline measurement system, that is, Δα≥θ.

[0053] The specific constraints for non-co-occlusion in formation configuration design are as follows:

[0054]

[0055] The process of designing the orbital parameters of multiple satellites in a formation satellite system based on the latitudinal distribution requirements of the mission needs, to form a formation system that meets the mission requirements, includes:

[0056] Based on the regression characteristics and observation performance requirements of remote sensing satellites, the semi-major axis a a The size is determined by the specific mission; for any pair of satellites forming the baseline, the horizontally side-by-side formation required by the mission necessitates that the baseline in the R direction be zero, i.e., Δr. R =-a c e a cos(u c -ω a ) is zero, that is, e a1 =e a2 =0,e a1 and e a2 This represents the eccentricity of satellites M1 and M2; simultaneously, a a1 =aa2 a a1 and a a2 This represents the semi-major axis of satellites M1 and M2; similarly, the eccentricity e of satellites M(m-1) and Mm can be obtained. a(m-1) and e am , semi-major axis a a(m-1) and a am ;

[0057] From the design constraints, where M1, O, M2 and M(m-1), O, Mm are constraints on straight lines, we can obtain... For any pair of satellites forming a baseline, given the mission requirements, the maximum baseline length B in the normal direction N. y Given the latitude Ψ of the baseline overlap failure interval, solve the system of equations simultaneously. Among them, Ω a1 -Ω c0 =-Ω a2 +Ω c0 i a1 -i c0 =-i a2 +i c0 Ω a1 and Ω a2 Indicate the right ascension of the ascending nodes of satellites M1 and M2, i a1 and i a2 By indicating the inclination angles of satellites M1 and M2, the right ascension Ω of the ascending node of satellites M1 and M2 can be obtained. a1 Ω a2 and tilt angle i a1 i a2 Similarly, the right ascension Ω of the ascending node of satellites M(m-1) and Mm can be obtained. a(m-1) Ω am and tilt angle i a(m-1) i am ;

[0058] Based on the mathematical expression of the baseline along the track T direction of the transverse side-by-side multi-star formation system, the mean latitude argument u is calculated. c And it remains unchanged at all times; for any pair of satellites forming a baseline, the baseline length in the T direction required by the mission is B. x That is, to obtain the difference in average latitude angle u between the two satellites. a1 -u a2 =B x a2-(Ω a1 -Ω a2 cosi a2 u a1 and u a2 The mean latitude argument of satellites M1 and M2 is given by u. a2 =ua1 -B x a2+(Ω a1 -Ω a2 cosi a2 Similarly, the mean latitude argument u of satellites M(m-1) and Mm can be obtained. a(m-1) and u am ;where u a1 u a2 u a(m-1) and u am To meet the inter-satellite safety distance requirements;

[0059] The baseline length along the track T direction of the horizontally parallel multi-satellite formation required by the mission is B. x Furthermore, based on the common-view constraint relationship of the relative measurement system, the baseline inclination α formed by any two pairs of satellites satisfies the angle difference Δα ≥ θ within the specified latitude range. The average latitude argument u is achieved through the constraint condition of multiple satellites not being in common-view. a1 u a2 u a3 and u a4 Value constraints;

[0060] Based on the remote sensing satellite regression characteristics and observation efficiency requirements, both the primary and secondary satellites are in circular orbits with a perigee argument ω. a Take any value, and use the angle M as the nearest point. a Characterizing the latitudinal argument u a ;

[0061] By setting the mean anomaly Ma of satellite M, the initial mean anomaly M of each satellite can be obtained. a =u a -ω a ; and thus we can obtain M a1 M a2… ;

[0062] This gives us the initial orbital parameters for each satellite in the formation, namely, semi-major axis a, eccentricity e, orbital inclination i, right ascension of the ascending node Ω, argument of perigee ω, and mean perigee M.

[0063] The advantages of this invention compared to existing technologies are: which component / step / solution is applied, what role it plays, and what benefits it provides; these can be listed in bullet points.

[0064] (1) This invention establishes a multi-satellite relative motion model for a distributed formation satellite system, providing a theoretical method for the design of formation satellite orbits and configurations for three-dimensional imaging observation missions.

[0065] (2) This invention establishes a mathematical expression for the length of the baseline in three dimensions and the orbital parameters of the formation satellites, establishes a direct correspondence between the length of the baseline along the track and the orbital parameters, obtains a baseline along the track that remains constant at any time, and configures an invalid region of the baseline within a specified latitude range through parameter design, which can be applied to the design of orbital parameters for horizontally parallel multi-satellite distributed formation satellites that meet specific requirements for the baseline along the track.

[0066] (3) This invention establishes the field of view design requirements for horizontally parallel multi-star inter-satellite baselines to be visible and unobstructed, and the constraint relationship between the inter-satellite baselines, thereby setting the initial state of the relative positions of the multi-star formation.

[0067] (4) In actual on-orbit operation, due to the Earth's gravity and space perturbation, the orbital drift and configuration divergence are caused by the Earth's gravity. This invention uses real-time orbital parameters to determine whether multiple satellites meet the requirements of non-co-viewing occlusion, thereby realizing the execution of on-board autonomous maintenance control tasks.

[0068] (5) The method constructed by the present invention can solve the problem of horizontally parallel multi-star distributed formation configuration design, and at the same time solve the problem of autonomous stability and maintenance control of formation configuration during operation. During the entire process of on-orbit operation, the satellite can autonomously plan and execute tasks, which is highly efficient and fast, and helps to respond flexibly to tasks, and has practical engineering significance. Attached Figure Description

[0069] Figure 1 A schematic diagram of a distributed, horizontally aligned, multi-star formation system and its configuration;

[0070] Figure 2 This is a schematic diagram of the inter-satellite baseline inclination.

[0071] Figure 3 A diagram showing the satellite formation configuration;

[0072] Figure 4 This describes the distribution of satellite normal baselines.

[0073] Figure 5 This shows the distribution of satellites along the flight path baseline;

[0074] Figure 6 This shows the distribution of baseline tilt angle difference. Detailed Implementation

[0075] like Figure 1As shown, this invention uses four satellites in formation as an example. The mission requires four satellites, M1, M2, M3, and M4, to form a formation. These satellites fly side-by-side laterally and are symmetrically distributed around a virtual center O. The satellite flight direction is T, the Earth's center direction is R, and the N direction is obtained using the right-hand rule. The four satellites are paired into groups (M1, M2), (M1, M3), (M1, M4), (M2, M3), (M2, M4), and (M3, M4), forming six spatial baselines B. 12 B 13 B 14 B 23 B 24 B 34 The minimum safe distance between any two satellites is ΔR. For example... Figure 2 As shown, any two sets of inter-satellite baselines form a baseline inclination angle α in space. When the baseline inclination angle difference Δα < the field of view angle θ, the two distant satellites become collinear, making the baseline unmeasurable. By setting the orbital parameters of the four formation satellites, the mission's formation baseline requirements are met, while simultaneously addressing the issues of multi-satellite shared-view occlusion avoidance and collision avoidance in the formation satellite system.

[0076] Includes the following steps:

[0077] Step 1, as follows Figure 1 As shown, based on orbital kinematics theory, a mathematical model of the relative motion of multiple satellites in a formation is established. This model is then simplified to obtain a relative motion model of multiple satellites in a circular orbit. Using any group of satellites as master and slave satellites, the simplified relative motion model is used to establish mathematical expressions for the baseline vector and the six orbital roots in the RTN coordinate system. This allows us to obtain a direct correspondence between the baseline requirements of the formation system and the orbital parameters.

[0078] Furthermore, the specific steps of step 1 are as follows:

[0079] Step 1.1: Establish the RTN coordinates of the secondary star relative to the primary star, and simplify them to obtain the expression for the relative motion of the secondary star relative to the primary star:

[0080] Δr R =a a -a c +a c [-(e a cosω a -e c cosω c cosu c -(e a sinω a -e c sinω c )sinu c (1)

[0081]

[0082] Δr N =a c [-(Ω a -Ω c )sini c cosu c +(i a -i c )sinu c (3)

[0083] Where u c It is the mean latitude argument of the primary star, u c =ω c +M c ω c M is the perigee argument. c It is the angle of approach, Ω c (h c ) and r c These are the right ascension of the ascending node and the geocentric distance of the primary star, i c It is the inclination of the primary star, e c It is the eccentricity of the primary star, a c It is the semi-major axis of the primary star. a e a u a M a Ω a i a and r a The physical meaning of the orbital variables of a star is the same as described above.

[0084] Step 1.2: Simplify the formula in Step 1.1, let a a -a c =0, the primary star has a circular orbit, e c =0, simplifying the above formula, we get,

[0085] Δr R =-a c e a cos(u c -ω a (4)

[0086] Δr T =a c (u a -u c )+2a c e a sin(u c -ω a (5)

[0087]

[0088] in, The remaining variables are the same as in the formula above.

[0089] Thus, the mathematical expression for the relationship between the baseline vector and the six orbital roots in the RTN coordinate system is obtained, and the mathematical expression for the relationship between the baseline vector and the six orbital roots of the formation system in step 1 is established.

[0090] Step 2, as follows Figure 1 As shown, considering the inter-satellite baseline requirements of the formation system, the correspondence between the baseline vector and the six orbital roots obtained in step 1, as well as the baseline requirements of the lateral multi-satellite formation system mission, is used to decompose the three-dimensional baseline vector. The three directions are the R direction, T direction, and N direction, respectively, to obtain the design basis for the lateral multi-satellite formation system configuration and the design input for the multi-satellite orbital parameters. Specifically, the radial R-direction baseline is required to be zero during lateral side-by-side flight. The satellites at both ends of each baseline group must be on the same straight line as the virtual star O in the TN plane, and the distances between the two satellites and the virtual star O must be equal. Simultaneously, the inter-satellite baseline in the T direction must be stable and not periodically change over time, while also serving as a safety collision avoidance distance design constraint. The N-direction baseline serves as the lateral baseline to meet mission requirements. Orbital parameters are designed under these requirements to satisfy the formation configuration design requirements.

[0091] Furthermore, the specific steps of step 2 are as follows:

[0092] Step 2.1, according to the formula Δr in Step 1.2 R =-a c e a cos(u c -ω a The mission requires a zero baseline in the radial (R) direction, which necessitates that both satellites have an eccentricity of 0 and equal semi-major axes, i.e., e. c =e a =0, a c =a a .

[0093] Step 2.2, according to the formula Δr in Step 1.2 T =a c (u a -u c )+2a c e a sin(u c -ω a The mission requires the satellites to fly side-by-side in the normal direction, which requires the inter-satellite baseline in the T direction to be stable and basically not change periodically over time. At this time, the phase difference between the two satellites is needed to form the baseline in the T direction.

[0094] Step 2.3, according to the formula in Step 1.2 The task requires constructing a normal direction baseline, which necessitates designing the difference in right ascension ΔΩ and inclination Δi between the ascending nodes of the primary and secondary stars. Due to the influence of the divergent orbits of the primary and secondary stars, compensation is also required in the indicator phase.

[0095] At this point, the mathematical relationship between the spatial baseline and the orbital parameters is established, and the baseline Δr in the radial R direction is obtained. R , baseline Δr along track T T Baseline Δr in the normal N direction N They are respectively:

[0096] Δr R =0 (7)

[0097] Δr T =a c (u a -u c )+a c (Ω a -Ω c cosi c (8)

[0098]

[0099] At the same time, the baseline length Δr in the T direction will be... T =a c (u a -u c )+a c (Ω a -Ω c cosi c As a design constraint for safe collision avoidance distance, assuming the minimum safe distance between the formation satellites is ΔR, then the safe collision avoidance requirement is Δr. T >ΔR, which serves as a safety collision avoidance design constraint between satellites in the formation.

[0100] Step 3, as follows Figure 1 , Figure 2 As shown, the expression for establishing the inter-satellite baseline angle between the master and slave satellites and the satellite orbital parameters is as follows:

[0101]

[0102] Taking the diagram as an example, M1 and M2 form one group, and M3 and M4 form another group. We select point O as a virtual star. To ensure that M1, O, M2 and M3, O, M4 are each a straight line, the following conditions must be met:

[0103] (u a1 -u c0 )+(Ω a1 -Ω c0 cosi c0 =(-u a2+u c0 )+(-Ω a2 +Ω c0 cosi c0

[0104]

[0105] (u a3 -u c0 )+(Ω a3 -Ω c0 cosi c0 =(-u a4 +u c0 )+(-Ω a4 +Ω c0 cosi c0

[0106]

[0107] Simplifying the conditions, we can obtain

[0108]

[0109] The expression for the difference in baseline inclination between the two sets of satellites is as follows:

[0110]

[0111] Therefore, the constraint condition for multi-satellite non-co-line-of-view occlusion is that the baseline inclination angle α formed by any two satellites must be different, and the angle difference Δα is not less than the field of view angle θ of the baseline measurement system, i.e., Δα ≥ θ. The constraint condition for multi-satellite non-co-line-of-view occlusion in a formation satellite system is thus obtained.

[0112]

[0113] Step 4, the formation satellite design step, is based on the formulas and constraints in Steps 2 and 3. The orbital parameters of the formation satellites can be designed according to the specific baseline length and the latitudinal distribution requirements of the maximum baseline, so as to form a formation system that meets the mission requirements.

[0114] Furthermore, the specific steps of step 4 are as follows:

[0115] Step 4.1, based on the regression characteristics of remote sensing satellites and observation performance requirements, the semi-major axis a a The magnitude is given through mission calculations; for any pair of satellites forming a baseline, the baseline in the R direction is given as zero according to mission requirements, i.e., e a1 =e a2 =0,e a1 and e a2 This represents the eccentricity of satellites M1 and M2; simultaneously, a a1 =aa2 a a1 and a a2 This represents the semi-major axis of satellites M1 and M2; similarly, the eccentricity e of satellites M3 and M4 can be obtained. a3 and e a4 , semi-major axis a a3 and a a4 .

[0116] Step 4.2: As we know from Step 3, M1, M2, and M3, M4 will inevitably produce a baseline angle difference Δα less than the required θ. Given that M1, O, M2 and M3, O, M4 are each constrained by a straight line, we can obtain... For any pair of satellites forming a baseline, given the mission requirements, the maximum baseline length B in the normal direction N. y Given the latitude Ψ of the baseline overlap failure interval, solve the system of equations simultaneously. Among them, Ω a1 -Ω c0 =-Ω a2 +Ω c0 i a1 -i c0 =-i a2 +i c0 Ω a1 and Ω a2 Indicate the right ascension of the ascending nodes of satellites M1 and M2, i a1 and i a2 By indicating the inclination angles of satellites M1 and M2, the right ascension Ω of the ascending node of satellites M1 and M2 can be obtained. a1 Ω a2 and tilt angle i a1 i a2 Similarly, the right ascension Ω of the ascending node of satellites M3 and M4 can be obtained. a3 Ω a4 and tilt angle i a3 i a4 .

[0117] Step 4.3, based on the baseline length of the horizontally parallel multi-star formation along the track T direction according to mission requirements, the mean latitude angle u c The size is given by formula (8) and remains constant at all times; for any pair of satellites forming the baseline, the baseline length in the T direction required by the mission is B. 12 That is, to obtain the latitudinal argument difference u between the two satellites. a1 -u a2 =B x a2-(Ω a1 -Ω a2 cosi a2 u a1 and u a2The mean latitude argument of satellites M1 and M2 is given by... Similarly, the mean latitude argument u of satellites M3 and M4 can be obtained. a3 and u a4 Among them, u a1 u a2 u a3 and u a4 It meets the inter-satellite safety distance requirements.

[0118] Step 4.4, based on the mission requirements, the baseline length of the horizontally parallel multi-star formation along the track T direction is B. x Furthermore, based on the common-view constraint relationship of the relative measurement system, the baseline inclination α formed by any two pairs of satellites satisfies the angle difference Δα ≥ θ within the specified latitude range. The average latitude argument u is achieved through the constraint condition of multi-satellite non-common-view occlusion in step 3. a1 u a2 u a3 and u a4 Value constraints.

[0119] Step 4.5: Based on the remote sensing satellite's regression characteristics and observation performance requirements, both the primary and secondary satellites are in circular orbits with a perigee argument ω. a It's meaningless; the values ​​can be the same. Use the angle M, which is the closest to the point of intersection. a Characterizing the latitudinal argument u a .

[0120] By setting the mean anomaly Ma of satellite M, the initial mean anomaly M of each satellite can be obtained. a =u a -ω a From steps 4.3 and 4.4, we can obtain M. a1 M a2 Thus, the initial orbital parameters of the formation satellites are obtained, namely, semi-major axis a, eccentricity e, orbital inclination i, right ascension of the ascending node Ω, argument of perigee ω, and mean perigee M.

[0121] The effects of the present invention will be briefly introduced and explained below with specific examples.

[0122] The mission requires designing a four-star formation with a semi-major axis of 6873.68 km and an orbital inclination of 97.39°. The four stars are approximately side-by-side and evenly distributed. The maximum baseline along the flight path has a safe distance of 100 m. The maximum normal long baseline is 1 km, and the maximum normal short baseline is 0.33 km. This needs to be determined within the mean latitude angle u. c The baseline length reaches its maximum near the equator, and the two sets of inter-satellite baselines B 14 and B 23 The baseline direction angle must be no less than 3°. The overall formation parameters can be obtained through the following procedure:

[0123] 1. The eccentricity e of outer stars M1 and M2 a1 =e a2 =0, the eccentricity e of the inner stars M3 and M4 a3 =e a4 =0.

[0124] 2. The normal baseline reaches its maximum near the equator, with four satellites... This means i a1 =i a2 =i a3 =i a4 =i c0 .

[0125] 3. The maximum normal baseline is 1 km, and the four satellites are evenly distributed. Therefore, the difference in right ascension of the ascending nodes of the four satellites is ΔΩ = 0.0028. Let Ω... a1 =0, then Ω a2 =0.0084, Ω a3 =0.0028, Ω a4 =0.0056.

[0126] 4. The baseline of the four satellites along the track direction is 100m. The angle between the two sets of inter-satellite baselines B12 and B34 is Δα≥3°, and θ=3°.

[0127] 5. Since the argument of perigee is meaningless under a circular orbit, it is taken as 0 here. The solution obtained by combining the constraints from step 4 yields u. a1 =-0.00012、u a2 =0.00012, u a3 =0.00004 and u a4 = -0.00004, then M can be obtained. a1 =-0.00012, M a2 =0.00012, M a3 =0.00004 and M a4 = -0.00004.

[0128] The following formation design parameters can be obtained as a result:

[0129]

[0130] Using simulation software to simulate the above-mentioned formation design, the following results can be obtained: Figure 3 The satellite formation configuration diagram shown illustrates the spatial baseline distribution under this design configuration. Figure 4 and Figure 5 As shown. The variation of the baseline angle difference Δα is as follows. Figure 6 As shown, through design and configuration, the requirement of Δα≥3° is met in most working conditions.

[0131] The design method for a horizontally parallel multi-satellite distributed formation configuration proposed in this invention can meet the requirements of multi-satellite formation design and on-orbit autonomous control in terms of both theoretical design and actual operation. This method can provide baseline design at any latitude and ensure high-precision measurement of inter-satellite baselines.

[0132] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention based on the above-disclosed technical content without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for autonomously controllable horizontal multi-satellite formation, characterized in that, include: Based on orbital kinematics theory, a mathematical model of the relative motion of multiple satellites in a formation is established, and it is simplified to obtain a model of the relative motion of multiple satellites in a circular orbit. Taking any group of satellites as master and slave satellites, the simplified model of the relative motion of multiple satellites is used to establish mathematical expressions for the baseline vector and the six orbital roots in the RTN coordinate system, thereby obtaining the direct correspondence between the baseline requirements of the formation system and the orbital parameters. Based on the inter-satellite baseline requirements of the formation system and the direct correspondence between the baseline requirements of the formation system and the orbital parameters, a preliminary design of the formation configuration is carried out. Under the obtained formation configuration, the mathematical expression of the relationship between the baseline vector and the orbital six roots is used to establish the expression of the inter-satellite baseline angle and satellite orbital parameters of the master and slave satellites, which serves as the constraint condition for non-co-existent occlusion in the formation configuration design. Based on the constraints of formation configuration design and non-co-existing occlusion in formation configuration design, and according to the latitudinal distribution requirements of the baseline for mission requirements, the orbital parameters of multiple satellites in the formation satellite system are designed to form a formation system that meets mission requirements.

2. The on-board autonomous and controllable horizontal multi-satellite formation method according to claim 1, characterized in that, Based on orbital kinematics theory, a mathematical model of the relative motion of multiple satellites in a formation is established, and simplified to obtain a model of the relative motion of multiple satellites in a circular orbit. Taking any group of satellites as master and slave satellites, the simplified model of the relative motion of multiple satellites is used to establish mathematical expressions for the baseline vector and the six orbital roots in the RTN coordinate system, thereby obtaining the direct correspondence between the baseline requirements of the formation system and the orbital parameters, including: Establish the RTN coordinates of the slave star relative to the master star, then the expression for the relative motion of the slave star relative to the master star is Δr. R For the relative motion of the formation satellite system in the radial R direction, Δr T For the relative motion of the formation satellite system along the track T direction, Δr N For the relative motion of the formation satellite system in the normal N direction: Δr R =a a -a c +a c [-(e a so a -e c so c )this c -(and a yes a -e c yes c )sinus c ] Δr N =a c [-(Ω a -Ω c )breasts c something c +(i a -i c )sinus c ] Where u c It is the mean latitude argument of the primary star, u c =ω c +M c ω c M is the perigee argument. c It is the angle of approach, Ω c (h c ) and r c These are the right ascension of the ascending node and the geocentric distance of the primary star, i c It is the inclination of the primary star, e c It is the eccentricity of the primary star, a c It is the semi-major axis of the primary star; a a e a u a M a Ω a i a r a For the orbital variables of the secondary star, its physical meaning is the same as that of the primary star mentioned above; The relative motion Δr of the formation satellite system in the radial R direction R The relative motion Δr of the formation satellite system along the track T direction T The relative motion Δr in the normal N direction of the satellite formation system N Simplify the three mathematical expressions, let a a -a c =0, the primary star has a circular orbit, e c =0, then simplifying to: Δr R =-a c e a cos(u c -oh a ) Δr T =a c (u a -u c )+2a c e a sin(u c -ω a ) in, Δr in the RTN coordinate system R , Δr T , Δr N The baselines are defined as the radial R-direction baseline, the trajectory T-direction baseline, and the normal N-direction baseline of the formation satellites, respectively, thereby establishing a mathematical expression for the relationship between the formation satellite baseline vector and the orbital six roots.

3. The on-board autonomous and controllable horizontal multi-satellite formation method according to claim 2, characterized in that, The preliminary design of the formation configuration is carried out based on the inter-satellite baseline requirements of the formation system and the direct correspondence between the baseline requirements of the formation system and the orbital parameters. This includes: using the mathematical expression of the relationship between the baseline vector and the orbital six roots in the RTN coordinate system, the inter-satellite baseline required by the mission is decomposed into baseline requirements in the R direction, T direction, and N direction for preliminary design of the formation configuration.

4. The on-board autonomous and controllable horizontal multi-satellite formation method according to claim 3, characterized in that, The mathematical expression relating baseline vectors and orbital root numbers in the RTN coordinate system is used to decompose the inter-satellite baseline requirements of the mission into baseline requirements in the R, T, and N directions for preliminary formation configuration design, including: According to the formula for relative motion in the radial (R) direction of a satellite formation system, the mission requires the baseline in the radial (R) direction to be zero. This necessitates that the eccentricity of both satellites be zero, and that their semi-major axes be equal, i.e., e. c =e a =0, a c =a a ; According to the formula for relative motion of the formation satellite system along the track T, the mission requires the satellites to maintain normal parallel flight, and the inter-satellite baseline in the T direction needs to be stable and basically not change periodically with time. At this time, the phase difference between the two satellites is needed to form the baseline in the T direction. According to the formula for relative motion in the normal N direction of the formation satellite system, the mission requires the construction of a normal direction baseline, which requires designing the difference in right ascension ΔΩ and inclination Δi between the ascending nodes of the primary and secondary stars. Due to the influence of the different orbits of the primary and secondary stars, compensation needs to be made in the indicator phase. Establish the mathematical relationship between the space baseline and the orbital parameters to obtain the baseline Δr in the radial R direction. R , baseline Δr along track T T Baseline Δr in the normal N direction N They are respectively: Δr R =0 Δr T =a c (u a -u c )+a c (Oh a -Oh c )so c The baseline length Δr in the T direction T =a c (u a -u c )+a c (Ω a -Ω c cosi c As a design constraint for safe collision avoidance distance, assuming the minimum safe distance between the formation satellites is ΔR, then the safe collision avoidance requirement is Δr. T >ΔR, which serves as a safety collision avoidance design constraint between satellites in the formation.

5. The on-board autonomous and controllable horizontal multi-satellite formation method according to claim 1, characterized in that, Under the obtained formation configuration, the mathematical expression relating the baseline vector and the orbital root numbers is used to establish expressions for the inter-satellite baseline angles and satellite orbital parameters of the master and slave satellites. These expressions serve as constraints for non-co-existent occlusion in the formation configuration design, including: Let the expressions for the inter-satellite baseline angle between the master and slave satellites and the satellite orbital parameters be: When the number of satellites arranged in a horizontal row is even, let's assume it's m satellites, where m > 3 and is a natural number. We select the middle point O as a virtual star. Satellites M1 and M2 located on either side of point O form one group, and satellites M(m-1) and Mm located on either side of point O form another group. To ensure that M1, O, M2...M(m-1), O, and Mm are all on a straight line, the following conditions must be met: (in a1 -in c0 )+(Ω a1 -Ω c0 )something c0 =(-u a2 +in c0 )+(-Ω a2 +Ω c0 )something c0 (in a(m-1) -in c0 )+(Ω a(m-1) -Ω c0 )something c0 =(-u am +in c0 )+(-Ω am +Ω c0 )something c0 When the number of satellites arranged in a horizontal row is odd, let's say (m+1) satellites, where m is even, we select the middle satellite as the center point O. Satellites M1 and M2 located on either side of point O form one group, and satellites M(m-1) and Mm located on either side of point O form another group. Satellites M1, M2, ..., M(m-1) and Mm also need to satisfy the following conditions: (in a1 -in c0 )+(Ω a1 -Ω c0 )something c0 =(-u a2 +in c0 )+(-Ω a2 +Ω c0 )something c0 (in a(m-1) -in c0 )+(Ω a(m-1) -Ω c0 )something c0 =(-u am +in c0 )+(-Ω am +Ω c0 )something c0 Simplifying the conditions yields u a1 -u c0 =-u a2 +u c0 ,Ω a1 -Ω c0 =-Ω a2 +Ω c0 ,i a1 -i c0 =-i a2 +i c0 u a(m-1) -u c0 =-u am +u c0 ,Ω a(m-1) -Ω c0 =-Ω am +Ω c0 ,i a(m-1) -i c0 =-i am +i c0 and The expression for the difference in baseline inclination between the two sets of satellites is as follows: Based on the constraint of multi-star non-co-view occlusion, the constraint of non-co-view occlusion in formation configuration design is obtained.

6. The on-board autonomous and controllable horizontal multi-satellite formation method according to claim 5, characterized in that, The constraint condition for multi-satellite non-co-viewing obstruction is that the baseline tilt angle α formed by any two satellites must be different, and the angle difference Δα must not be less than the field of view angle θ of the baseline measurement system, that is, Δα≥θ.

7. The on-board autonomous and controllable horizontal multi-satellite formation method according to claim 6, characterized in that, The specific constraints for non-co-occlusion in formation configuration design are as follows:

8. The on-board autonomous and controllable horizontal multi-satellite formation method according to claim 1, characterized in that, The process of designing the orbital parameters of multiple satellites in a formation satellite system based on the latitudinal distribution requirements of the mission needs, to form a formation system that meets the mission requirements, includes: Based on the regression characteristics and observation performance requirements of remote sensing satellites, the semi-major axis a a The size is determined by the specific mission; for any pair of satellites forming the baseline, the horizontally side-by-side formation required by the mission necessitates that the baseline in the R direction be zero, i.e., Δr. R =-a c e a cos(u c -ω a ) is zero, that is, e a1 =e a2 =0,e a1 and e a2 This represents the eccentricity of satellites M1 and M2; simultaneously, a a1 =a a2 a a1 and a a2 This represents the semi-major axis of satellites M1 and M2; similarly, the eccentricity e of satellites M(m-1) and Mm can be obtained. a(m-1) and e am , semi-major axis a a(m-1) and a am ; From the design constraints, where M1, O, M2 and M(m-1), O, Mm are constraints on straight lines, we can obtain... For any pair of satellites forming a baseline, given the mission requirements, the maximum baseline length B in the normal direction N. y Given the latitude Ψ of the baseline overlap failure interval, solve the system of equations simultaneously. Among them, Ω a1 -Ω c0 =-Ω a2 +Ω c0 i a1 -i c0 =-i a2 +i c0 Ω a1 and Ω a2 Indicate the right ascension of the ascending nodes of satellites M1 and M2, i a1 and i a2 By indicating the inclination angles of satellites M1 and M2, the right ascension Ω of the ascending node of satellites M1 and M2 can be obtained. a1 Ω a2 and tilt angle i a1 i a2 Similarly, the right ascension Ω of the ascending node of satellites M(m-1) and Mm can be obtained. a(m-1) Ω am and tilt angle i a(m-1) i am ; Based on the mathematical expression of the baseline along the track T direction of the transverse side-by-side multi-star formation system, the mean latitude argument u is calculated. c And it remains unchanged at all times; for any pair of satellites forming a baseline, the baseline length in the T direction required by the mission is B. x That is, to obtain the difference in average latitude angle u between the two satellites. a1 -u a2 =B x a2-(Ω a1 -Ω a2 cosi a2 u a1 and u a2 The mean latitude argument of satellites M1 and M2 is given by u. a2 =u a1 -B x / a2+(Ω a1 -Ω a2 cosi a2 Similarly, the mean latitude argument u of satellites M(m-1) and Mm can be obtained. a(m-1) and u am ;where u a1 u a2 u a(m-1) and u am To meet the inter-satellite safety distance requirements; The baseline length along the track T direction of the horizontally parallel multi-satellite formation required by the mission is B. x Furthermore, based on the common-view constraint relationship of the relative measurement system, the baseline inclination α formed by any two pairs of satellites satisfies the angle difference Δα ≥ θ within the specified latitude range. The average latitude argument u is achieved through the constraint condition of multiple satellites not being in common-view. a1 u a2 u a3 and u a4 Value constraints; Based on the remote sensing satellite regression characteristics and observation efficiency requirements, both the primary and secondary satellites are in circular orbits with a perigee argument ω. a Take any value, and use the angle M as the nearest point. a Characterizing the latitudinal argument u a ; By setting the mean anomaly Ma of satellite M, the initial mean anomaly M of each satellite can be obtained. a =u a -ω a ; and thus we can obtain M a1 M a2 …; This gives us the initial orbital parameters for each satellite in the formation, namely, semi-major axis a, eccentricity e, orbital inclination i, right ascension of the ascending node Ω, argument of perigee ω, and mean perigee M.

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