Multi-body flyby sequence rapid evaluation method based on flyby state feasible region

Abstract

The application discloses a multi-body borrowing sequence fast evaluation method based on a borrowing state feasible region and belongs to the technical field of aerospace. The application realizes the method as follows: adopting a plane circle constraint, on the basis of a normalized borrowing state parameter hyperbolic overspeed size and a direction angle, a departure condition met when a spacecraft leaves a celestial body and an arrival condition met when the spacecraft arrives at the celestial body are derived; a multi-body borrowing state feasible region is obtained through analytical calculation; a multi-body borrowing phase difference and a transfer arc angle are semi-analytically extracted from the multi-body borrowing state feasible region; a launch window is obtained by comparison under ephemeris according to a combination of the multi-body borrowing phase difference and the transfer arc angle; and the fast evaluation of the multi-body borrowing sequence is realized. The application is suitable for any long outward flight sequence, can provide a feasible multi-body borrowing sequence and a corresponding launch window at an early stage of multi-body borrowing flight mission planning, avoids a large amount of numerical optimization in an infeasible window, and improves the efficiency of multi-body borrowing flight mission planning.

Description

Technical Field

[0001] This invention relates to a multi-body leveraging sequence planning method, and more particularly to a rapid multi-body leveraging flight sequence planning method based on the feasible region of leveraging state and considering initial and final constraints, belonging to the field of aerospace technology. Background Technology

[0002] In deep space exploration missions, the distant targets and limited rocket and onboard fuel pose challenges to the design of interplanetary orbits. Multi-body maneuvering is an effective means of shortening flight time and reducing fuel consumption, and it is widely used in deep space exploration orbit design. However, in multi-body maneuvering orbit design, the number of maneuvers and their order are unknown, theoretically resulting in an infinite number of multi-body maneuvering sequences. To obtain the optimal multi-body maneuvering flight trajectory, rapid multi-body maneuvering sequence planning is essential.

[0003] To evaluate multi-object assisted sequences, various multi-object assisted sequence planning methods have been developed. Prior art [1] (see: Gad A., Abdelkhalik O. Hidden Genes Genetic Algorithm for Multi-Gravity-Assist Trajectories Optimization[J]. Journal of Spacecraft and Rockets, 2011, 48(4):629-641.) optimizes the integer variables of the multi-object assisted sequence and the continuous variables of the flight trajectory parameters in the multi-object assisted sequence planning problem using an improved genetic algorithm. The first half of the chromosome uses integer encoding and adds hidden genes to change the multi-object assisted sequence, while the second half of the chromosome uses real number encoding to represent the corresponding trajectory parameters, thus achieving simultaneous optimization of the multi-object assisted sequence and trajectory parameters. This method is limited by chromosome length; the length of the multi-object assisted sequence cannot exceed a preset value.

[0004] The prior art [2] (see: Wagner S., Wie B. Hybrid Algorithm for Multiple Gravity-Assist and Impulsive Delta-V Maneuvers[J]. Journal of Guidance, Control, and Dynamics, 2015, 38(11): 2096-2107.) uses different algorithms to process the integer variables of the multi-body leverage sequence and the continuous variables of the flight trajectory parameters in the multi-body leverage sequence planning problem in a hierarchical manner. The outer layer uses a nonlinear programming algorithm to optimize the multi-body leverage sequence based on the performance index fed back by the inner layer, and the inner layer uses a differential evolution algorithm to optimize the corresponding trajectory parameters based on the trajectory optimization problem defined by the outer layer. The multi-body leverage sequence planning is realized through the inner and outer double loops. Since each performance index calculation called by the outer layer is an inner loop trajectory optimization problem, the computational load is huge and the computation time is long.

[0005] Prior technology [3] (see: Vasile M., Becerra VM Computational Intelligence in Aerospace Sciences, 1) st [M] American Institute of Aeronautics and Astronautics, Inc., Reston, VA 20191-5807, 2014, Chap. 5.) This paper addresses the multi-body leveraging sequence planning problem by defining certain performance indices and pruning criteria for progressively increasing multi-body leveraging sequences. During sequence planning, poorly performing sequences and their growing branches are discarded, thereby achieving pruning of the understanding space and finding the parameter range of local minima, which can reduce the computational cost of orbit optimization. The definition of certain performance indices and pruning criteria in this method requires considerable skill; inappropriate definitions may lead to ineffective pruning or over-pruning of the optimal solution. Summary of the Invention

[0006] The technical problem addressed by the multi-body leveraging sequence rapid evaluation method based on the feasible region of leveraging states disclosed in this invention is to provide a rapid planning method for multi-body leveraging sequences that avoids extensive numerical optimization calculations. This method establishes planetary departure and arrival state conditions, analytically calculates the feasible region of multi-body leveraging states based on these conditions, semi-analytically extracts the multi-body leveraging phase difference and transfer arc angle from this region, and then compares the combination of the multi-body leveraging phase difference and transfer arc angle under ephemeris to obtain the launch window, thus achieving rapid evaluation of the multi-body leveraging sequence. This invention is applicable to any long outward flight sequence, can provide a window set for multi-body leveraging sequences, and improves the evaluation efficiency of multi-body leveraging sequences.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] The present invention discloses a fast evaluation method for multi-body lever-borrowing sequences based on the feasible region of lever-borrowing states, defining a planetary coordinate system O under planar circular constraints. i -x i y i z i The normalized hyperbolic overspeed magnitude α and its direction angle ψ are determined using the leveraged state parameters, and the spacecraft's kinematic equations are established based on these parameters. Based on the defined planetary coordinate system and the kinematic model with normalized parameters, the spacecraft's kinematic equations in state are then written. Leaving the Celestial P i Initiate interplanetary transfer and in state Arrival at Celestial P i+1 During the end of the interplanetary transfer, and The envelope of the range of variation, i.e., P i Departure Condition C dep and P i+1 Arrival Condition C arr Based on the known entry and exit parameters of the same celestial body, celestial body P... i Arrival conditions are standardized to O i -x i y i z i and The conditions for arrival are obtained. Following the order i = 0, 1, ..., N, based on the initial constraint α 0,max pass through in sequence and C dep Find the intersection to construct During the construction process, if any If the given sequence is empty, it is determined that the sequence is infeasible, and the evaluation of that sequence ends. Based on the branching strategy of tree search, the next sequence is given, and the evaluation restarts. Following the order i = N, N-1, ..., 0, based on the terminal constraints, the solution is obtained through inverse kinematics. Relationships to be pruned During the pruning process, if any If the result is empty, the given sequence is deemed infeasible, the evaluation of that sequence ends, and according to the branching strategy of tree search, the next sequence is given, and the evaluation restarts. If all If none of them are empty, then the feasible domain for leveraging the power of multiple celestial bodies is obtained. In each leveraged state feasible region Find the maximum value of the relative phase Δθ on the boundary. i:i+1,max Minimum value Δθ i:i+1,min The maximum value of the transfer arc angle Δf i:i+1,max Minimum value Δf i:i+1,min Based on this, the maximum initial phase difference Δθ of all celestial bodies is estimated. 0:i,max Minimum value Δθ 0:i,min Divide the given launch window into time intervals, and calculate planet P at each time interval t. i The phase difference Δθ between (i = 1, 2, ..., N) and planet P0 0:i+1,t and with Δθ 0:i,max , Δθ 0:i,min In contrast, if at time t all Δθ 0:i+1,t ∈[Δθ 0:i,min ,Δθ 0:i,max If a time t is recorded, then that time is recorded. This process is repeated for all times within a given launch window. If a window time t is recorded, the sequence is deemed feasible, the recorded window is output, the sequence evaluation ends, and the given new sequence is re-evaluated according to the tree search branching strategy. If no time t is recorded, the sequence is deemed to have no launch window within the given window, the sequence evaluation ends, and the given new sequence is re-evaluated according to the tree search branching strategy. When all sequences generated by the tree search have been evaluated, rapid evaluation of multi-body leveraging sequences based on the feasible region of the leveraging state is achieved.

[0009] The present invention discloses a rapid evaluation method for multi-celestial body leveraging sequences based on the feasible domain of leveraging state, comprising the following steps:

[0010] Step 1: Define the planetary coordinate system O under the constraints of a planar circle. i -x i y i z i The normalized hyperbolic hypervelocity magnitude α and its direction angle ψ are determined, and the spacecraft's kinematic equations are established based on these parameters. Using the defined planetary coordinate system and the kinematic model with normalized parameters, the spacecraft's departure from celestial body P is described.i Time state and spacecraft arrive at celestial body P i+1 Time state The envelope of the range of variation, i.e., P i Departure Condition C dep and P i+1 Arrival Condition C arr .

[0011] In interplanetary orbit analysis, the planar circular constraint is defined as follows: all orbits lie in the same plane, and the planetary orbits are concentric circles centered on the Sun.

[0012] For N+1 planets involved in the multi-body glide flight, numbered sequentially as P0, P1, ..., P N Where P0 represents the launching celestial body, P1, ..., P N-1 To leverage celestial bodies, P N The destination is planet P. In the inertial frame of reference, the planet P at a given time is determined based on the planetary ephemeris. i Dimensional position and velocity vectors Regarding the current celestial body P i Define an inertial coordinate system O i -x i y i z i The coordinate system x i Axial direction is defined as y i The axis is perpendicular to x in the orbital plane. i The axis points to planet P. i velocity direction, z i The axis is perpendicular to the orbital plane and parallel to the x-axis. i ,y i The axes form a right-handed coordinate system. N+1 different planets will correspond to N+1 different coordinate systems, each with an inertial coordinate system O. i -x i y i z i Chinese x i The angle between the current celestial body P and the X-axis of the inertial frame is defined as the angle between the current celestial body P and the X-axis of the inertial frame. i phase angle θ i (i = 0, 1, ..., N).

[0013] For coordinate system O i -x i y i z i Normalization is performed so that the state conditions derived in one coordinate system can be applied to different celestial bodies through unit scaling. The normalized units of mass, length, and time are respectively...

[0014]

[0015] Among them G, μ Sun ,and These are the gravitational constant, the solar gravitational constant, and planet P. i The semi-major axis of the heliocentric orbit. In coordinate system O i -x i y i z i and normalized units [M] i [R] i [T] i Below, planet P i Position and velocity vectors are

[0016] r i =[1,0,0] T ,v i =[0,1,0] T (2)

[0017] In coordinate system O i -x i y i z i and normalized units [M] i [R] i [T] i Let the dimensionless magnitude and direction angle of a spacecraft's hyperbolic hypervelocity relative to a planet be α (>0) and ψ (∈[0,2π)), respectively. Then, the spacecraft's entry / exit from planet P... i The state of leveraging is denoted as The corresponding interplanetary velocity vector is

[0018]

[0019] Furthermore, the spacecraft's position vector coincides with the planet's position vector during the glide flight. The next flyby object P... i+1 The radius of its heliocentric orbit is denoted as β (β > 1). According to... The spacecraft left planet P i The angular momentum h and eccentricity e of the heliocentric orbit:

[0020]

[0021]

[0022] It is known that the spacecraft has left planet P i Position and velocity vector By combining the equations of motion of conic sections, the state of leveraging forces is derived. Feasible domain C arr C dep Regarding the departure condition C depThe spacecraft is able to [obtain information from] current celestial bodies P i Arrive at the next body P i+1 The orbit must satisfy two constraints: Constraint ① The semi-major axis of the determined transfer orbit is greater than or equal to that of the celestial body P. i+1 The semi-major axis of the orbit is β; constraint ② is a prograde interplanetary orbit. The equations corresponding to the two constraints ① and ② are as follows:

[0023] h 2 / (1-e)>β (6)

[0024] h>0 (7)

[0025] Substituting equations (4) and (5) into equations (6) and (7), we obtain two conditions after simplification: and in

[0026]

[0027]

[0028] comprehensive and Two conditions are required: the spacecraft leaves the current celestial body P. i leverage state Leaving condition C dep g1 and g2 intersect at Place.

[0029] For satisfying C dep The interplanetary transfer orbit, according to the conic section equations of motion, yields the system O. i -x i y i z i The spacecraft arrived at celestial body P i+1 Entering the leverage state during orbit for:

[0030]

[0031] The range of change in equation (10) is used to calculate the state of entering the leverage state. The envelope of the feasible region, i.e., C arr Upper and lower boundary functions:

[0032]

[0033]

[0034] in: α i,max For α i The maximum allowed value,

[0035]

[0036]

[0037] Combining equations (11) to (14), we obtain the spacecraft's arrival at the next celestial body P. i+1 The state condition C of leveraging force at that time arr for

[0038]

[0039] Step 2: Based on the known entry and exit parameters for the same celestial body, determine the entry and exit parameters for celestial body P. i Arrival conditions are standardized to O i -x i y i z i and The conditions for arrival are obtained. Following the order i = 0, 1, ..., N, based on the initial constraint α 0,max pass through in sequence and C dep Find the intersection to construct During the construction process, if any If the given sequence is empty, it is determined that the given sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, the next sequence is given, and the process returns to step one to update the starting celestial body P. i and arriving at celestial body P i+1 The corresponding planetary coordinate system and the starting condition C dep and arrival conditions C arr Following the order i = N, N-1, ..., 0, based on the end constraints, the pruning is achieved by inversely solving the leverage state relation. During the pruning process, if any If the given sequence is empty, it is determined that the sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr If all If none of them are empty, then the feasible domain for leveraging the power of multiple celestial bodies is obtained. That is, by establishing the planetary departure state conditions and the planetary arrival state conditions, the feasible region of the multi-celestial body leveraging state is obtained through analytical calculation.

[0040] The system O has been constructed in step one. i -x i y i z i Next Celestial Body Pi+1 Entry condition C arr Based on this, simply add C arr α in i+1 Numerical expansion Times, that is, to obtain system O i+1 -x i+1 y i+1 z i+1 Next Celestial Body P i+1 Entry condition C arr This achieves the unification of units for celestial bodies, parameters, and coordinate systems. From this point onward, the entry condition C will be mentioned. arr Unless otherwise specified, all values ​​are assumed to be C after unit unification. arr .

[0041] Given the entry and exit parameters for the same celestial body, the set of all leverage states that simultaneously satisfy both the entry and exit conditions constitutes the feasible region of leverage states. To facilitate directly obtaining the feasible region by finding the intersection, let C... arr of The parameter is projected onto the lever angle δ. Parameters, obtained from Entry conditions Right now

[0042]

[0043] in

[0044]

[0045]

[0046]

[0047] in, For the dimensional lever celestial body P i gravitational constant, The minimum radius of leverage with dimensions is defined. For α i The corresponding dimensional hyperbolic overspeed magnitude.

[0048] Leveraging celestial bodies P i The feasible region of leveraged states for (i = 1, 2, ..., N-1) That is, the corresponding and C dep The intersection, that is

[0049]

[0050] The feasible regions of each celestial body's borrowing state collectively constitute the feasible regions of multi-celestial body borrowing. Right now

[0051]

[0052] Among them, the launching celestial bodies Destination and There are mutual influences between them. The solution is divided into two steps: forward construction and reverse pruning.

[0053] Step 2.1: Following the order i = 0, 1, ..., N, sequentially pass the initial constraint α. 0,max Construction of formula (19)

[0054] For multi-body glide, P i C arr From and Only P i-1 C arr A proper subset whose boundary differs from the descriptions in equations (11) to (14). P in multi-body glide flight i C arr The upper boundary has one additional variation, while the lower boundary has four variations depending on the number of feature points, namely (a) with 3 feature points. (b) Has 2 feature points (c) Has 2 feature points (d) Has 1 feature point

[0055] The upper boundary is:

[0056]

[0057] in By point Substituting into equation (10) yields the result. If If it does not exist, the lower boundary is still represented by equation (11).

[0058] The lower boundaries are as follows:

[0059] (a) It has 3 feature points:

[0060]

[0061] (b) Has 2 feature points:

[0062]

[0063] (c) It has 2 feature points:

[0064]

[0065] (d) Has 1 feature point:

[0066]

[0067] in for With P i-1 C dep The intersection point is substituted into equation (10) to calculate the result.

[0068] leverage state parameter α i Maximum and minimum values ​​α i,max ,α i,min There have also been some changes, with the maximum value being the point substituted into equation (10). The minimum value obtained from the calculation and the same unit is the point substituted into equation (10). calculate.

[0069] Constructing the feasible domain of leveraged states During the process, if any If the given sequence is empty, it is determined that the sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr .

[0070] Step 2.2: Prune sequentially according to the order i = N, N-1, ..., 0, using the end constraints and equation (10).

[0071] For a given end-hyperbolic overspeed magnitude constraint α N ≤α N,cr or α N ≥α N,cr Transform the critical value into a segmentation curve Segmentation curve feasible domain Divide the data into two parts, left and right, and select to keep the parts that satisfy the constraints and prune the parts that do not: when the constraint is α N ≤α N,cr Preserve the original The left side corresponds to the deceleration and rendezvous task; when the constraint is α N ≥α N,cr Preserve the original The right side corresponds to the accelerated flight mission.

[0072] Targeting the celestial body P i (i = N-1, N-2, ..., 1), based on the known... And solve for the corresponding equation using equation (10). Still the original Divide the process into left and right parts, selecting to retain the parts that satisfy the constraints and pruning the parts that do not: when the end constraint is α N ≤α N,cr Preserve the original Left side; when the end constraint is α N ≥α N,cr Preserve the original Right side. Then... Mapped to In order to provide for the continuation The pruning provides a basis. For the launching object P0, it is only necessary to base it on known... And solve for the corresponding equation (10). Will Divided into two parts, and according to α N ≤α N,cr or α N ≥α N,cr Preserve the original The left or right part is then complete. Pruning.

[0073] Based on the above known information And combined with the mapping relationship of equation (10) Solve In order to obtain the corresponding unique solution during the process, the following steps are performed: ① In The curve is divided by inverse solution of equation (10) on the lower boundary. lower vertex Right now ②In upper boundary or Inside The curve is segmented by inverse solution of equation (10) on the straight line. Top vertex Right now ③From Start solving Extension curve Until we meet (4) If but Solution complete, if Then Symmetry has been determined Partial, excerpt Internal parts, completed Please provide a solution.

[0074] Pruning leveraged state feasible region During the process, if any If the given sequence is empty, it is determined that the sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr .

[0075] If steps 2.1 and 2.2 have been completed, all If none of them are empty, then the multi-celestial body leverage feasible region as defined in equation (20) is obtained, and step three is continued.

[0076] Step 3: In each leveraged state, within the feasible region The maximum value of the relative phase Δθ is extracted semi-analytically from the boundary. i:i+1,max Minimum value Δθ i:i+1,min The maximum value of the transfer arc angle Δf i:i+1,max Minimum value Δf i:i+1,min The maximum initial phase difference Δθ of all celestial bodies is estimated based on the combination of the phase difference due to the multi-body leverage and the transfer arc angle. 0:i,max Minimum value Δθ 0:i,min Divide the given launch window into time intervals, and calculate planet P at each time interval t. i The phase difference Δθ between (i = 1, 2, ..., N) and planet P0 0:i+1,t and with Δθ 0:i,max , Δθ 0:i,min In contrast, if at time t all Δθ 0:i+1,t ∈[Δθ 0:i,min ,Δθ 0:i,max If a time t is recorded, then that time is recorded. This process is repeated for all times within a given launch window. If a window time t is recorded, the sequence is deemed feasible, the recorded window is output, the sequence evaluation ends, and the given new sequence is re-evaluated according to the tree search branching strategy. If no time t is recorded, it is determined that the sequence has no launch window within the given window, the sequence evaluation ends, and the given new sequence is re-evaluated according to the tree search branching strategy. When all sequences generated by the tree search have been evaluated, rapid evaluation of multi-body leveraging sequences based on the feasible domain of leveraging states is achieved.

[0077] Known feasible region for multi-celestial body leverage In each On the boundary, the relative phase Δθ is obtained according to the conic section equation. i:i+1 =θ i+1 -θ i The maximum value Δθ i:i+1,max and minimum value Δθi:i+1,min and the transfer arc angle Δf i:i+1 The maximum value Δf i:i+1,max and minimum value Δf i:i+1,min .

[0078] According to Δθ i:i+1,max , Δθ i:i+1,min , Δf i:i+1,max , Δf i:i+1,min Estimate the maximum and minimum initial phase differences of all celestial bodies:

[0079]

[0080]

[0081] Within a given launch window, obtain the planetary position r at time t in the ephemeris every one day. 0,t ,r 1,t ,…,r N,t Calculate P for each planet i The phase difference between (i = 1, 2, ..., N) and planet P0, i.e., r i,t (i=1,2,...,N) and r 0,t The included angle Δθ 0:i,t (i = 1, 2, ..., N) ∈ [0, 2π). If time t has Δθ for all planets 0:i,t ∈[Δθ 0:i,min ,Δθ 0:i,max If (i = 1, 2, ..., N) is selected, then record that time as the window for the given sequence; otherwise, continue searching for time. After searching each time within the given emission window, if a window time t is recorded, then determine that the sequence is feasible and output the recorded window. The evaluation of the sequence ends, and according to the tree search branching strategy, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr If no time t is recorded, it is determined that the sequence has no emission window within the given window, the sequence evaluation ends, and according to the tree search branching strategy, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr Once the tree search is complete, a rapid evaluation of multi-celestial leveraging sequences based on the feasible region of the leveraging state is achieved.

[0082] It also includes step four: based on the rapid evaluation results of the multi-body leveraging sequence obtained in step three, quickly obtain feasible multi-body leveraging sequences and provide a set of feasible launch windows. In the early stage of multi-body leveraging flight mission planning, provide feasible multi-body leveraging sequences and corresponding launch windows, eliminate infeasible windows, avoid a lot of numerical optimization in infeasible windows, which is beneficial to multi-body leveraging flight mission planning and saves computing resources and computing time, significantly improving the efficiency of multi-body leveraging flight mission planning.

[0083] Beneficial effects:

[0084] 1. The present invention discloses a rapid evaluation method for multi-body leverage sequences based on the feasible domain of leverage state. Using planar circular constraints, and based on the normalized leverage state parameters hyperbolic overspeed magnitude α and its direction angle ψ, the method derives the spacecraft's departure from the celestial body P. i The starting condition C is satisfied at that time dep and reaching celestial body P i+1 Arrival condition C that is met at the time arr This can improve the computational efficiency of the feasible domain of spacecraft levered states.

[0085] 2. The multi-celestial body leveraging sequence rapid evaluation method disclosed in this invention, based on the known entry and exit leveraging parameters of the same celestial body, sequentially passes through the leveraging sequence in the forward direction. and C dep Find the intersection to construct Pruning is achieved by sequentially reversing the leverage sequence and solving the leverage state relation. The feasible region for multi-celestial-body lever-based states is obtained through semi-analytical calculation.

[0086] 3. The multi-body leveraging sequence fast evaluation method disclosed in this invention, based on the feasible domain of the leveraging state, calculates the feasible domain of the multi-body leveraging state and extracts the relative phase and the maximum and minimum values ​​of the transfer arc angle within the feasible domain. It estimates the initial phase difference of all planets and uses the relationship between the phase and the actual ephemeris time and position to determine the feasibility of the multi-body leveraging sequence and the launch window, rather than through numerical optimization that can only output specific solutions. This increases the window evaluation range and improves the reliability of window finding.

[0087] 4. The fast evaluation method for multi-body leveraging sequences based on the feasible domain of leveraging state disclosed in this invention performs multi-body sequence planning and window search based on the feasible domain of multi-body leveraging state and phase information, without the need for a large amount of numerical optimization, thereby improving the speed and efficiency of multi-body leveraging sequence evaluation.

[0088] 5. The rapid evaluation method for multi-body leveraging sequences based on the feasible domain of leveraging states disclosed in this invention is based on a tree search strategy. It judges the feasibility of the sequence by the feasible domain of multi-body leveraging and compares the phase information of the feasible domain of multi-body leveraging with planetary ephemeris search. It can quickly give the window range that satisfies the initial and final constraints of a given multi-body leveraging sequence, thereby improving the mission planning efficiency of deep space exploration missions. Attached Figure Description

[0089] Figure 1 The flowchart of the multi-celestial body leveraging sequence rapid evaluation method based on the feasible domain of leveraging state in this invention.

[0090] Figure 2 Definitions of planetary coordinate system and leverage state parameters, etc.

[0091] Figure 3 The respective arrival conditions for Earth, Jupiter, and Neptune Departure Condition C dep And the feasible region of the leveraged state, where: Figure 3 (a) is the feasible region for Earth's leverage state. Figure 3 (b) represents the feasible region for the Jupiter-assisted state. Figure 3 (c) represents the feasible region for Neptune's borrowed state.

[0092] Figure 4 Feasible window record for the “Earth-Jupiter-Neptune-100AU” sequence. Detailed Implementation

[0093] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0094] Example 1:

[0095] like Figure 1 As shown in the figure, this example discloses a fast evaluation method for multi-body leveraging sequences based on the feasible domain of leveraging state. The specific implementation steps are as follows:

[0096] Step 1: Define the planetary coordinate system O under the constraints of a planar circle. i -x i y i z i The normalized hyperbolic hypervelocity magnitude α and its direction angle ψ are determined, and the spacecraft's kinematic equations are established based on these parameters. Using the defined planetary coordinate system and the kinematic model with normalized parameters, the spacecraft's departure from celestial body P is described. i Time state and spacecraft arrive at celestial body P i+1 Time state The envelope of the range of variation, i.e., P iDeparture Condition C dep and P i+1 Arrival Condition C arr .

[0097] The tree search branching strategy provides a multi-body borrowing sequence "Earth-Jupiter-Neptune-100AU". For the two borrowing bodies in this multi-body borrowing flight, they are numbered P1 and P2, respectively, with P0 representing Earth and P3 representing the destination 100AU. In the International Celestial Reference System (ICRS), planet P can be obtained at a given time based on the JPL DE440 ephemeris. i Dimensional position and velocity vectors Regarding the current celestial body P i Define an inertial coordinate system O i -x i y i z i The coordinate system x i Axial direction is defined as y i The axis is perpendicular to x in the orbital plane. i The axis points to planet P. i velocity direction, z i The axis is perpendicular to the orbital plane and parallel to the x-axis. i ,y i The axes form a right-handed coordinate system. The four different planets will correspond to four different coordinate systems and different normalized units, each with an inertial coordinate system O. i -x i y i z i Chinese x i The angle between the axis and the X-axis of the ICRS is defined as the current celestial body P. i phase angle θ i (i = 0, 1, ..., N). The coordinate system, i.e., the parameters, is defined as follows: Figure 2 As shown.

[0098] Step 2: Based on the known entry and exit parameters for the same celestial body, determine the entry and exit parameters for celestial body P. i Arrival conditions are standardized to O i -x i y i z i and The conditions for arrival are obtained. Following the order i = 0, 1, 2, 3, based on the initial constraint α 0,max pass through in sequence and C dep Find the intersection to construct Following the order i = 3, 2, 1, 0, based on the terminal constraint α3 ≥ α 3,min Pruning by inverse solution of the leverage state relation (10) like Figure 3 As shown, all If none of them are empty, then the feasible domain for leveraging the power of multiple celestial bodies is obtained. That is, by establishing the planetary departure state conditions and the planetary arrival state conditions, the feasible region of the multi-celestial body leveraging state is obtained through analytical calculation.

[0099] Step 3: In each leveraged state, within the feasible region The maximum value of the relative phase Δθ is extracted semi-analytically from the boundary. i:i+1,max Minimum value Δθ i:i+1,min The maximum value of the transfer arc angle Δf i:i+1,max Minimum value Δf i:i+1,min The maximum initial phase difference Δθ of all celestial bodies is estimated based on the combination of the phase difference due to the multi-body leverage and the transfer arc angle. 0:i,max Minimum value Δθ 0:i,min The period from 2020 to 2025 is divided into grids with a one-day interval. At time t at each grid point, planet P is calculated. i The phase difference Δθ between (i = 1, 2, 3) and planet P0 0:i+1,t and with Δθ 0:i,max , Δθ 0:i,min In contrast, if at time t all Δθ 0:i+1,t ∈[Δθ 0:i,min ,Δθ 0:i,max If a time value is found, record that time. Continue this search for all times between 2020 and 2050, determining if the "Earth-Jupiter-Neptune-100AU" sequence is feasible, and outputting the recorded window as shown. Figure 4 The largest window is located between March 26 and April 12, 2032.

[0100] Step Four: Based on the rapid evaluation results of the multi-body leveraging sequence obtained in Step Three, feasible multi-body leveraging sequences are quickly obtained, and a set of feasible launch windows is provided. This allows for the rapid provision of feasible multi-body leveraging sequences and corresponding launch windows in the early stages of multi-body leveraging flight mission planning, eliminating 98.8957% of infeasible windows and avoiding extensive numerical optimization within infeasible windows. The multi-body leveraging sequence evaluation process, which requires 13 hours using numerical optimization methods, is reduced to only 4 seconds using the semi-analytical calculation method disclosed in this invention. This significantly improves the efficiency of multi-body leveraging flight mission planning, saves computational resources and time, and greatly enhances the planning efficiency of multi-body leveraging flight missions.

[0101] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A rapid evaluation method for multi-body leveraging sequences based on the feasible domain of leveraging states, characterized in that: Includes the following steps, Step 1: Define the planetary coordinate system O under the constraints of a planar circle. i -x i y i z i The normalized leverage state parameters hyperbolic overspeed magnitude α and direction angle ψ are used to establish the spacecraft kinematic equations based on hyperbolic overspeed magnitude α and direction angle ψ. Based on the defined planetary coordinate system and the kinematic model with normalized parameters, we can write the equations for the spacecraft leaving the celestial body P. i Time state and spacecraft arrive at celestial body P i+1 Time state The envelope of the range of variation, i.e., P i Departure Condition C dep and P i+1 Arrival Condition C arr ; Step 2: Based on the known entry and exit parameters for the same celestial body, determine the entry and exit parameters for celestial body P. i Arrival conditions are standardized to O i -x i y i z i and The conditions for arrival are obtained. Following the order i = 0, 1, ..., N, based on the initial constraint α 0,max pass through in sequence and C dep Find the intersection to construct During the construction process, if any If the given sequence is empty, it is determined that the given sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, the next sequence is given, and the process returns to step one to update the starting celestial body P. i and arriving at celestial body P i+1 The corresponding planetary coordinate system and the starting condition C dep and arrival conditions C arr Following the order i = N, N-1, ..., 0, based on the end constraints, the pruning is achieved by inversely solving the leverage state relation. During the pruning process, if any If the given sequence is empty, it is determined that the sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr If all If none of them are empty, then the feasible domain for leveraging the power of multiple celestial bodies is obtained. That is, by establishing the planetary departure state conditions and the planetary arrival state conditions, the feasible region of the multi-celestial body leverage state is obtained through analytical calculation. Step 3: In each leveraged state, within the feasible region The maximum value of the relative phase Δθ is extracted semi-analytically from the boundary. i:i+1,max Minimum value Δθ i:i+1,min The maximum value of the transfer arc angle Δf i:i+1,max Minimum value Δf i:i+1,min The maximum initial phase difference Δθ of all celestial bodies is estimated based on the combination of the phase difference due to the multi-body leverage and the transfer arc angle. 0:i,max Minimum value Δθ 0:i,min Divide the given launch window into time intervals, and calculate planet P at each time interval t. i The phase difference Δθ between (i = 1, 2, ..., N) and planet P0 0:i+1,t and with Δθ 0:i,max , Δθ 0:i,min In contrast, if at time t all Δθ 0:i+1,t ∈[Δθ 0:i,min ,Δθ 0:i,max If a time t is recorded, then that time is recorded. This process continues, searching all times within a given launch window. If a window time t is recorded, the sequence is deemed feasible, and the recorded window is output. The sequence evaluation ends, and the given new sequence is re-evaluated according to the tree search branching strategy. If no time t is recorded, it is determined that the sequence has no launch window within the given window. The sequence evaluation ends, and the given new sequence is re-evaluated according to the tree search branching strategy. When all sequences generated by the tree search are evaluated, rapid evaluation of multi-body leveraging sequences based on the feasible domain of leveraging state is achieved.

2. The method for rapid evaluation of multi-body leveraging sequences based on the feasible domain of leveraging state as described in claim 1, characterized in that: The implementation method for step one is as follows: In interplanetary orbit analysis, the planar circular constraint is defined as follows: all orbits lie in the same plane, and the planetary orbits are concentric circles centered on the Sun. For N+1 planets involved in the multi-body glide flight, numbered sequentially as P0, P1, ..., P N Where P0 represents the launching celestial body, P1, ..., P N-1 To leverage celestial bodies, P N The destination; in the inertial frame of reference, the planet P at a given time is obtained according to the planetary ephemeris. i Dimensional position and velocity vectors Regarding the current celestial body P i Define an inertial coordinate system O i -x i y i z i The coordinate system x i Axial direction is defined as y i The axis is perpendicular to x in the orbital plane. i The axis points to planet P. i velocity direction, z i The axis is perpendicular to the orbital plane and parallel to the x-axis. i ,y i The axes form a right-handed coordinate system; N+1 different planets will correspond to N+1 different coordinate systems, each with an inertial coordinate system O. i -x i y i z i Chinese x i The angle between the current celestial body P and the X-axis of the inertial frame is defined as the angle between the current celestial body P and the X-axis of the inertial frame. i phase angle θ i (i = 0, 1, ..., N); For coordinate system O i -x i y i z i Normalization is performed so that the state conditions derived in one coordinate system can be applied to different celestial bodies through unit scaling. The normalized units of mass, length, and time are respectively Among them G, μ Sun ,and These are the gravitational constant, the solar gravitational constant, and planet P. i The semi-major axis of the heliocentric orbit; in coordinate system O i -x i y i z i and normalized units [M] i [R] i [T] i Below, planet P i Position and velocity vectors are r i ＝[1,0,0] T ,v i ＝[0,1,0] T (2) In coordinate system O i -x i y i z i and normalized units [M] i [R] i [T] i Let the dimensionless magnitude and direction angle of a spacecraft's hyperbolic hypervelocity relative to a planet be α (>0) and ψ (∈[0,2π)), respectively. Then, the spacecraft's entry / exit from planet P... i The state of leveraging is denoted as The corresponding interplanetary velocity vector is Furthermore, the spacecraft's position vector coincides with the planet's position vector during the glide flight; and the next flyby object P... i+1 The radius of the heliocentric orbit is denoted as β (β > 1); according to r i , The spacecraft left planet P i The angular momentum h and eccentricity e of the heliocentric orbit: It is known that the spacecraft has left planet P i Position and velocity vector r i , By combining the equations of motion of conic sections, the state of leveraging forces is derived. Feasible domain C arr C dep Regarding departure condition C dep The spacecraft is able to [obtain information from] current celestial bodies P i Arrive at the next body P i+1 The orbit must satisfy two constraints: constraint ①r i , The semi-major axis of the determined transfer orbit is greater than or equal to that of the celestial body P. i+1 The semi-major axis of the orbit is β; constraint ② is that the transfer orbit is an interplanetary prograde orbit; the equations corresponding to the two constraints ① and ② are as follows: h 2 / (1-e)>β (6) h＞0 (7) Substituting equations (4) and (5) into equations (6) and (7), we obtain two conditions after simplification: and in comprehensive and Two conditions are required: the spacecraft leaves the current celestial body P. i leverage state Leaving condition C dep g1 and g2 intersect at Place; For satisfying C dep The interplanetary transfer orbit, according to the conic section equations of motion, yields the system O. i -x i y i z i The spacecraft arrived at celestial body P i+1 Entering the leverage state during orbit for: The range of change in equation (10) is used to calculate the state of entering the leverage state. The envelope of the feasible region, i.e., C arr Upper and lower boundary functions: in: α i,max For α i The maximum allowed value, Combining equations (11) to (14), we obtain the spacecraft's arrival at the next celestial body P. i+1 The state condition C of leveraging force at that time arr for 3. The rapid evaluation method for multi-body leveraging sequences based on the feasible domain of leveraging state as described in claim 2, characterized in that: The second step is implemented as follows: The system O has been constructed in step one. i -x i y i z i Next Celestial Body P i+1 Entry condition C arr Based on this, simply add C arr α in i+1 Numerical expansion Times, that is, to obtain system O i+1 -x i+1 y i+1 z i+1 Next Celestial Body P i+1 Entry condition C arr This achieves the unification of units for celestial bodies, parameters, and coordinate systems; Given the known entry and exit parameters for the same celestial body, the set of leverage states that simultaneously satisfy both the entry and exit conditions constitutes the feasible region of leverage states; C arr of The parameter is projected onto the lever angle δ. Parameters, obtained from Entry conditions Right now in in, For the dimensional lever celestial body P i gravitational constant, The minimum radius of leverage with dimensions is defined. For α i The corresponding dimensional hyperbolic overspeed magnitude; Leveraging celestial bodies P i Feasible region of leveraged states for (i = 1, 2, ..., N-1) That is, the corresponding and C dep The intersection, that is The feasible regions of each celestial body's borrowing state collectively constitute the feasible regions of multi-celestial body borrowing. Right now Among them, the launching celestial bodies Destination and There are mutual influences between them; The solution consists of two steps: forward construction and reverse pruning; Step 2.1: Following the order i = 0, 1, ..., N, sequentially pass the initial constraint α. 0,max Construction of formula (19) For multi-body glide, P i C arr From and Only P i-1 C arr A proper subset whose boundary differs from the descriptions in equations (11) to (14); P in multi-body glide flight i C arr The upper boundary has one additional variation, while the lower boundary has four variations depending on the number of feature points, namely (a) with 3 feature points. (b) Has 2 feature points (c) Has 2 feature points (d) Has 1 feature point The upper boundary is: in By point Substituting into equation (10) yields the result; if If it does not exist, the lower boundary is still represented by equation (11); The lower boundaries are as follows: (a) It has 3 feature points: (b) Has 2 feature points: (c) It has 2 feature points: (d) Has 1 feature point: in for With P i-1 C dep The intersection point is substituted into equation (10) to calculate the result; leverage state parameter α i Maximum and minimum values ​​α i,max ,α i,min There have also been some changes, with the maximum value being the point substituted into equation (10). The minimum value obtained from the calculation and the same unit is the point substituted into equation (10). calculate; Constructing the feasible domain of leveraged states During the process, if any If the given sequence is empty, it is determined that the sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr ; Step 2.2: Prune sequentially according to the order i = N, N-1, ..., 0, using the end constraints and equation (10). For a given end-hyperbolic overspeed magnitude constraint α N ≤α N,cr or α N ≥α N,cr Transform the critical value into a segmentation curve Segmentation curve feasible domain Divide the data into two parts, left and right, and select to keep the parts that satisfy the constraints and prune the parts that do not: when the constraint is α N ≤α N,cr Preserve the original The left side corresponds to the deceleration and rendezvous task; when the constraint is α N ≥α N,cr Preserve the original The right side corresponds to the accelerated flight mission; Targeting the celestial body P i (i = N-1, N-2, ..., 1), based on the known... And solve for the corresponding equation (10). Still the original Divide the process into left and right parts, selecting to retain the parts that satisfy the constraints and pruning the parts that do not: when the end constraint is α N ≤α N,cr Preserve the original Left side; when the end constraint is α N ≥α N,cr Preserve the original Right side; then Mapped to In order to provide for the continuation Pruning provides a foundation; For the launching object P0, only based on the known... And solve for the corresponding equation (10). Will Divided into two parts, and according to α N ≤α N,cr or α N ≥α N,cr Preserve the original The left or right part is then complete. Pruning; Based on the above known information And combined with the mapping relationship of equation (10) Solve In order to obtain the corresponding unique solution during the process, the following steps are performed: ① In The curve is divided by inverse solution of equation (10) on the lower boundary. lower vertex Right now ②In upper boundary or Inside The curve l is divided by inverse solution of equation (10) on the straight line. i - Top vertex Right now ③From Start solving Extension curve Until we meet (4) If but Solution complete, if Then Symmetry has been determined Partial, excerpt Internal parts, completed Solve this problem; Pruning leveraged state feasible region During the process, if any If the given sequence is empty, it is determined that the sequence is infeasible, and the evaluation of the sequence ends. According to the branching strategy of tree search, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr ; If steps 2.1 and 2.2 have been completed, all If none of them are empty, then the multi-celestial body leverage feasible region as defined in equation (20) is obtained, and step three is continued.

4. The method for rapid evaluation of multi-body leveraging sequences based on the feasible domain of leveraging state as described in claim 3, characterized in that: The method for implementing step three is as follows: Known feasible region for multi-celestial body leverage In each On the boundary, the relative phase Δθ is obtained according to the conic section equation. i:i+1 =θ i+1 -θ i The maximum value Δθ i:i+1,max and minimum value Δθ i:i+1,min and the transfer arc angle Δf i:i+1 The maximum value Δf i:i+1,max and minimum value Δf i:i+1,min ; According to Δθ i:i+1,max , Δθ i:i+1,min , Δf i:i+1,max , Δf i:i+1,min Estimate the maximum and minimum initial phase differences of all celestial bodies: Within a given launch window, obtain the planetary position r at time t in the ephemeris every one day. 0,t ,r 1,t ,…,r N,t Calculate P for each planet i The phase difference between (i = 1, 2, ..., N) and planet P0, i.e., r i,t (i=1,2,...,N) and r 0,t The included angle Δθ 0:i,t (i = 1, 2, ..., N) ∈ [0, 2π); if time t has Δθ for all planets 0:i,t ∈[Δθ 0:i,min ,Δθ 0:i,max If (i = 1, 2, ..., N) is selected, then record that time as the window of the given sequence; otherwise, continue searching for time. After searching each time within the given launch window, if a window time t is recorded, then determine that the sequence is feasible and output the recorded window. The evaluation of the sequence ends, and according to the tree search branching strategy, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr If no time t is recorded, it is determined that the sequence has no emission window within the given window, the sequence evaluation ends, and according to the tree search branching strategy, given the next sequence, return to step one to update the planetary coordinate system and planet P. i Departure Condition C dep and planet P i+1 Arrival Condition C arr When the tree search ends, the rapid evaluation of multi-celestial leveraging sequences based on the feasible domain of the leveraging state is achieved.

5. The rapid evaluation method for multi-body leveraging sequences based on the feasible domain of leveraging state as described in claim 1, 2, 3, or 4, characterized in that: It also includes step four, which, based on the rapid evaluation results of the multi-body leveraging sequence obtained in step three, quickly obtains feasible multi-body leveraging sequences and provides a set of feasible launch windows. In the early stages of multi-body leveraging flight mission planning, feasible multi-body leveraging sequences and corresponding launch windows are provided quickly, and infeasible windows are excluded, avoiding a large amount of numerical optimization in infeasible windows and improving the efficiency of multi-body leveraging flight mission planning.

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