Interplanetary transfer orbit optimization method based on three-body system low-energy crossing

Abstract

The invention discloses an interplanetary transfer orbit optimization method for low-energy crossing by using a three-body system, and belongs to the technical field of aerospace. The implementation method comprises the following steps: establishing a planar circular restrictive three-body model for describing the motion of the spacecraft in a rotation system, changing the flight energy of the spacecraft by fully utilizing three-body orbit dynamics based on the planar circular restrictive three-body model, and reducing the fuel consumption required by interplanetary transfer. And establishing a high-fidelity ephemeris model under the heliocentric inertial system. The initial proximal point state of a spacecraft is represented by adopting proximal point Poincare mapping, a feasible subset corresponding to low-energy traversing motion in a phase space is determined through parameter scanning, and the feasible subset corresponds to the initial proximal point state which can be weakly captured by a planetary system; and on the basis of the feasible subset and a proximal point maneuvering strategy, a low-precision transfer orbit between planets is obtained under a planar circular restrictive three-body model, and the low-precision transfer orbit is corrected under a high-fidelity ephemeris model to obtain a high-precision transfer orbit.

Description

Technical Field

[0001] The present invention relates to a planetary exploration transfer orbit optimization method, in particular to an interplanetary transfer orbit optimization method using a three-body system low-energy crossing motion, which is suitable for spacecraft to explore solar system planets and belongs to the field of aerospace technology. Background Art

[0002] The atmospheres of giant planets such as Jupiter and Saturn contain a lot of hydrogen and helium, which is similar to the composition of the primordial nebula in the early days of the formation of the solar system. The detection of these giant planets can not only promote the study of the formation and evolution of the solar system, but also reveal the possibility of the existence of life in the solar system.

[0003] Designing an interplanetary transfer orbit in the complex gravitational field of the solar system is a prerequisite for exploration missions. The current transfer orbit design is mostly based on the multi-celestial body leverage model, which increases the speed of the spacecraft through the gravity assistance of multiple planets, while reducing the launch cost and the transfer time. In the prior art [1], (see Gad A, Abdelkhalik O. Hiddengenes genetic algorithm for multi-gravity-assist trajectories optimization [J]. Journal of Spacecraft and Rockets, 2011, 48 (4): 629-641.) Gad and Abdelkhalik designed the Earth-Venus-Earth-Jupiter (EVEJ) gravity-assisted orbit for Jupiter exploration orbit design using the proposed hidden gene genetic algorithm and the Multiple Gravity Assists with Deep Space Maneuver (MGA-DSM). In the prior art [2], (see Englander JA, Conway BA, Williams T. Automated mission planning via evolutionary algorithms [J]. Journal of Guidance, Control, and Dynamics, 2012, 35 (6): 1878-1887.) Englander et al. used a nested loop algorithm and MGA-DSM model to design the Earth-Venus-Venus-Earth-Jupiter-Saturn (EVVEJS) gravity assist sequence for the Cassini mission to Saturn exploration orbit design. These methods can efficiently design interplanetary exploration orbits, but during the gravity assist process, the spacecraft flies over the planet at high speed, which makes the interplanetary exploration window subject to strict constraints of the interplanetary phase, and cannot meet the requirements of full space and wide area planetary exploration.

[0004] The in-depth utilization of three-body dynamics is a hot area in interplanetary transfer orbits at present and in the future. In a three-body system, there are rich dynamic behaviors near the secondary main body, such as weak stability boundaries, temporary capture, and low-energy crossings. The basic characteristics of these trajectories are that they can fly over the planets multiple times, thus providing more opportunities for planetary exploration and possibly bringing additional scientific returns. For low-energy crossing motions, weak capture of spacecraft after entering the planetary system instead of direct escape can improve the phase relationship between the planets. Designing interplanetary transfer orbits based on this motion may expand the launch window for planetary exploration. Summary of the invention

[0005] The purpose of the present invention is to provide an interplanetary transfer orbit optimization method for low-energy crossing of a three-body system, construct a pericenter Poincare mapping that characterizes the initial state of a spacecraft, obtain a feasible set of low-energy crossing motions through parameter scanning and screening strategies, and optimize the interplanetary transfer orbit based on the low-energy crossing motions and pericenter maneuvering strategies corresponding to the feasible set. Due to the full use of three-body dynamics, the present invention can reduce the launch cost of the spacecraft and expand the interplanetary transfer window. In addition, the spacecraft can cross the same planetary system multiple times, thereby increasing the spacecraft's detection opportunities for the planetary system.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] The present invention discloses an interplanetary transfer orbit optimization method using a three-body system low-energy crossing. A plane circular restricted three-body model describing the motion of a spacecraft is established in a rotating system. Based on the plane circular restricted three-body model, the three-body orbit dynamics are fully utilized to change the flight energy of the spacecraft, thereby reducing the fuel consumption required for interplanetary transfer. A high-fidelity ephemeris model is established in a heliocentric inertial system. The initial pericenter state of the spacecraft is characterized by a pericenter Poincare mapping. A feasible subset corresponding to the low-energy crossing motion in the phase space is determined by parameter scanning. The feasible subset corresponds to the initial pericenter state that can be weakly captured by the planetary system. Based on the feasible subset and the pericenter maneuver strategy, a low-precision transfer orbit between planets is obtained under the plane circular restricted three-body model. The low-precision transfer orbit is corrected under the high-fidelity ephemeris model to obtain a high-precision transfer orbit. The high-precision transfer orbit of the spacecraft is used to realize multiple flybys of the spacecraft over the same planetary system, thereby improving the spacecraft's detection opportunities for the planetary system.

[0008] The present invention discloses an interplanetary transfer orbit optimization method based on low-energy crossing of a three-body system, comprising the following steps:

[0009] Step 1. Establish a planar circular restricted three-body dynamics model PCRTBP (Planar Circular Restricted Three-Body Problem) to describe the motion of the spacecraft in the Sun-Planet P mass center rotation system. Based on the planar circular restricted three-body model, make full use of the three-body orbital dynamics to change the flight energy of the spacecraft and reduce the fuel consumption required for interplanetary transfer; establish a high-fidelity ephemeris model in the heliocentric J2000.0 ecliptic inertial system; construct a pericenter Poincare map to describe the initial state of the spacecraft.

[0010] Step 1.1: Establish a plane circular restricted three-body motion model to describe the motion of the spacecraft in the Sun-Planet P mass center rotation system. Based on the plane circular restricted three-body model, make full use of the three-body orbital dynamics to change the flight energy of the spacecraft and reduce the fuel consumption required for interplanetary transfer. Establish an ephemeris model in the heliocentric J2000.0 ecliptic coordinate system.

[0011] The plane circular restricted three-body motion model of the spacecraft in the rotating system is expressed as

[0012]

[0013] where r = [x, y], Represent the position and velocity vector of the spacecraft respectively. μ is the mass ratio of the system, μ=m p / (m s +m p ), where m s is the mass of the sun, m p is the mass of planet P. r1 and r2 represent the distances between the spacecraft and the sun and planet P respectively.

[0014]

[0015] The integration constant of the three-body system, namely the Jacobi constant, is expressed as

[0016]

[0017] Where Ω represents the pseudo potential energy of the system.

[0018]

[0019] The transfer trajectory designed under the planar circular restricted three-body dynamics model PCRTBP needs to be transitioned to a high-fidelity ephemeris model to accurately describe the motion of the spacecraft under the influence of multiple gravitational accelerations. s The motion of the sun is modeled, and multiple perturbations relative to the central body are considered, with a mass of m i(i=1,...,n) The perturbation bodies include the Earth, the Moon, Jupiter, Saturn, and Jupiter's satellites. In the ecliptic J2000.0 inertial coordinate system centered on the sun, the motion model of the spacecraft is expressed as

[0020]

[0021] The first term represents the gravitational acceleration of the central body on the spacecraft, and the summation term covers the gravitational interactions between the perturbing body and the spacecraft and between the perturbing body and the central body. ps is the heliocentric ecliptic J2000.0 inertial coordinate system, with the position vector from the sun to the spacecraft, r pi is the position vector from the sun to the disturbance body i, r si is the position vector of the i-th disturbance body pointed by the spacecraft. The vector is obtained from the ephemeris JPL DE440.

[0022] Step 1.2: Create a pericenter Poincare map that describes the initial state of the spacecraft.

[0023] By establishing a polar coordinate system with planet P as the center, the pericentric state of the spacecraft relative to planet P at time t0 is described. The pericentric state of the spacecraft in the polar coordinate system is described by two parameters: the pericentric distance r between the spacecraft and Jupiter. p , the vector r pointing from Jupiter to the spacecraft p The polar angle α between the x-axis of the sun-planet P mass center rotation system. For a given Jacobian constant C, the position vector r of the spacecraft is expressed as

[0024] r=[1-μ+r p cosα,r p sinα] T (7)

[0025] The magnitude of the velocity vector v is calculated by

[0026]

[0027] Since at pericenter, the spacecraft's position vector relative to the planet and velocity vector are orthogonal, so the velocity vector v is calculated using the flight path angle β. For antegrade motion, The direction of the angular momentum of the system is consistent, and β = α + π / 2. On the contrary, for retrograde motion, that is, vector The direction of the angular momentum is opposite to that of the spacecraft system, and β = α-π / 2. Then the velocity vector v is expressed as

[0028] v=[vcosβ,vsinβ] T (9)

[0029] Step 2: Set the range of polar angle, Jacobian constant and pericentric distance, and discretize them with a predetermined step size to obtain a discrete phase space. For each discrete point, determine whether it corresponds to low-energy through motion, and obtain a feasible set of low-energy through motion by traversing the discrete phase space.

[0030] Step 2.1: Set the range of variation of the polar angle, Jacobian constant and pericentric distance, and discretize them with a predetermined step size to obtain a discrete phase space.

[0031] When the motion type, such as prograde or retrograde motion, is selected, the pericentric state of the spacecraft at time t0 can be determined by the Jacobian constant C, the polar angle α, and the pericentric distance r p The only decision. Set C within the feasible range [C min ,C max ] is discretized into M points with a step size ΔC, and α is set in the feasible range [α min ,α max ] is discretized into N points with a step size of Δα, and r p In the feasible range [r pmin ,r pmax ] with a step length of Δr p The discrete points are P, and then the phase space consisting of M×N×P groups of discrete initial states is obtained, where the state of the i-th group of pericentric points is expressed as (r p ,α,C) i , i = 1, 2, 3 ... M × N × P. According to equations (7) and (9), the state of the spacecraft corresponding to the i-th group of pericentric states in the sun-planet P mass center rotation system is x i =[r i ,v i ], the combination of all discrete initial states constitutes the phase space of the Sun-planet P mass-center rotation system.

[0032] Step 2.2: For each discrete point in the phase space, determine whether it corresponds to low-energy penetration motion, and obtain the feasible set of low-energy penetration motion by traversing the discrete phase space.

[0033] In the Sun-Planet P mass center rotation system, the low-energy crossing motion occurs in a disk region with Planet P as the center and a radius of three times the Hill radius of Planet P. i Corresponding to the pericenter state of the low-energy crossing motion at time t0, the following three conditions need to be met at the same time.

[0034] Condition ①: Reverse integral x i If the reverse trajectory intersects the boundary of the disk area, it means that the spacecraft enters the planetary system from outside the planetary system, and the next judgment process is executed. If there is no intersection, then x i The corresponding (rp ,α,C) i It does not belong to the feasible set U of low-energy crossing motion.

[0035] Condition ②: Positive integral x i If the forward trajectory intersects the boundary of the disk area, it means that the spacecraft can eventually escape from the planetary system and the next judgment process is executed. If there is no intersection, then x i The corresponding (r p ,α,C) i It does not belong to the feasible set U of low-energy crossing motion.

[0036] Condition ③: The total number of pericenters of the spacecraft trajectory relative to the planet P in the disk region is q, among which the constraint r is satisfied. p <r pmax The number of pericentric points is p. If p is greater than or equal to 2, then x i The corresponding (r p ,α,C) i The feasible set U of low-energy crossing motion p .

[0037] For the M×N×P discrete points in the phase space, the discrete points (r p ,α,C) i Whether it belongs to low-energy crossing motion, so as to obtain the feasible set U of low-energy crossing motion p .

[0038] Step 3. Based on the low-energy crossing motion of the Sun-Planet P three-body system under the PCRTBP model, with minimizing the maneuvering cost as the optimization goal, and with the constraint that the trajectory of the spacecraft after the maneuver intersects and is tangent to the orbit of planet P1, optimize the transfer orbit of planet P1-Planet P, obtain the low-precision transfer orbit of planet P1-Planet P, the transfer time Δt1 and the maneuvering cost of the spacecraft from planet P1 to planet P, and determine the Julian date when the spacecraft departs from planet P1.

[0039] Step 3.1: Optimize the transfer trajectory of the planet P1-planet P segment based on the low-energy transit motion of the Sun-Planet P three-body system under the PCRTBP model.

[0040] The feasible set U for low-energy crossing motion of the Sun-Planet P three-body system p , assuming that the feasible set contains Q discrete initial pericentric states, where the jth state can be expressed as (r p ,α,C) j ,j=1,2,3…Q. Its state in the sun-planet P mass center rotation system can be expressed as x j =[r j ,v j]. By integrating x backward and forward j , we get x j The corresponding low-energy transit orbit has a first pericentric state relative to planet P in the disk region: The last pericentric state is expressed as The difference in the orbital inclination of planets P1 and P in the heliocentric inertial system is very small, and the eccentricity of both is close to zero. In the sun-planet P mass center rotation system, the orbit of P1 is equivalent to a circular orbit centered on the sun, and its normalized radius is a1. In the heliocentric J2000.0 ecliptic coordinate system, the semi-major axis of planet P1 is smaller than the semi-major axis of planet P. At pericenter Apply the pericenter maneuver Δv1, and the state after the maneuver is in Under the PCRTBP model, the reverse integration The back propagation trajectory S1 is obtained. Taking the maneuver cost Δv1 as the minimum as the optimization goal and the spacecraft trajectory after the maneuver being able to intersect with the planet P1 as the constraint condition, an optimization problem for solving the maneuver pulse Δv1 is constructed. As shown in formula (10)

[0041]

[0042] In the above formula, the constraint It is used to constrain the reverse propagation trajectory S1 to intersect with the orbit of P1. When the spacecraft intersects with the planet P1, S1 can be tangent to the orbit of the planet P1 in the sun-planet P mass center rotation system, so as to reduce the launch cost of the spacecraft. When the spacecraft is restricted to rendezvous with P1, the orbit of the spacecraft is tangent to the orbit of P1. The optimization variables are the pulse maneuver Δv1 and the reverse propagation time Δt1. The optimization goal is to minimize the modulus of the maneuver Δv1. Solve the optimization problem Obtain the transfer time Δt1 from planet P1 to P in the rotating system, the pulse maneuver size Δv1, and the state of the spacecraft when it departs from P1

[0043] Step 3.2: According to the spacecraft and planet P 1· The position constraint of the rendezvous obtains the position vector of planet P1 in the rotating system, and the position state of planet P1 in the inertial system is obtained by transforming the position vector of planet P1. By setting the launch time interval, the Julian date when the spacecraft departs from planet P1 is determined by the position constraint.

[0044] When the spacecraft encounters planet P1, the state of the sun-planet P mass center rotation system is Since the positions of the spacecraft and planet P1 coincide when the spacecraft and planet P1 meet, the state of planet P1 in this rotation system is: The range of emission time JD0 is [JD 0min , J.D. 0max ], and obtain the state X(JD0) of the planet P1 in the heliocentric J2000.0 ecliptic coordinate system through the ephemeris DE440. Through coordinate transformation, obtain the state of the planet P1 in the rotating system at JD0 By constraint Determine the Julian date JD0 when the spacecraft departs from planet P1.

[0045] As a preferred optimization problem The solution is obtained by using the fmincon function of the MATLAB Optimization Toolbox.

[0046] Step 4. Based on the low-energy crossing motion of the Sun-Planet P three-body system under the PCRTBP model, with minimizing the maneuvering cost as the optimization goal and the intersection of the trajectory of the spacecraft after the maneuver with the orbit of planet P2 as the constraint condition, optimize the transfer orbit of planet P-Planet P2, and obtain the low-precision transfer orbit of planet P-Planet P2, as well as the transfer time Δt2 and maneuvering cost of the spacecraft from planet P to planet P2. In the heliocentric J2000.0 ecliptic coordinate system, the semi-major axis of planet P2 is greater than the semi-major axis of planet P.

[0047] At the pericenter Apply the pericenter maneuver Δv2, and the state after the maneuver is in Under the PCRTBP model, the positive integral The forward propagation trajectory S2 is obtained. Taking minimizing the maneuvering cost Δv2 as the optimization goal and the orbital intersection of the spacecraft after maneuvering with the planet P2 as the constraint condition, the optimization problem is constructed.

[0048]

[0049] In the above formula, Δt m is the glide time of the low-energy flyby orbit from the first periapsis to the last periapsis, and Δt2 is the transfer time from planet P to planet P2. is the position vector of planet P2 in the sun-planet P mass center rotation system. After obtaining the state of P2 in the heliocentric J2000.0 ecliptic system through the ephemeris DE440, it is obtained through coordinate transformation. The constraints in formula (11) ensure that the spacecraft can rendezvous with planet P2 in the rotation system. The optimization variables are the pulse maneuver Δv2 and the reverse propagation time Δt2. The optimization goal is to minimize the modulus of the maneuver Δv2. Solve the optimization problem The transfer time Δt2 of planet P to P2 and the magnitude of pulse maneuver Δv2 are obtained in the rotating system.

[0050] As a preferred optimization problem The solution is obtained by using the fmincon function of the MATLAB Optimization Toolbox.

[0051] Step 5: Combine the low-precision transfer orbit of planet P1-Planet P obtained in step 3 and the low-precision transfer orbit of planet P-Planet P2 obtained in step 4 to obtain the low-precision transfer orbit of planet P1-Planet P2. Correct the low-precision transfer orbit of planet P1-Planet P2 under the high-fidelity ephemeris model to obtain the high-precision transfer orbit of planet P1-Planet P2, that is, to achieve the optimization of the interplanetary transfer orbit of the three-body system with low-energy crossing.

[0052] The low-precision transfer orbit of planet P1-Planet P obtained in step 3 and the low-precision transfer orbit of planet P-Planet P2 obtained in step 4 are combined to obtain the low-precision transfer orbit from planet P1 to planet P2 after the low-energy transit of the planet P system. The Julian date JD0 of the spacecraft's departure from P1, the date of arrival at planet P JD1, the time of departure from planet P JD2, and the time of arrival at planet P2 JD3 are known, where JD1=JD0+Δt1, JD2=JD1+Δt m , JD3=JD2+Δt2. Since the state of the spacecraft in the rotation system at the first pericenter of the low-energy crossing orbit and JD2 are known, the state of this point in the heliocentric J2000.0 ecliptic system can be obtained through coordinate changes. Positive integral Able to obtain the state of the last pericenter of the low-energy crossing trajectory JD2=JD1+Δt' m , Δt' m is Δt m Correction values ​​under high-fidelity ephemeris. Construct an optimization problem to solve the correction maneuvers Δv1' and Δv'2 As shown in formula (12).

[0053]

[0054] Among them, Δt1' and Δt'2 are the transfer times from planet P1 to P and from planet P to P2, respectively. Δt1' and Δt'2 are optimization variables. The transfer time Δt1 of the low-precision transfer orbit from planet P1 to P obtained in the third step and the transfer time Δt2 of the low-precision transfer orbit from planet P to P2 obtained in the fourth step are used as the optimization problem. The optimization goal is to minimize the cost J of the maneuver. Δv1' and Δv'2 are the periapsis maneuvers applied at the first and last periapsis of the low-energy transit orbit relative to the planet, respectively. The periapsis maneuver pulse Δv1 of the low-precision transfer orbit from planet P1 to P obtained in step 3 and the periapsis maneuver pulse Δv2 of the low-precision transfer orbit from planet P to P2 obtained in step 4 are used as the initial values ​​of the optimization. Constraints This ensures that the spacecraft can rendezvous with planet P1 at JD0 = JD1 - Δt1'. Constraint It ensures that the spacecraft is in JD3=JD1+Δt' m +Δt'2 time can rendezvous with planet P2, where is the state of the spacecraft after performing maneuver Δv1' The position vector in the heliocentric J2000.0 ecliptic coordinate system after reverse integration of Δt1', is the state of the spacecraft after performing maneuver Δv'2 The position vector in the heliocentric J2000.0 ecliptic coordinate system after forward integration of Δt'2, and are the position vectors of planet P1 and planet P2 in the heliocentric J2000.0 ecliptic coordinate system at the corresponding time. Solve the optimization problem Get the launch date JD0, the transfer duration of different segments, Δt1', Δt'2 and Δt' m , and the magnitudes of the periapsis maneuvers Δv1' and Δv'2.

[0055] As a preferred optimization problem The solution is obtained by using the fmincon function of the MATLAB Optimization Toolbox.

[0056] It also includes step 6: according to the high-precision transfer orbit of planet P1-planet P obtained in step 5, the spacecraft performs pulse maneuvers at the corresponding time, and under the constraints of the given transfer starting state and terminal state, fully utilizes the three-body orbital dynamics to change the flight energy of the spacecraft, and reduces the fuel consumption required for the transfer of planet P1-planet P2. According to the high-precision transfer orbit of planet P1-planet P obtained in step 5, since the spacecraft is weakly captured by planet P after entering the planetary system instead of escaping after the gravity assistance of planet P, the spacecraft can fly over the same planetary system multiple times, thereby improving the spacecraft's detection opportunities for the planetary system. The time delay caused by the temporary capture of the spacecraft by planet P in the planet P system is used to adjust the phase relationship between planets P, P1, and P2, and the transfer window of the interplanetary orbit is expanded according to the adjusted phase relationship, thereby improving the spacecraft's interplanetary detection opportunities.

[0057] Beneficial effects:

[0058] 1. The present invention discloses an interplanetary transfer orbit optimization method using the low-energy crossing of a three-body system. The interplanetary orbit is designed using the low-energy crossing motion of the three-body system, and the advantage of the three-body orbital dynamics in changing the flight energy of the spacecraft is fully utilized. Compared with the multi-celestial body leverage method based on two-body dynamics and conic section splicing model, the fuel consumption required for transfer can be reduced.

[0059] 2. The present invention discloses an interplanetary transfer orbit optimization method utilizing the low-energy crossing of a three-body system. After entering the planetary system, the spacecraft is weakly captured by the planet and can achieve multiple planetary flybys. Compared with the multi-body leverage transfer, the spacecraft only flies over the planetary system once at high speed, providing additional exploration opportunities for planetary exploration.

[0060] 3. The present invention discloses an interplanetary transfer orbit optimization method utilizing the low-energy crossing of a three-body system. After the spacecraft enters the planetary system at low energy, it is temporarily captured by the planet. The spacecraft flies with the planet to adjust the phase relationship between the planets. Compared with the multi-body leverage transfer with strict phase relationship constraints, this expands the transfer window for planetary exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A flow chart of an interplanetary transfer orbit optimization method utilizing low-energy crossing of a three-body system according to the present invention.

[0062] Figure 2 Schematic diagram of the low-energy transit orbit of the Sun-Jupiter system.

[0063] Figure 3 Schematic diagram of the Earth-Jupiter-Saturn transfer orbit designed based on the low-energy transit orbit of the Sun-Jupiter system under the PCRTBP model.

[0064] Figure 4 Schematic diagram of the Earth-Jupiter-Saturn transfer orbit designed based on the low-energy transit orbit of the Sun-Jupiter system under the ephemeris model. DETAILED DESCRIPTION

[0065] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying figures and an example of the Earth-Jupiter-Saturn transfer based on the low-energy transit motion of the Sun-Jupiter three-body system.

[0066] Embodiment 1:

[0067] like Figure 1 As shown, the present embodiment discloses an interplanetary transfer orbit optimization method using a three-body system low-energy crossing, and the specific implementation steps are as follows:

[0068] Step 1. Establish a planar circular restricted three-body dynamics model PCRTBP (Planar Circular Restricted Three-Body Problem) to describe the motion of the spacecraft in the Sun-Jupiter mass center rotation system. Based on the planar circular restricted three-body model, make full use of the three-body orbital dynamics to change the flight energy of the spacecraft and reduce the fuel consumption required for interplanetary transfer; establish a high-fidelity ephemeris model in the heliocentric J2000.0 ecliptic inertial system; construct a pericenter Poincare map to describe the initial state of the spacecraft.

[0069] Step 1.1: Establish a plane circular restricted three-body motion model to describe the motion of the spacecraft in the Sun-Jupiter mass center rotation system. Based on the plane circular restricted three-body model, make full use of the three-body orbital dynamics to change the flight energy of the spacecraft and reduce the fuel consumption required for interplanetary transfer. Establish an ephemeris model in the heliocentric J2000.0 ecliptic coordinate system.

[0070] The plane circular restricted three-body motion model of the spacecraft in the rotating system is expressed as:

[0071]

[0072] where r = [x, y], They represent the position and velocity vector of the spacecraft respectively. μ is the mass ratio of the system, μ=9.5388609×10 -4 r1 and r2 represent the distances between the spacecraft and the Sun and Jupiter, respectively.

[0073]

[0074] The integral constant of the three-body system, namely the Jacobi constant, can be expressed as,

[0075]

[0076] Where Ω represents the pseudo potential energy of the system.

[0077]

[0078] The transfer trajectory designed under the planar circular restricted three-body dynamics model PCRTBP needs to be transitioned to a high-fidelity ephemeris model to accurately describe the motion of the spacecraft under the influence of multiple gravitational accelerations. s The motion of the sun is modeled, and multiple perturbations relative to the central body are considered, with a mass of m i (i=1,...,n) The disturbance bodies include the Earth, the Moon, Jupiter, Saturn, and Jupiter's satellites. In the ecliptic J2000.0 inertial coordinate system centered on the sun, the motion model of the spacecraft is expressed as:

[0079]

[0080] Among them, the first term represents the gravitational acceleration of the central body on the spacecraft, and the summation term covers the gravitational interactions between the perturbing body and the spacecraft and between the perturbing body and the central body. ps is the heliocentric ecliptic J2000.0 inertial coordinate system, with the position vector from the sun to the spacecraft, r pi is the position vector from the sun to the disturbance body i, r si is the position vector of the i-th perturbation body pointed by the spacecraft, which is obtained from the ephemeris JPL DE440.

[0081] Step 1.2: Create a pericenter Poincare map that describes the initial state of the spacecraft.

[0082] In order to describe the pericentric state of the spacecraft relative to Jupiter at time t0, a polar coordinate system centered on Jupiter was established. The pericentric state of the spacecraft in the polar coordinate system is described by two parameters: the pericentric distance r between the spacecraft and Jupiter. p , the vector r pointing from Jupiter to the spacecraft p The polar angle α with the x-axis of the Sun-Jupiter mass center rotation system. For a given Jacobi constant C, r can be expressed as

[0083] r=[1-μ+r p cosα,r p sinα] T (19)

[0084] The magnitude of the velocity vector v can be calculated as follows

[0085]

[0086] Since at pericenter, the spacecraft's position vector relative to Jupiter and velocity vector are orthogonal, so the velocity vector can be calculated using the flight path angle β. For antegrade motion, that is, The direction of the angular momentum of the Sun-Jupiter three-body system is consistent, and β = α + π / 2. On the contrary, for retrograde motion, that is, vector The angular momentum direction is opposite to that of the Sun-Jupiter three-body system, and at this time β = α-π / 2. Then v can be expressed as

[0087] v=[vcosβ,vsinβ] T (twenty one)

[0088] Step 2: First, set the range of polar angle, Jacobian constant and pericentric distance, and discretize them with specific step sizes to obtain discrete phase space. For each discrete point, determine whether it corresponds to low-energy through motion, and obtain the feasible set of low-energy through motion by traversing the discrete phase space.

[0089] Step 2.1: Set the range of variation of the polar angle, Jacobian constant and pericentric distance, and discretize them with a predetermined step size to obtain a discrete phase space.

[0090] When the motion type, such as prograde or retrograde motion, is selected, the pericentric state of the spacecraft at time t0 can be determined by the Jacobian constant C, the polar angle α, and the pericentric distance r p The only decision is to discretize C into 31 points in the feasible range [3,3.03] with a step size of 0.001, discretize α into 721 points in the feasible range [0,360°] with a step size of 0.5°, and discretize r p In the feasible range [9.5730×10 -5 ,0.0023] with a step size of 2.2043×10 -5 The number of points is discretized into 101. Thus, 31×721×101 groups of initial states are obtained, among which the i-th group of pericentric states can be expressed as (r p ,α,C) i ,i=1,2,3…31×721×101. According to equations (19) and (21), the corresponding state of the spacecraft in the Sun-Jupiter mass center rotation system is x i =[r i ,v i ].

[0091] Step 2.2: For each discrete point in the phase space, determine whether it corresponds to low-energy penetration motion, and obtain the feasible set of low-energy penetration motion by traversing the discrete phase space.

[0092] In the Sun-Jupiter mass center rotation system, it is assumed that the low-energy crossing motion occurs in a disk region centered on Jupiter with a radius of three times the Hill radius of Jupiter (normalized to 0.0681). i Corresponding to the pericenter state of the low-energy crossing motion at time t0, the following three conditions need to be met at the same time.

[0093] Condition ①: Reverse integral x i If the reverse trajectory intersects the boundary of the disk area, it means that the spacecraft enters the Jupiter system from outside the Jupiter system, and the next judgment process is executed. If there is no intersection, then x i The corresponding (r p ,α,C) i It does not belong to the feasible set U of low-energy crossing motion.

[0094] Condition ②: Positive integral x i If the forward trajectory intersects the boundary of the disk area, it means that the spacecraft can eventually escape from the Jupiter system and the next judgment process is executed. If there is no intersection, then x i The corresponding (r p ,α,C) i It does not belong to the feasible set U of low-energy crossing motion.

[0095] Condition ③: The total number of pericenters of the spacecraft in the disk region relative to Jupiter is q, among which the constraint r is satisfied. p <r pmax The number of pericentric points is p. If p is greater than or equal to 2, then x i The corresponding (r p ,α,C) i The feasible set U of low-energy crossing motion p .

[0096] For the 31×721×101 discrete points in the phase space, the discrete points (r p ,α,C) i Whether it belongs to low-energy crossing motion, so as to obtain the feasible set U of low-energy crossing motion p .

[0097] Step 3: Based on the low-energy transit motion of the Sun-Jupiter three-body system under the PCRTBP model, with the minimization of maneuvering cost as the optimization goal, and with the constraint that the trajectory of the spacecraft after maneuvering intersects and is tangent to the orbit of Jupiter, optimize the Earth-Jupiter transfer orbit, obtain the low-precision Earth-Jupiter transfer orbit, the transfer time Δt1 of the spacecraft from the Earth to Jupiter, and the maneuvering cost. And determine the Julian date when the spacecraft departs from the Earth.

[0098] Step 3.1: Optimize the Earth-Jupiter transfer trajectory based on the low-energy transit motion of the Sun-Jupiter three-body system under the PCRTBP model.

[0099] The feasible set U for the low-energy crossing motion of the Sun-Jupiter three-body system p , assuming that the feasible set contains 78329 discrete initial pericentric states, of which the 42856th state can be expressed as (r p =9.5730×10 -5 ,α=300.5°,C=3.02). Its state in the heliocentric rotation system can be expressed as x 42856 =[0.999095,-8.251004×10 -5 ,-3.866858,-2.274892]. By integrating x backward and forward 42856 , we can get x 42856The corresponding low-energy transit orbit has a first pericentric state relative to Jupiter in the disk region: The last pericenter state can be expressed as The low-energy crossing trajectory in the Sun-Xyrigen center rotation system is as follows Figure 2 Assume that the difference in the orbital inclination of the Earth and Jupiter in the heliocentric inertial system is very small, and the eccentricity of both is close to zero, then in the heliocentric rotation system, the Earth's orbit can be approximated as a circular orbit centered on the Sun, and its normalized radius is a1 = 0.192211. At the pericenter Apply the pericenter maneuver Δv1, and the state after the maneuver is in Under the PCRTBP model, the reverse integration The reverse propagation trajectory S1 is obtained. In order to reduce the launch cost, it is assumed that when the spacecraft intersects with the Earth, S1 can be tangent to the orbit of the Earth in the heliocentric rotation system. Taking the minimum maneuvering cost Δv1 as the optimization goal and the constraint that the spacecraft trajectory can intersect with the Earth after the maneuver, an optimization problem for solving the maneuvering pulse Δv1 is constructed. As shown in formula (22).

[0100]

[0101] In the above formula, the constraint The back propagation trajectory S1 is constrained to intersect with the Earth's orbit, The spacecraft is restricted to have its orbit tangent to the Earth's orbit when it intersects with the Earth. The optimization variables are the pulse maneuver Δv1 and the reverse propagation time Δt1. The optimization goal is to minimize the modulus of the maneuver Δv1. By using the fmincon function of the MATLAB optimization toolbox to solve, we obtain the transfer time from Earth to Jupiter in the rotating system, Δt1 = 1206.18 days, the impulse maneuver size Δv1 = 323.85 m / s, and the position state of the spacecraft when it departs from P1

[0102] Step 3.2: Based on the position constraint of the spacecraft and the Earth, the position vector of the Earth in the rotating system is obtained. By performing coordinate transformation on the Earth's position vector, the position state of the Earth in the inertial system is obtained. By setting the launch time interval, the Julian date when the spacecraft departs from the Earth is determined by the position constraint.

[0103] When the spacecraft intersects the Earth, the state of the Sun-Jupiter center rotation system is Since the positions of the spacecraft and the earth coincide when the spacecraft intersects with the earth, the state of the earth in this rotation system is obtained as follows: In order to determine the Julian date when the spacecraft departs from the Earth, we assume that the launch time JD0 ranges from January 1, 2033 to January 1, 2034. Therefore, through the ephemeris DE440, we can get the state X(JD0) of the Earth in the heliocentric J2000.0 ecliptic coordinate system. Through coordinate transformation, we can get the state of the Earth in the rotating system at JD0 By constraint The Julian date JD0 when the spacecraft departs from Earth can be determined to be April 20, 2033.

[0104] Step 4. Based on the low-energy crossing motion of the Sun-Earth three-body system under the PCRTBP model, with minimizing the maneuvering cost as the optimization goal and the intersection of the spacecraft's trajectory after maneuvering with Saturn's orbit as the constraint condition, optimize the Jupiter-Saturn transfer orbit to obtain the Jupiter-Saturn low-precision transfer orbit, as well as the spacecraft's transfer time Δt2 from Jupiter to Saturn and the maneuvering cost.

[0105] At the pericenter Apply the pericenter maneuver Δv2, and the state after the maneuver is in Under the PCRTBP model, the positive integral The forward propagation trajectory S1 is obtained. Taking the maneuver cost Δv2 as the minimum optimization goal and the spacecraft trajectory after the maneuver being able to rendezvous with Saturn as the constraint condition, an optimization problem for solving the maneuver pulse Δv2 is constructed. As shown in formula (23).

[0106]

[0107] In the above formula, Δt m is the glide time from the first periapsis to the last periapsis of the low-energy flyby orbit, which is about 849 days. Δt2 is the transfer time from Jupiter to Saturn. is the position vector of Saturn in the heliocentric rotation system, obtained by coordinate transformation after obtaining the state of Saturn in the heliocentric J2000.0 ecliptic system through the ephemeris DE440. The constraints in formula (23) ensure that the spacecraft can rendezvous with Saturn in the rotation system. The optimization variables are the pulse maneuver Δv2 and the reverse propagation time Δt2, and the optimization goal is to minimize the modulus of the maneuver Δv2. Optimization problem By using the fmincon function of the MATLAB optimization toolbox to solve, we obtained the transfer time from Earth to Saturn in the rotating system, Δt2 = 4136.98 days, the impulse maneuver size Δv2 = 61.05 m / s, and the Earth-Jupiter-Saturn transfer trajectory designed based on the low-energy crossing motion of the Sun-Jupiter system under PCRTBP as follows: Figure 3 shown.

[0108] Step 5: Combine the low-precision transfer orbit of Earth-Jupiter obtained in step 3 and the low-precision transfer orbit of Jupiter-Saturn obtained in step 4 to obtain the low-precision transfer orbit of Earth-Saturn. Correct the low-precision transfer orbit of Earth-Saturn under the high-fidelity ephemeris model to obtain the high-precision transfer orbit of Earth-Saturn, that is, to achieve the optimization of the interplanetary transfer orbit of the three-body system with low-energy crossing.

[0109] By combining the transfer orbits designed in steps 3 and 4, we get the transfer orbit from Earth to Saturn after a low-energy transit through the Jupiter system. The Julian date JD0 of the spacecraft's departure from Earth is April 20, 2033, the date of arrival at Jupiter is JD1 is August 24, 2035, the time of departure from Jupiter is JD2 is December 20, 2037, and the time of arrival at Saturn is JD3 is April 18, 2049, where JD1 = JD0 + Δt1, JD2 = JD1 + Δt m , JD3=JD2+Δt2. Since the state of the spacecraft in the rotation system at the first pericenter of the low-energy crossing orbit and JD2 are known, the state of this point in the heliocentric J2000.0 ecliptic system can be obtained through coordinate changes. Forward integration based on ephemeris model Able to obtain the state of the last pericenter of the low-energy crossing trajectory JD2=JD1+Δt' m , Δt' m is Δt m Correction value under high-fidelity ephemeris. Taking minimizing the maneuver cost as the optimization goal and the constraint that the corrected trajectory can intersect with the Earth and Saturn, the optimization problem for solving the correction maneuvers Δv1' and Δv'2 is constructed as shown in Equation (24).

[0110]

[0111] Among them, Δt1' and Δt'2 are the transfer times from Earth to Jupiter and from Jupiter to Saturn, respectively, which are optimization variables. The transfer time Δt1 of the low-precision transfer orbit of Earth-Jupiter obtained in the third step and the transfer time Δt2 of the low-precision transfer orbit of Jupiter-Saturn obtained in the fourth step are used as optimization problems. The optimization goal is to minimize the cost J of the maneuver. Δv1' and Δv'2 are the periapsis maneuvers applied at the first and last periapsis of the low-energy transit orbit relative to Jupiter, respectively. Similarly, the periapsis maneuver pulse Δv1 of the Earth-Jupiter low-precision transfer orbit obtained in step 3 and the periapsis maneuver pulse Δv2 of the Jupiter-Saturn low-precision transfer orbit obtained in step 4 can be used as the initial values ​​of the optimization. Constraints This ensures that the spacecraft can rendezvous with the Earth at JD0 = JD1 - Δt1'. Constraint It ensures that the spacecraft is in JD3=JD1+Δt' m +Δt'2 time can rendezvous with Saturn, where is the state of the spacecraft after performing maneuver Δv1' The position vector in the heliocentric J2000.0 ecliptic coordinate system after reverse integration of Δt1', is the state of the spacecraft after performing maneuver Δv'2 The position vector in the heliocentric J2000.0 ecliptic coordinate system after forward integration of Δt'2, and are the position vectors of the Earth and Saturn in the heliocentric J2000.0 ecliptic coordinate system at the corresponding time. By using the fmincon function of the MATLAB optimization toolbox to solve, it can be obtained that the launch date JD0 is May 11, 2033, the transfer time of the Earth-Jupiter segment is 845 days, and after executing the maneuver Δv1'=336.36m / s, it enters the low-energy transit orbit of the Jupiter system. After staying in the Jupiter system for 1023.78 days, it reaches the second pericenter of the low-energy transit trajectory relative to Saturn before escaping from the Jupiter system. Subsequently, after executing the maneuver Δv'2=91.47m / s, the spacecraft enters the Jupiter-Saturn transfer orbit, and the Julian date when leaving Saturn is June 20, 2038. After flying for 2851.15 days, it will rendezvous with Saturn on April 9, 2046. Since the maneuver Δv'2 under the ephemeris model is larger than the maneuver Δv2 of the preliminary designed trajectory under PCRTBP, the transfer time of the Jupiter-Saturn segment is reduced. The Earth-Jupiter-Saturn transfer trajectory designed based on the low-energy transit motion of the Sun-Jupiter system under the high-fidelity ephemeris model is as follows Figure 4 shown.

[0112] Step 6: Based on the high-precision Earth-Saturn transfer orbit obtained in step 5, the spacecraft performs pulse maneuvers at the corresponding time. Under the constraints of the given transfer start and end states, the three-body orbital dynamics is fully utilized to change the flight energy of the spacecraft, reducing the fuel consumption required for the Earth-Saturn transfer. Based on the high-precision Earth-Jupiter transfer orbit obtained in step 5, since the spacecraft is weakly captured by Jupiter after entering the Jupiter system instead of escaping after Jupiter's gravitational assist, the spacecraft can fly over the Jupiter system multiple times, increasing the spacecraft's detection opportunities for the Jupiter system. The time delay caused by the spacecraft being temporarily captured by Jupiter in the Jupiter system is used to adjust the phase relationship between the Earth, Jupiter, and Saturn. The Earth-Saturn transfer window is expanded according to the adjusted phase relationship, increasing the spacecraft's interplanetary detection opportunities.

[0113] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above 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 in the scope of protection of the present invention.

Claims

1. A method for optimizing interplanetary transfer orbit based on low-energy crossing of a three-body system, characterized by: The following steps are included: Step 1: Establish a planar circular restricted three-body dynamics model PCRTBP to describe the motion of the spacecraft in the sun-planet P mass center rotation system. Based on the planar circular restricted three-body model, make full use of the three-body orbital dynamics to change the flight energy of the spacecraft and reduce the fuel consumption required for interplanetary transfer. Establish a high-fidelity ephemeris model in the heliocentric J2000.0 ecliptic inertial system; construct a pericentric Poincare map describing the initial state of the spacecraft; Step 2: set the range of polar angle, Jacobian constant and pericentric distance, and discretize them with a predetermined step size to obtain a discrete phase space; for each discrete point, determine whether it corresponds to a low-energy crossing motion, and obtain a feasible set of low-energy crossing motion by traversing the discrete phase space; Step 3: Based on the low-energy transit motion of the Sun-Planet P three-body system under the PCRTBP model, with minimizing the maneuvering cost as the optimization goal, and with the constraint that the trajectory of the spacecraft after the maneuver intersects and is tangent to the orbit of Planet P1, optimize the transfer orbit of Planet P1-Planet P, obtain the low-precision transfer orbit of Planet P1-Planet P, the transfer time Δt1 and the maneuvering cost of the spacecraft from Planet P1 to Planet P, and determine the Julian date when the spacecraft departs from Planet P1; Step 4: Based on the low-energy transit motion of the Sun-Planet P three-body system under the PCRTBP model, with minimizing the maneuvering cost as the optimization goal, and with the orbit intersection of the spacecraft after the maneuver and the planet P2 as the constraint condition, optimize the transfer orbit of planet P-Planet P2, and obtain the low-precision transfer orbit of planet P-Planet P2, as well as the transfer time Δt2 and maneuvering cost of the spacecraft from planet P to planet P2, where in the heliocentric J2000 ecliptic coordinate system, the semi-major axis of planet P2 is greater than the semi-major axis of planet P; Step 5. Splice the low-precision transfer orbit of planet P1-planet P obtained in step 3 and the low-precision transfer orbit of planet P-planet P2 obtained in step 4 to obtain the low-precision transfer orbit of planet P1-planet P2; correct the low-precision transfer orbit of planet P1-planet P2 under the high-fidelity ephemeris model to obtain the high-precision transfer orbit of planet P1-planet P2, thereby realizing the optimization of the interplanetary transfer orbit for low-energy crossing of the three-body system.

2. The interplanetary transfer orbit optimization method based on low-energy transit of a three-body system as claimed in claim 1, characterized in that: The implementation method of step one is: Step 1.1: Establish a planar circular restricted three-body motion model to describe the motion of the spacecraft in the Sun-Planet P mass center rotation system. Based on the planar circular restricted three-body model, make full use of the three-body orbital dynamics to change the flight energy of the spacecraft and reduce the fuel consumption required for interplanetary transfer. Establish the ephemeris model in the heliocentric J2000.0 ecliptic coordinate system; The plane circular restricted three-body motion model of the spacecraft in the rotating system is expressed as where r = [x, y], Represent the position and velocity vector of the spacecraft respectively; μ is the mass ratio of the system, μ=m p / (m s +m p ), where m s is the mass of the sun, m p is the mass of planet P; r1 and r2 represent the distances between the spacecraft and the sun and planet P respectively; The integration constant of the three-body system, namely the Jacobi constant, is expressed as Where Ω represents the pseudo potential energy of the system; The transfer trajectory designed under the planar circular restricted three-body dynamics model PCRTBP needs to be transitioned to a high-fidelity ephemeris model to accurately describe the motion of the spacecraft under the influence of multiple gravitational accelerations; in the planar circular restricted three-body dynamics model, the spacecraft is s The motion of the sun is modeled, and multiple perturbations relative to the central body are considered, with a mass of m i (i=1,...,n) The disturbance bodies include the Earth, the Moon, Jupiter, Saturn, and Jupiter's satellites; in the ecliptic J2000.0 inertial coordinate system centered on the Sun, the motion model of the spacecraft is expressed as Among them, the first term represents the gravitational acceleration of the central body on the spacecraft, and the summation term covers the gravitational interactions between the perturbing body and the spacecraft and between the perturbing body and the central body; r ps is the heliocentric ecliptic J2000.0 inertial coordinate system, with the position vector from the sun to the spacecraft, r pi is the position vector from the sun to the disturbance body i, r si is the position vector pointed by the spacecraft to the i-th disturbance body; the vector is obtained from the ephemeris JPL DE440; Step 1.2: Establish the pericenter Poincare map describing the initial state of the spacecraft; By establishing a polar coordinate system with planet P as the center, the pericentric state of the spacecraft relative to planet P at time t0 is described; the pericentric state of the spacecraft in the polar coordinate system is described by two parameters: the pericentric distance r between the spacecraft and Jupiter p , the vector r pointing from Jupiter to the spacecraft p The polar angle α between the x-axis of the sun-planet P mass center rotation system; For a given Jacobi constant C, the position vector r of the spacecraft is expressed as r=[1-μ+r p cosα,r p sinα] T (7) The magnitude of the velocity vector v is calculated by Since at pericenter, the spacecraft's position vector relative to the planet and velocity vector are orthogonal, so the velocity vector v is calculated using the flight path angle β; for antegrade motion, that is, The direction of the angular momentum of the system is consistent, at this time β = α + π / 2; on the contrary, for retrograde motion, that is, vector The direction of the angular momentum of the spacecraft system is opposite, and β = α-π / 2; then the velocity vector v is expressed as v=[vcosβ,vsinβ] T (9) 3. The interplanetary transfer orbit optimization method based on low-energy transit of a three-body system as claimed in claim 2, characterized in that: The implementation method of step 2 is: Step 2.1: Set the range of polar angle, Jacobian constant and pericentric distance, and discretize them with a predetermined step size to obtain a discrete phase space; When the motion type, such as prograde or retrograde motion, is selected, the pericentric state of the spacecraft at time t0 can be determined by the Jacobian constant C, the polar angle α, and the pericentric distance r p The only decision is to set C within the feasible range [C min ,C max ] is discretized into M points with a step size ΔC, and α is set in the feasible range [α min ,α max ] is discretized into N points with a step size of Δα, and r p In the feasible range [r pmin ,r pmax ] with a step length of Δr p The discrete points are P, and then the phase space consisting of M×N×P groups of discrete initial states is obtained, where the state of the i-th group of pericentric points is expressed as (r p ,α,C) i , i = 1, 2, 3 ... M × N × P; According to equations (7) and (9), the state of the spacecraft corresponding to the i-th group of pericentric states in the sun-planet P mass center rotation system is x i =[r i ,v i ], the combination of all discrete initial states constitutes the phase space of the Sun-planet P mass center rotation system; Step 2.2: For each discrete point in the phase space, determine whether it corresponds to a low-energy through motion, and obtain a feasible set of low-energy through motion by traversing the discrete phase space; In the Sun-Planet P mass center rotation system, the low-energy crossing motion occurs in a disk region with Planet P as the center and a radius of three times the Hill radius of Planet P; if x i Corresponding to the pericenter state of low-energy crossing motion at time t0, the following three conditions need to be met at the same time; Condition ①: Reverse integral x i ,If the reverse trajectory intersects the boundary of the disk region, it means that the spacecraft enters the planetary system from outside the planetary system, and the next judgment process is executed; If there is no intersection, then x i The corresponding (r p ,α,C) i It does not belong to the feasible set U of low-energy crossing motion; Condition ②: Positive integral x i ,If the forward trajectory intersects the boundary of the disk area, it means that the spacecraft can eventually escape from the planetary system and execute the next judgment process; If there is no intersection, then x i The corresponding (r p ,α,C) i It does not belong to the feasible set U of low-energy crossing motion; Condition ③: The total number of pericenters of the spacecraft trajectory relative to the planet P in the disk region is q, among which the constraint r is satisfied. p <r pmax The number of pericentric points is p. If p is greater than or equal to 2, then x i The corresponding (r p ,α,C) i The feasible set U of low-energy crossing motion p ; For the M×N×P discrete points in the phase space, the discrete points (r p ,α,C) i Whether it belongs to low-energy crossing motion, so as to obtain the feasible set U of low-energy crossing motion p .

4. The interplanetary transfer orbit optimization method based on low-energy transit of a three-body system as claimed in claim 3, characterized in that: The implementation method of step three is: Step 3.1: Optimize the transfer trajectory of the planet P1-planet P segment based on the low-energy transit motion of the Sun-Planet P three-body system under the PCRTBP model; The feasible set U for low-energy crossing motion of the Sun-Planet P three-body system p , assuming that the feasible set contains Q discrete initial pericentric states, where the jth state can be expressed as (r p ,α,C) j , j = 1, 2, 3…Q; its state in the sun-planet P mass center rotation system can be expressed as x j =[r j ,v j ]; by integrating x backward and forward j , we get x j The corresponding low-energy transit orbit has a first pericentric state relative to planet P in the disk region: The last pericentric state is expressed as The difference in the orbital inclination of planets P1 and P in the heliocentric inertial system is very small, and the eccentricity of both is close to zero. In the sun-planet P mass center rotation system, the orbit of P1 is equivalent to a circular orbit centered on the sun, and its normalized radius is a1; in the heliocentric J2000.0 ecliptic coordinate system, the semi-major axis of planet P1 is smaller than the semi-major axis of planet P; At the pericenter Apply the pericenter maneuver Δv1, and the state after the maneuver is in Under the PCRTBP model, the reverse integration Get the back propagation trajectory S1; take the maneuver cost Δv1 as the minimum optimization goal, and take the spacecraft trajectory after the maneuver to be able to intersect with the planet P1 as the constraint condition, and construct an optimization problem for solving the maneuver pulse Δv1 As shown in formula (10) In the above formula, the constraint It is used to constrain the reverse propagation trajectory S1 to intersect with the orbit of P1. When the spacecraft intersects with the planet P1, S1 can be tangent to the orbit of the planet P1 in the sun-planet P mass center rotation system, so as to reduce the launch cost of the spacecraft. When the spacecraft is restricted to rendezvous with P1, the orbit of the spacecraft is tangent to the orbit of P1; The optimization variables are the pulse maneuver Δv1 and the reverse propagation time Δt1. The optimization goal is to minimize the modulus of the maneuver Δv1. Solve the optimization problem Obtain the transfer time Δt1 from planet P1 to P in the rotating system, the pulse maneuver size Δv1, and the state of the spacecraft when it departs from P1 Step 3.2: According to the spacecraft and planet P 1· The position constraint of the rendezvous is used to obtain the position vector of planet P1 in the rotating system. By performing coordinate transformation on the position vector of planet P1, the position state of planet P1 in the inertial system is obtained. By setting the launch time interval, the Julian date when the spacecraft departs from planet P1 is determined by the position constraint condition. When the spacecraft encounters planet P1, the state of the sun-planet P mass center rotation system is Since the positions of the spacecraft and planet P1 coincide when the spacecraft and planet P1 meet, the state of planet P1 in this rotation system is: The range of emission time JD0 is [JD 0min , J.D. 0max ], the state X(JD0) of the planet P1 in the heliocentric J2000 ecliptic coordinate system is obtained through the ephemeris DE440; the state of the planet P1 in the rotating system at JD0 is obtained through coordinate transformation By constraint Determine the Julian date JD0 when the spacecraft departs from planet P1.

5. The interplanetary transfer orbit optimization method based on low-energy crossing of a three-body system as claimed in claim 4, characterized in that: Step 4 is implemented as follows: At the pericenter Apply the pericenter maneuver Δv2, and the state after the maneuver is in Under the PCRTBP model, the positive integral Get the forward propagation trajectory S2; take minimizing the maneuvering cost Δv2 as the optimization goal, and take the trajectory of the spacecraft after the maneuver and the orbit of the planet P2 as the constraint condition to construct the optimization problem In the above formula, Δt m is the glide time from the first periapsis to the last periapsis of the low-energy flyby orbit, Δt2 is the transfer time from planet P to planet P2; is the position vector of planet P2 in the sun-planet P mass center rotation system; after obtaining the state of P2 in the heliocentric J2000.0 ecliptic system through the ephemeris DE440, it is obtained through coordinate transformation; the constraints in formula (11) ensure that the spacecraft can rendezvous with planet P2 in the rotation system; the optimization variables are the pulse maneuver Δv2 and the reverse propagation time Δt2, and the optimization goal is to minimize the modulus of the maneuver Δv2; solve the optimization problem The transfer time Δt2 of planet P to P2 and the magnitude of pulse maneuver Δv2 are obtained in the rotating system.

6. The interplanetary transfer orbit optimization method based on low-energy transit of a three-body system as claimed in claim 5, characterized in that: Step 5 is implemented as follows: The low-precision transfer orbit of planet P1-Planet P obtained in step 3 and the low-precision transfer orbit of planet P-Planet P2 obtained in step 4 are combined to obtain a low-precision transfer orbit starting from planet P1 and reaching planet P2 after a low-energy crossing of the planet P system. The Julian date JD0 of the spacecraft’s departure from P1, the date JD1 of its arrival at planet P, the time JD2 of its departure from planet P, and the time JD3 of its arrival at planet P2 are known, among which JD1=JD0+Δt1, JD2=JD1+Δt m , JD3=JD2+Δt2; Since the state of the spacecraft in the rotation system at the first pericenter of the low-energy crossing orbit and JD2 are known, the state of this point in the heliocentric J2000.0 ecliptic system can be obtained by coordinate change Positive integral Able to obtain the state of the last pericenter of the low-energy crossing trajectory JD2=JD1+Δt' m , Δt' m is Δt m Correction values ​​under high-fidelity ephemeris; construct an optimization problem for solving the correction maneuvers Δv1' and Δv'2 As shown in formula (12); Among them, Δt'1 and Δt'2 are the transfer times from planet P1 to P and from planet P to P2, respectively. Δt'1 and Δt'2 are optimization variables. The transfer time Δt1 of the low-precision transfer orbit from planet P1 to P obtained in the third step and the transfer time Δt2 of the low-precision transfer orbit from planet P to P2 obtained in the fourth step are used as the optimization problem. The optimization goal is to minimize the cost J of the maneuver. Δv'1 and Δv'2 are the periapsis maneuvers applied at the first and last periapsis of the low-energy transit orbit relative to the planet, respectively. The periapsis maneuver pulse Δv1 of the low-precision transfer orbit from planet P1 to P obtained in step 3 and the periapsis maneuver pulse Δv2 of the low-precision transfer orbit from planet P to P2 obtained in step 4 are used as the initial values ​​of the optimization. Constraint It ensures that the spacecraft can rendezvous with planet P1 at JD0 = JD1-Δt'1; constraint It ensures that the spacecraft is in JD3=JD1+Δt' m +Δt'2 time can rendezvous with planet P2, where is the state of the spacecraft after performing maneuver Δv'1 The position vector in the heliocentric J2000.0 ecliptic coordinate system after reverse integration of Δt'1, is the state of the spacecraft after performing maneuver Δv'2 The position vector in the heliocentric J2000.0 ecliptic coordinate system after forward integration of Δt'2, and are the position vectors of planets P1 and P2 in the heliocentric J2000.0 ecliptic coordinate system at the corresponding time; solve the optimization problem Get the launch date JD0, the transfer duration of different segments, Δt'1, Δt'2 and Δt' m , and the magnitudes of the periapsis maneuvers Δv'1 and Δv'2.

7. The interplanetary transfer orbit optimization method based on low-energy transit of a three-body system as claimed in claim 1 or 2, characterized in that: Optimization Problem Solve by using the fmincon function of the MATLAB Optimization Toolbox; Optimization Problem Solve by using the fmincon function of the MATLAB Optimization Toolbox; Optimization Problem The solution is obtained by using the fmincon function of the MATLAB Optimization Toolbox.

8. The interplanetary transfer orbit optimization method based on low-energy transit of a three-body system as described in claim 1, 2, 3, 4, 5, 6 or 7, characterized in that: It also includes step six: according to the high-precision transfer orbit from planet P1 to planet P obtained in step five, a pulse maneuver is performed on the spacecraft at a corresponding time, and under the constraints of a given transfer starting state and terminal state, the three-body orbital dynamics is fully utilized to change the flight energy of the spacecraft, so as to reduce the fuel consumption required for the transfer from planet P1 to planet P2; according to the high-precision transfer orbit from planet P1 to planet P obtained in step five, since the spacecraft is weakly captured by planet P after entering the planetary system instead of escaping after the gravitational assist of planet P, the spacecraft can fly over the same planetary system multiple times, thereby improving the spacecraft's detection opportunity of the planetary system; the phase relationship between planets P, P1, and P2 is adjusted by utilizing the time delay caused by the temporary capture of the spacecraft by planet P in the planet P system, and the transfer window of the interplanetary orbit is expanded according to the adjusted phase relationship, thereby improving the spacecraft's interplanetary detection opportunity.

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