An interplanetary transfer orbit optimization method based on low-energy transfer of three-body system

Abstract

The application discloses a kind of interplanetary transfer orbit optimization method using three-body system low-energy crossing, belong to aerospace technical field.The application implementation method is: in rotating system, the plane circular restricted three-body model describing the movement of spacecraft is established, based on plane circular restricted three-body model, three-body orbit dynamics is fully utilized to change the flight energy of spacecraft, and the fuel consumption required for interplanetary transfer is reduced.In the heliocentric inertial system, a high-fidelity ephemeris model is established.The perihelion Poincare mapping is used to represent the initial perihelion state of the spacecraft, and the 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 perihelion state that can be weakly captured by the planetary system.Based on the feasible subset and the perihelion maneuvering strategy, a low-precision transfer orbit between planets is obtained in the plane circular restricted three-body model, and the high-precision transfer orbit is obtained by correcting the low-precision transfer orbit in the high-fidelity ephemeris model.

Description

Technical Field

[0001] This invention relates to a method for optimizing planetary exploration transfer orbits, and more particularly to an interplanetary transfer orbit optimization method based on low-energy cross-travel motion of a three-body system. This method is applicable to spacecraft exploration of planets in the solar system and belongs to the field of aerospace technology. Background Technology

[0002] The atmospheres of giant planets like Jupiter and Saturn contain large amounts of hydrogen and helium, similar to the composition of the primordial nebula in the early stages of the solar system's formation. Exploring these giant planets can not only advance research into the formation and evolution of the solar system but also reveal the possibility of life existing within it.

[0003] Designing interplanetary transfer orbits in the complex gravitational field of the solar system is a prerequisite for exploration missions. Current transfer orbit designs are mostly based on multi-body gravitational assistance models, which use the gravitational assistance of multiple planets to increase the speed of spacecraft, thereby reducing launch costs and 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 a gravitational assist orbit for Jupiter exploration using the proposed hidden gene genetic algorithm and the multiple Gravity Assists with Deep Space Maneuver (MGA-DSM) model for Earth-Venus-Earth-Jupiter (EVEJ). In 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.) for the Saturn probe orbit design problem, Englander et al. used a nested loop algorithm and the MGA-DSM model to design the Cassini Earth-Venus-Venus-Earth-Jupiter-Saturn (EVVEJS) gravity-assisted sequence. These methods can efficiently design interplanetary probe orbits, but during the gravity-assisted process, the spacecraft's high-speed flyby of planets makes the interplanetary probe window strictly constrained by the interplanetary phase, which cannot meet the needs of planetary probes in the whole space and wide area.

[0004] The in-depth utilization of three-body dynamics is a hot topic in interplanetary transfer orbits, both now and in the future. In three-body systems, rich dynamic behaviors exist near the secondary host body, such as weak stability boundaries, temporary capture, and low-energy crossovers. A fundamental characteristic of these trajectories is the ability to fly past planets multiple times, thus providing more opportunities for planetary exploration and potentially yielding additional scientific rewards. For low-energy crossover motions, the spacecraft's weak capture upon entering the planetary system, rather than its direct escape, can improve the phase relationships between 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 this invention is to provide an interplanetary transfer orbit optimization method for low-energy traversal of three-body systems. This method constructs a pericentric Poincaré map characterizing the initial state of the spacecraft, obtains a feasible set of low-energy traversal motions through parameter scanning and filtering strategies, and optimizes the interplanetary transfer orbit based on the low-energy traversal motions and pericentric maneuver strategies corresponding to the feasible set. Due to the full utilization of three-body dynamics, this invention can reduce spacecraft launch costs, expand the interplanetary transfer window, and enable the spacecraft to traverse the same planetary system multiple times, increasing the spacecraft's opportunities to explore planetary systems.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses an interplanetary transfer trajectory optimization method based on low-energy three-body system crossings. A planar circular restricted three-body model describing the spacecraft's motion is established in a rotating frame. Based on this model, the spacecraft's flight energy is altered by utilizing three-body orbital dynamics, reducing fuel consumption for interplanetary transfer. A high-fidelity ephemeris model is established in a heliocentric inertial frame. The initial pericentric state of the spacecraft is characterized using a pericentric Poincaré map. Feasible subsets corresponding to low-energy crossing motions in phase space are determined through parameter scanning. These feasible subsets correspond to initial pericentric states that can be weakly captured by planetary systems. Based on these feasible subsets and pericentric maneuvering strategies, a low-precision interplanetary transfer trajectory is obtained under the planar circular restricted three-body model. This low-precision transfer trajectory is then corrected under the high-fidelity ephemeris model to obtain a high-precision transfer trajectory. Utilizing this high-precision transfer trajectory, the spacecraft can perform multiple flybys of the same planetary system, increasing its opportunities for planetary system detection.

[0008] This invention discloses an interplanetary transfer trajectory 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) to describe the spacecraft's motion in the Sun-planet P center-of-mass rotating frame. Based on the planar circular restricted three-body model, make full use of the three-body orbital dynamics to change the spacecraft's flight energy and reduce the fuel consumption required for interplanetary transfer. Establish a high-fidelity ephemeris model in the heliocentric J2000.0 ecliptic inertial frame. Construct a pericentric Poincaré map to describe the spacecraft's initial state.

[0010] Step 1.1: Establish a planar circular restricted three-body motion model describing the spacecraft's motion in the Sun-planet P center-of-mass rotating frame. Based on the planar circular restricted three-body model, fully utilize the three-body orbital dynamics to change the spacecraft's flight energy and reduce the fuel consumption required for interplanetary transfer. Establish an ephemeris model in the heliocentric J2000.0 ecliptic coordinate system.

[0011] The planar circular restricted three-body motion model of a spacecraft in a rotating frame is represented as follows:

[0012]

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

[0014]

[0015] The integral constant of the three-body system, namely the Jacobian 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 spacecraft's motion under the influence of multiple gravitational accelerations. In this planar circular restricted three-body dynamics model, the spacecraft is relative to a mass m s The motion of the Sun is modeled, and multiple perturbations relative to the central body, with mass m, are considered. iThe perturbations (i = 1, ..., n) include the Earth, the Moon, Jupiter, Saturn, and Jupiter's moons. In the ecliptic J2000.0 inertial coordinate system centered on the Sun, the spacecraft's motion model is represented as follows:

[0020]

[0021] The first term represents the gravitational acceleration of the spacecraft by the central celestial body, while the summation term covers the gravitational interactions between the perturbation body and the spacecraft, as well as between the perturbation body and the central celestial body. ps In the heliocentric ecliptic J2000.0 inertial coordinate system, the position vector from the Sun to the spacecraft is r. pi Let r be the position vector pointing from the sun to the perturbation body i. si Let be the position vector pointing from the spacecraft to the i-th perturbation body. This vector is obtained from the ephemeris table JPL DE440.

[0022] Step 1.2: Establish a Poincaré map describing the initial state of the spacecraft.

[0023] By establishing a polar coordinate system centered on planet P, 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 spacecraft and the x-axis of the Sun-planet P center-of-mass rotational system. For a given Jacobian constant C, the spacecraft's position vector r 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 the following formula.

[0026]

[0027] Because at the pericenter, the spacecraft's position vector relative to the planet... and velocity vector Since they are orthogonal, the velocity vector v is calculated using the flight path angle β. For forward motion, i.e. When the direction is consistent with the angular momentum of the system, β = α + π / 2. Conversely, for retrograde motion, i.e., vector... The direction of angular momentum is opposite to that of the spacecraft system, and β = α - π / 2. Therefore, the velocity vector v is expressed as...

[0028] v = [vcosβ, vsinβ] T (9)

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

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

[0031] Once the motion type, such as anterograde 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. Place C within the feasible range [C min C max Discretize α into M points with a step size ΔC within the feasible range [α]. min ,α max The area is discretized into N points with a step size Δα, and r is... p Within the feasible range [r pmin ,r pmax [Within step size Δr] p Discretize into P points, thus obtaining a phase space consisting of M×N×P discrete initial states, where the i-th group of proximal point states is represented 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 in the Sun-planet P center-of-mass rotating system.

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

[0033] In the Sun-planet P center-of-mass rotating system, low-energy traversal motion occurs within a disk region centered on planet P and with a radius three times the Hill radius of planet P. If x i For the pericentric state of the low-energy crossing motion at time t0, the following three conditions must be met simultaneously.

[0034] Condition ①: Inverse integral x i If the reverse trajectory intersects with the boundary of the disk region, it indicates that the spacecraft has entered the planetary system from outside the system, and the next judgment process is executed. If there is no intersection, then x i The corresponding (r)p ,α,C) i The feasible set U does not belong to low-energy crossing motion.

[0035] Condition ②: positive integral x i If the positive trajectory intersects the boundary of the disk region, it indicates that the spacecraft will eventually escape from the planetary system and proceed to the next judgment step. If there is no intersection, then x i The corresponding (r) p ,α,C) i The feasible set U does not belong to low-energy crossing motion.

[0036] Condition ③: The total number of pericentric points of the spacecraft's trajectory relative to planet P within the disk region is q, where constraint r is satisfied. p <r pmax Let p be the number of pericentric points. If p is greater than or equal to 2, then x i The corresponding (r) p ,α,C) i Up belongs to the feasible set of low-energy cross-country sports.

[0037] For M×N×P discrete points in the phase space, each discrete point (r) is determined one by one using conditions ①②③. p ,α,C) i Determine whether it belongs to low-energy crossing motion, and thus obtain the feasible set Up of low-energy crossing motion.

[0038] Step 3: Based on the low-energy cross-travel motion of the Sun-Planet P three-body system under the PCRTBP model, with minimizing the maneuver cost as the optimization objective, and with the spacecraft's trajectory after maneuvering intersecting and being tangent to the orbit of Planet P1 as the constraint, optimize the transfer orbit from Planet P1 to Planet P, obtain the low-precision transfer orbit from Planet P1 to Planet P, as well as the transfer time Δt1 and maneuver 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 planet P1 to planet P segment based on the low-energy cross-travel motion of the Sun-Planet P three-body system under the PCRTBP model.

[0040] For the feasible set Up of low-energy traversal motion in the Sun-Planet P three-body system, assume that the feasible set contains Q discrete initial pericentric states, where the j-th state can be represented as (r p ,α,C) j j = 1, 2, 3…Q. Its state in the Sun-planet P center-of-mass rotating frame can be represented as x j =[r j ,v j [By integrating x in both the inverse and forward directions] j , to obtain xj The corresponding low-energy crossing orbit's state relative to the first pericenter of planet P within the disk region is: The state of the last pericentric point is represented as The orbital inclinations of planets P1 and P in the heliocentric inertial frame are very similar, and their eccentricities are both close to zero. Therefore, in the Sun-planet P center-of-mass rotation frame, the orbit of P1 is equivalent to a circular orbit centered on the Sun, with a normalized radius of a1. In the heliocentric J2000.0 ecliptic coordinate system, the semi-major axis of planet P1 is smaller than that of planet P. At the pericenter... Applying a proximal maneuver Δv1, the state after the maneuver is: in In the PCRTBP model, inverse integral The backpropagation trajectory S1 is obtained. With the goal of minimizing the maneuver cost Δv1 and the constraint that the spacecraft's trajectory after the maneuver intersects with planet P1, an optimization problem is constructed to solve for the maneuver pulse Δv1. As shown in equation (10)

[0041] In the above formula, constraints This constraint is used to ensure that the backpropagation trajectory S1 intersects with the orbit of planet P1. When the spacecraft rendezvous with planet P1, S1 will be tangent to the orbit of planet P1 in the Sun-planet P center-of-mass rotation frame, thereby reducing spacecraft launch costs and constraining... The spacecraft's orbit is restricted to be tangent to P1's orbit when it rendezvous with P1. The optimization variables are the pulse maneuver Δv1 and the backpropagation time Δt1. The optimization objective is to minimize the magnitude of the maneuver Δv1. Solve the optimization problem. The transfer time Δt1 from planet P1 to P in the rotating system, the pulse maneuver magnitude Δv1, and the spacecraft's state when it departs from P1 are obtained.

[0042] Step 3.2: Based on the spacecraft and planet P 1· By defining the rendezvous position constraints, the position vector of planet P1 in the rotating frame is obtained. Then, by performing a coordinate transformation on this position vector, the position state of planet P1 in the inertial frame is obtained. Finally, by setting a launch time interval, the Julian date when the spacecraft departs from planet P1 is determined based on the position constraints.

[0043] Because when the spacecraft rendezvouses with planet P1, the state of the rotating system at the center of mass of the Sun-planet P is... Since the spacecraft and planet P1 coincided at the time of their rendezvous, the state of planet P1 in this rotating frame at that moment is: The range of launch time JD0 is [JD 0min JD 0maxThe state X(JD0) of planet P1 in the heliocentric J2000.0 ecliptic coordinate system is obtained using ephemeris DE440. Through coordinate transformation, the state of planet P1 in the rotating frame at JD0 is obtained. By constraints Determine the Julian date JD0 when the spacecraft departs from planet P1.

[0044] As a preferred option, the optimization problem The solution is obtained using the fmincon function from the MATLAB Optimization Toolbox.

[0045] Step 4: Based on the low-energy cross-travel motion of the Sun-Planet P three-body system under the PCRTBP model, with minimizing the maneuver cost as the optimization objective and the intersection of the spacecraft's maneuvered trajectory with the orbit of Planet P2 as the constraint, optimize the transfer trajectory from Planet P to Planet P2, and obtain the low-precision transfer trajectory from Planet P to Planet P2, as well as the transfer time Δt2 and maneuver 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 larger than that of Planet P.

[0046] At the pericentric point Applying a proximal maneuver Δv2, the state after the maneuver is: in In the PCRTBP model, the positive integral The forward propagation trajectory S2 is obtained. With minimizing the maneuver cost Δv2 as the optimization objective, and the intersection of the spacecraft's maneuvered trajectory with the orbit of planet P2 as the constraint, an optimization problem is constructed.

[0047]

[0048] In the above formula, Δt m Δt2 is the glide time from the first pericenter to the last pericenter in the low-energy flyby orbit, and Δt2 is the transfer time from planet P to planet P2. Let be the position vector of planet P2 in the Sun-planet P center-of-mass rotation system. This vector is obtained by coordinate transformation after obtaining the state of P2 in the heliocentric J2000.0 ecliptic system using ephemeris DE440. The constraints in equation (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 objective is to minimize the magnitude of the maneuver Δv2. Solving the optimization problem... We obtain the transfer time Δt2 from planet P to P2 and the pulse maneuver magnitude Δv2 in the rotating system.

[0049] As a preferred option, the optimization problem The solution is obtained using the fmincon function from the MATLAB Optimization Toolbox.

[0050] Step 5: Combine the low-precision transfer orbits of planet P1 to planet P obtained in Step 3 with the low-precision transfer orbits of planet P to planet P2 obtained in Step 4 to obtain the low-precision transfer orbit of planet P1 to planet P2. Then, correct the low-precision transfer orbit of planet P1 to planet P2 under a high-fidelity ephemeris model to obtain the high-precision transfer orbit of planet P1 to planet P2, thus achieving the optimization of the interplanetary transfer orbit for low-energy crossing of the three-body system.

[0051] By combining the low-precision transfer orbits from planet P1 to planet P obtained in step three and from planet P to planet P2 obtained in step four, a low-precision transfer orbit is obtained from planet P1, through the low-energy crossing of the planet P system, to planet P2. The Julian date JD0 of the spacecraft's departure from P1, the date JD1 of its arrival at planet P, the time of departure from planet P JD2, and the time JD3 of its arrival at planet P2 are known, where JD1 = JD0 + Δt1, JD2 = JD1 + Δt m JD3 = JD2 + Δt2. Since the spacecraft's state in the rotating frame at the first pericenter of its low-energy crossing orbit and JD2 are known, the state of the first pericenter in the heliocentric J2000.0 ecliptic frame can be obtained through coordinate transformation. positive integral It is possible to obtain the state of the last pericenter of the low-energy traversal trajectory. JD2 = JD1 + Δt' m , Δt' m It is Δt m Corrections are given under high-fidelity ephemeris. An optimization problem is constructed to solve the corrected maneuvers Δv'1 and Δv'2. As shown in equation (12).

[0052]

[0053] Where Δt'1 and Δt'2 are the transfer times from planet P1 to P and from planet P to P2, respectively, and 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 optimization problems. The initial values ​​are: The optimization objective is to minimize the cost J of the maneuver. Δv'1 and Δv'2 are the pericentric maneuvers applied at the first and last pericentric points relative to the planet in the low-energy transfer orbit, respectively. The pericentric maneuver pulse Δv1 of the low-precision transfer orbit from planet P1 to P obtained in step three and the pericentric maneuver pulse Δv2 of the low-precision transfer orbit from planet P to P2 obtained in step four are used as the initial values ​​for optimization. Constraints This ensures that the spacecraft can rendezvous with planet P1 at time JD0 = JD1 - Δt'1. (Constraint) This ensured that the spacecraft was in JD3=JD1+Δt' m At time +Δt'2, it can intersect with planet P2, where The state of the spacecraft after performing maneuver Δv'1 The position vector in the heliocentric J2000.0 ecliptic coordinate system after inverse integration of Δt'1. The state of the spacecraft after performing maneuver Δv'2 The position vector in the heliocentric J2000.0 ecliptic coordinate system after positive integration of Δt'2. and Let be the position vectors of planets P1 and P2 in the heliocentric J2000.0 ecliptic coordinate system at the corresponding times. Solve the optimization problem. We obtain the launch date JD0, the transition durations for different segments, Δt'1, Δt'2, and Δt' m And the magnitudes of the pericentric maneuvers, Δv'1 and Δv'2.

[0054] As a preferred option, the optimization problem The solution is obtained using the fmincon function from the MATLAB Optimization Toolbox.

[0055] The process also includes step six: Based on the high-precision transfer orbit from planet P1 to planet P obtained in step five, the spacecraft performs pulse maneuvers at the corresponding time. Under the constraints of the given initial and final transfer states, the spacecraft's flight energy is altered by fully utilizing three-body orbital dynamics, reducing fuel consumption required for the planet P1-P2 transfer. Based on 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 rather than escaping with the gravitational assistance of planet P, the spacecraft can fly over the same planetary system multiple times, increasing its opportunities to explore the planetary system. The time delay caused by the spacecraft's temporary capture by planet P within the planetary system is used to adjust the phase relationship between planets P, P1, and P2. Based on the adjusted phase relationship, the transfer window for interplanetary orbit is expanded, further increasing the spacecraft's interplanetary exploration opportunities.

[0056] Beneficial effects:

[0057] 1. The present invention discloses an interplanetary transfer orbit optimization method based on low-energy crossing of a three-body system. It utilizes the low-energy crossing motion of a three-body system to design an interplanetary orbit, and makes full use of the advantage of the three-body orbit dynamics to change the spacecraft's flight energy. Compared with the multi-body leveraging method based on two-body dynamics and conic section splicing model, it can reduce the fuel consumption required for transfer.

[0058] 2. The present invention discloses an interplanetary transfer orbit optimization method based on low-energy crossing of a three-body system. After the spacecraft enters the planetary system, it is weakly captured by the planet and can achieve multiple planetary flybys. Compared with the multi-body gravitational transfer method, the spacecraft only flies past the planetary system at high speed once, providing additional detection opportunities for planetary exploration.

[0059] 3. The present invention discloses an interplanetary transfer orbit optimization method based on low-energy crossing of a three-body system. After the spacecraft enters the planetary system with low energy, it is temporarily captured by the planet. The spacecraft and the planet fly together to adjust the phase relationship between the planets. Compared with the multi-body transfer with strict phase relationship constraints, this method expands the transfer window for planetary exploration. Attached Figure Description

[0060] Figure 1 A flowchart of an interplanetary transfer orbit optimization method based on low-energy traversal of a three-body system according to the present invention.

[0061] Figure 2 Schematic diagram of the low-energy crossing trajectory of the Sun-Jupiter system.

[0062] Figure 3 A schematic diagram of the Earth-Jupiter-Saturn transfer orbit designed based on the low-energy crossing orbit of the Sun-Jupiter system in the PCRTBP model.

[0063] Figure 4 A schematic diagram of the Earth-Jupiter-Saturn transfer orbit designed based on the low-energy crossing orbit of the Sun-Jupiter system under the ephemeris model. Detailed Implementation

[0064] To better illustrate the purpose and advantages of this invention, the following description, in conjunction with accompanying illustrations and an example of an Earth-Jupiter-Saturn transfer based on low-energy transit motion of the Sun-Jupiter three-body system, further explains the invention.

[0065] Example 1:

[0066] like Figure 1 As shown in the figure, this embodiment discloses an interplanetary transfer trajectory optimization method based on low-energy travel of a three-body system. The specific implementation steps are as follows:

[0067] Step 1: Establish a planar circular restricted three-body problem (PCRTBP) dynamic model in the Sun-Jupiter center-of-mass rotating frame to describe the spacecraft's motion. Based on the planar circular restricted three-body model, fully utilize the three-body orbital dynamics to change the spacecraft's flight energy and reduce the fuel consumption required for interplanetary transfer. Establish a high-fidelity ephemeris model in the heliocentric J2000.0 ecliptic inertial frame. Construct a pericentric Poincaré map to describe the spacecraft's initial state.

[0068] Step 1.1: Establish a planar circular restricted three-body motion model describing the spacecraft's motion within the Sun-Jupiter center-of-mass rotating frame. Based on this model, fully utilize the three-body orbital dynamics to alter the spacecraft's flight energy and reduce fuel consumption required for interplanetary transfer. Establish an ephemeris model in the heliocentric J2000.0 ecliptic coordinate system.

[0069] The planar circular restricted three-body motion model of a spacecraft in a rotating frame is represented as follows:

[0070]

[0071] Where r = [x, y], These represent the spacecraft's position and velocity vectors, respectively. μ is the system's mass ratio, μ = 9.5388609 × 10⁻⁶. -4 r1 and r2 represent the distances between the spacecraft and the Sun and Jupiter, respectively.

[0072]

[0073] The integral constant of a three-body system, namely the Jacobian constant, can be expressed as:

[0074]

[0075] Where Ω represents the pseudo-potential energy of the system.

[0076]

[0077] 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 spacecraft's motion under the influence of multiple gravitational accelerations. In this planar circular restricted three-body dynamics model, the spacecraft is relative to a mass m s The motion of the Sun is modeled, and multiple perturbations relative to the central body, with mass m, are considered. i The perturbations (i = 1, ..., n) include the Earth, the Moon, Jupiter, Saturn, and Jupiter's moons. In the ecliptic J2000.0 inertial coordinate system centered on the Sun, the spacecraft's motion model is represented as:

[0078]

[0079] The first term represents the gravitational acceleration of the spacecraft by the central celestial body, while the summation term covers the gravitational interactions between the perturbation body and the spacecraft, as well as between the perturbation body and the central celestial body. ps In the heliocentric ecliptic J2000.0 inertial coordinate system, the position vector from the Sun to the spacecraft is r. pi Let r be the position vector pointing from the sun to the perturbation body i. siThe position vector pointing from the spacecraft to the i-th perturbation body is obtained from the ephemeris table JPL DE440.

[0080] Step 1.2: A Poincaré map describing the initial state of the spacecraft was established.

[0081] To describe the spacecraft's pericentric state relative to Jupiter at time t0, a polar coordinate system centered on Jupiter was established. The spacecraft's pericentric state in this 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 Sun and the x-axis of the Sun-Jupiter mass rotation frame. For a given Jacobian constant C, r can be expressed as

[0082] r=[1-μ+r p cosα,r p sinα] T (19)

[0083] The magnitude of the velocity vector v can be calculated by the following formula.

[0084]

[0085] Because at the pericenter, the spacecraft's position vector relative to Jupiter and velocity vector They are orthogonal; therefore, the velocity vector can be calculated using the flight path angle β. For forward motion, i.e. The angular momentum direction is consistent with that of the Jupiter-Sun three-body system, in which case β = α + π / 2. Conversely, for retrograde motion, i.e., vector... The angular momentum of the Sun-Jupiter three-body system is opposite in direction, and β = α - π / 2. Therefore, v can be expressed as...

[0086] v = [vcosβ, vsinβ] T (twenty one)

[0087] Step 2: First, define the range of variation for the polar angle, Jacobian constant, and pericentric distance, and then discretize each of these ranges with a specific step size to obtain a discrete phase space. For each discrete point, determine whether it corresponds to a low-energy crossing motion. By traversing the discrete phase space, obtain the feasible set of low-energy crossing motions.

[0088] Step 2.1: Set the range of variation for polar angle, Jacobian constant and pericentric distance, and discretize them with predetermined step sizes to obtain discrete phase spaces.

[0089] Once the motion type, such as anterograde 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. pThe only decision. Discretize C within the feasible range [3, 3.03] into points of 31 with a step size of 0.001, discretize α within the feasible range [0, 360°] into points of 721 with a step size of 0.5°, and discretize r... p Within the feasible range [9.5730×10] -5 [0.0023] with a step size of 2.2043×10 -5 The points are discrete, each with a value of 101. This yields 31 × 721 × 101 initial states, where the i-th group of near-center states can be represented as (r... p ,α,C) i ,i=1,2,3…31×721×101. According to equations (19) and (21), the state of the corresponding spacecraft in the Sun-Jupiter mass center rotation system is x i =[r i ,v i ].

[0090] Step 2.2: For each discrete point in the phase space, determine whether it corresponds to a low-energy crossing motion. By traversing the discrete phase space, obtain the feasible set of low-energy crossing motions.

[0091] In a Sun-Jupiter barycentric rotating system, assume that the low-energy cross-penetration motion occurs within a disk region centered on Jupiter with a radius three times the Hill radius of Jupiter (normalized to 0.0681). If x i For the pericentric state of the low-energy crossing motion at time t0, the following three conditions must be met simultaneously.

[0092] Condition ①: Inverse integral x i If the reverse trajectory intersects with the boundary of the disk region, it indicates that the spacecraft has entered the Jupiter system from outside, and the next judgment process will proceed. If there is no intersection, then x i The corresponding (r) p ,α,C) i The feasible set U does not belong to low-energy crossing motion.

[0093] Condition ②: positive integral x i If the positive trajectory intersects the boundary of the disk region, it indicates that the spacecraft will eventually escape from the Jupiter system and proceed to the next judgment step. If there is no intersection, then x i The corresponding (r) p ,α,C) i The feasible set U does not belong to low-energy crossing motion.

[0094] Condition ③: The total number of pericentric points of the spacecraft's trajectory relative to Jupiter within the disk region is q, where constraint r is satisfied. p <r pmax Let p be the number of pericentric points. If p is greater than or equal to 2, then xi The corresponding (r) p ,α,C) i Up belongs to the feasible set of low-energy cross-country sports.

[0095] For 31×721×101 discrete points in the phase space, each discrete point (r) is determined one by one using conditions ①②③. p ,α,C) i Determine whether it belongs to low-energy crossing motion, and thus obtain the feasible set Up of low-energy crossing motion.

[0096] Step 3: Based on the low-energy transit motion of the Sun-Jupiter three-body system under the PCRTBP model, with minimizing maneuvering cost as the optimization objective and the constraint that the spacecraft's trajectory after maneuvering intersects and is tangent to Jupiter's orbit, the Earth-Jupiter transfer orbit is optimized to obtain the low-precision Earth-Jupiter transfer orbit, as well as the spacecraft's transfer time Δt1 from Earth to Jupiter and the maneuvering cost. The Julian date of the spacecraft's departure from Earth is also determined.

[0097] Step 3.1: Optimize the Earth-Jupiter segment transfer trajectory based on the low-energy cross-entry motion of the Sun-Jupiter tribody system under the PCRTBP model.

[0098] For the feasible set Up of low-energy traversal motion in the Sun-Jupiter three-body system, assuming that the feasible set contains 78329 discrete initial pericentric states, the 42856th state can be represented as (r p =9.5730×10 -5 (α = 300.5°, C = 3.02). Its state in the Sun-wood-centric rotational system can be represented as x 42856 = [0.999095, -8.251004 × 10 -5 [-3.866858, -2.274892]. Through inverse and forward integration of x... 42856 , can obtain x 42856 The corresponding low-energy crossing orbit's state relative to Jupiter's first pericenter within the disk region is: The state of the last pericentric point can be represented as This low-energy crossing trajectory, in a Sun-centric rotating system, is as follows: Figure 2 As shown. Assuming the difference in orbital inclination between Earth and Jupiter in a heliocentric inertial frame is very small, and both have eccentricities close to zero, then in a heliocentric rotational frame, Earth's orbit can be approximated as a circular orbit centered on the Sun, with a normalized radius of a1 = 0.192211. At the pericenter... Applying a proximal maneuver Δv1, the state after the maneuver is: in In the PCRTBP model, inverse integral The backpropagation trajectory S1 is obtained. To reduce launch costs, it is assumed that S1 will be tangent to Earth's orbit in the Sun-Jupiter-centered rotation frame when the spacecraft rendezvous with Earth. An optimization problem is constructed to solve for the maneuver pulse Δv1, with the objective of minimizing the maneuver cost Δv1 and the constraint that the spacecraft's trajectory after the maneuver will rendezvous with Earth. As shown in equation (22).

[0099] In the above formula, constraints This constrains the backpropagation trajectory S1 to intersect with Earth's orbit, constraining... The spacecraft's orbit is restricted to be tangent to Earth's orbit during its rendezvous with Earth. The optimization variables are the pulse maneuver Δv1 and the backpropagation time Δt1, and the optimization objective is to minimize the magnitude of the maneuver Δv1. Optimization Problem By using the fmincon function from the MATLAB Optimization Toolbox, we obtained the transfer time from Earth to Jupiter in a rotating frame, Δt1 = 1206.18 days, the pulse maneuver magnitude, Δv1 = 323.85 m / s, and the spacecraft's position at launch from P1.

[0100] Step 3.2: Based on the positional constraints of the spacecraft's rendezvous with Earth, obtain the Earth's position vector in the rotating frame. By performing a coordinate transformation on the Earth's position vector, obtain the Earth's position in the inertial frame. By setting the launch time interval, determine the Julian date when the spacecraft departs from Earth based on the positional constraints.

[0101] Because the state of the spacecraft in the Jupiter-centered rotational system at the time of its rendezvous with Earth is... Since the spacecraft and Earth coincided at the time of their rendezvous, the state of Earth in that rotating frame at that moment can be obtained as follows: To determine the Julian date of the spacecraft's launch from Earth, we assume the launch time JD0 falls between January 1, 2033, and January 1, 2034. Therefore, using ephemeris DE440, we can obtain Earth's state X(JD0) in the heliocentric J2000.0 ecliptic coordinate system. Through coordinate transformation, we can obtain Earth's state in the rotating frame at JD0. By constraints The Julian date JD0 when the spacecraft departed from Earth can be determined to be April 20, 2033.

[0102] Step 4: Based on the low-energy crossing motion of the Sun-Earth three-body system under the PCRTBP model, with the optimization objective of minimizing maneuvering cost and the constraint of the intersection of the spacecraft's maneuvered trajectory with Saturn's orbit, optimize the Jupiter-Saturn transfer orbit to obtain the low-precision Jupiter-Saturn transfer orbit, as well as the spacecraft's transfer time Δt2 and maneuvering cost from Jupiter to Saturn.

[0103] At the pericentric point Applying a proximal maneuver Δv2, the state after the maneuver is: in In the PCRTBP model, the positive integral The forward propagation trajectory S1 is obtained. With the goal of minimizing the maneuver cost Δv2 and the constraint that the spacecraft's trajectory after the maneuver intersects with Saturn, an optimization problem is constructed to solve for the maneuver pulse Δv2. As shown in equation (23).

[0104] In the above formula, Δt m The glide time from the first perigee to the last perigee in the low-energy flyby orbit is approximately 849 days. Δt2 is the transfer time from Jupiter to Saturn. Let be the position vector of Saturn in the heliocentric rotational system. This vector is obtained by coordinate transformation after obtaining Saturn's state in the heliocentric J2000.0 ecliptic system using ephemeris DE440. The constraints in equation (23) ensure that the spacecraft can rendezvous with Saturn in the rotational system. The optimization variables are the pulse maneuver Δv2 and the reverse propagation time Δt2, and the optimization objective is to minimize the magnitude of the maneuver Δv2. Optimization Problem By using the fmincon function in the MATLAB optimization toolbox, we obtained the Earth-Jupiter-Saturn transfer time Δt² = 4136.98 days and the pulse maneuver magnitude Δv² = 61.05 m / s in a rotating frame. The Earth-Jupiter-Saturn transfer trajectory designed based on the low-energy cross-plane motion of the Sun-Jupiter system under PCRTBP is as follows: Figure 3 As shown.

[0105] Step 5: Combine the low-precision Earth-Jupiter transfer orbit obtained in Step 3 with the low-precision Jupiter-Saturn transfer orbit obtained in Step 4 to obtain the low-precision Earth-Saturn transfer orbit. Then, refine the low-precision Earth-Saturn transfer orbit using a high-fidelity ephemeris model to obtain the high-precision Earth-Saturn transfer orbit, thus optimizing the interplanetary transfer orbit for low-energy three-body system crossings.

[0106] By piecing together the transfer orbits designed in steps three and four, a transfer orbit is obtained from Earth, passing through the Jupiter system at low energy, and arriving at Saturn. The Julian date of the spacecraft's departure from Earth, JD0, is April 20, 2033; the date of arrival at Jupiter, JD1, is August 24, 2035; the date of departure from Jupiter, JD2, is December 20, 2037; and the date of arrival at Saturn, JD3, is April 18, 2049, where JD1 = JD0 + Δt1, JD2 = JD1 + Δt m JD3 = JD2 + Δt2. Since the state of the spacecraft in the rotating frame at the first pericenter of its low-energy crossing orbit and JD2 are known, the state of that point in the heliocentric J2000.0 ecliptic frame can be obtained through coordinate transformation. Forward integral based on ephemeris model It is possible to obtain the state of the last pericenter of the low-energy traversal trajectory. JD2 = JD1 + Δt' m , Δt' m It is Δt m Correction values ​​under high-fidelity ephemeris. With minimizing maneuver cost as the optimization objective and the constraint that the corrected trajectory can intersect with Earth and Saturn as the condition, the optimization problem for solving the corrected maneuvers Δv'1 and Δv'2 is constructed as shown in Equation (24).

[0107]

[0108] Where Δt'1 and Δt'2 are the transfer times from Earth to Jupiter and from Jupiter to Saturn, respectively, and are optimization variables. The transfer time Δt1 of the low-precision transfer orbit from Earth to Jupiter obtained in the third step and the transfer time Δt2 of the low-precision transfer orbit from Jupiter to Saturn obtained in the fourth step are used as optimization problems. The initial values ​​are given. The optimization objective is to minimize the cost J of the maneuver. Δv'1 and Δv'2 are the pericentric maneuvers applied at the first and last pericentric points relative to Jupiter in the low-energy transfer orbit, respectively. Similarly, the pericentric maneuver pulse Δv1 of the low-precision Earth-Jupiter transfer orbit obtained in step three and the pericentric maneuver pulse Δv2 of the low-precision Jupiter-Saturn transfer orbit obtained in step four can be used as the initial values ​​for optimization. Constraints This ensures that the spacecraft can rendezvous with Earth at time JD0 = JD1 - Δt'1. (Constraint) This ensured that the spacecraft was in JD3=JD1+Δt' m At time +Δt'2, it can intersect with Saturn, where The state of the spacecraft after performing maneuver Δv'1 The position vector in the heliocentric J2000.0 ecliptic coordinate system after inverse integration of Δt'1. The state of the spacecraft after performing maneuver Δv'2 The position vector in the heliocentric J2000.0 ecliptic coordinate system after positive integration of Δt'2. and Let be the position vectors of Earth and Saturn in the heliocentric J2000.0 ecliptic coordinate system at the corresponding times. Optimization problem. By using the fmincon function in the MATLAB optimization toolbox, the launch date JD0 was determined to be May 11, 2033. The Earth-Jupiter transfer segment duration was 845 days. After performing a maneuver Δv'1 = 336.36 m / s, the spacecraft entered a low-energy crossing orbit around the Jupiter system. After staying in the Jupiter system for 1023.78 days, it reached the second pericenter relative to Saturn before escaping from the Jupiter system. Subsequently, after performing a maneuver Δv'2 = 91.47 m / s, the spacecraft entered a Jupiter-Saturn transfer orbit. The Julian date of departure from Saturn was June 20, 2038. After 2851.15 days of flight, it rendezvoused with Saturn on April 9, 2046. Because the maneuver Δv'2 under the ephemeris model was larger than the maneuver Δv2 of the preliminary trajectory designed under PCRTBP, the Jupiter-Saturn transfer segment duration was reduced. The Earth-Jupiter-Saturn transfer trajectory designed based on the low-energy transit motion of the Sun-Jupiter system under a high-fidelity ephemeris model is as follows: Figure 4 As shown.

[0109] Step Six: Based on the high-precision Earth-Saturn transfer orbit obtained in Step Five, perform pulse maneuvers on the spacecraft at the corresponding time. Under the constraints of the given initial and final transfer states, fully utilize three-body orbital dynamics to alter the spacecraft's flight energy, reducing fuel consumption required for the Earth-Saturn transfer. Based on the high-precision Earth-Jupiter transfer orbit obtained in Step Five, since the spacecraft is weakly captured by Jupiter after entering the Jupiter system rather than escaping with Jupiter's gravitational assistance, multiple flybys of the Jupiter system are achieved, increasing the spacecraft's opportunities to explore the Jupiter system. Utilizing the time delay caused by the spacecraft's temporary capture by Jupiter within the Jupiter system, the phase relationship between Earth, Jupiter, and Saturn is adjusted. Based on the adjusted phase relationship, the Earth-Saturn transfer window is expanded, further increasing the spacecraft's interplanetary exploration opportunities.

[0110] 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 method for optimizing interplanetary transfer orbits based on low-energy travel through a three-body system, characterized in that: Includes the following steps, Step 1: Establish a planar circular restricted three-body dynamics model (PCRTBP) to describe the spacecraft's motion in the Sun-Planet P center-of-mass rotating system. Based on the planar circular restricted three-body model, make full use of the three-body orbital dynamics to change the spacecraft's flight energy and reduce the fuel consumption required for interplanetary transfer. A high-fidelity ephemeris model was established in the heliocentric J2000.0 ecliptic inertial frame; a pericentric Poincaré map describing the initial state of the spacecraft was constructed. Step 2: Set the range of variation for polar angle, Jacobi constant, and pericentric distance, and discretize them with a predetermined step size to obtain discrete phase space; for each discrete point, determine whether it corresponds to low-energy crossing motion, and obtain the feasible set of low-energy crossing motion by traversing the discrete phase space. Step 3: Based on the low-energy cross-travel motion of the Sun-Planet P three-body system under the PCRTBP model, with the goal of minimizing the maneuvering cost, 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 trajectory of planet P1 to planet P, obtain the low-precision transfer trajectory of planet P1 to planet P, as well as the transfer time Δt1 and 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 cross-travel motion of the Sun-Planet P three-body system under the PCRTBP model, with minimizing the maneuver cost as the optimization objective and the intersection of the spacecraft's maneuvered trajectory with the orbit of Planet P2 as the constraint, optimize the transfer trajectory of Planet P to Planet P2, and obtain the low-precision transfer trajectory of Planet P to Planet P2, as well as the transfer time Δt2 and maneuver cost of the spacecraft from Planet P to Planet P2. In the heliocentric J2000 ecliptic coordinate system, the semi-major axis of Planet P2 is larger than that of Planet P. Step 5: Combine the low-precision transfer orbits of planet P1 to planet P obtained in Step 3 with the low-precision transfer orbits of planet P to planet P2 obtained in Step 4 to obtain the low-precision transfer orbit of planet P1 to planet P2; then correct the low-precision transfer orbits of planet P1 to planet P2 under a high-fidelity ephemeris model to obtain the high-precision transfer orbits of planet P1 to planet P2, thus achieving the optimization of the interplanetary transfer orbits for low-energy crossing of the three-body system.

2. The interplanetary transfer trajectory optimization method based on low-energy travel of a three-body system as described in claim 1, characterized in that: The implementation method for step one is as follows: Step 1.1: Establish a planar circular restricted three-body motion model to describe the spacecraft's motion in the Sun-Planet P center-of-mass rotating system. Based on the planar circular restricted three-body model, make full use of the three-body orbital dynamics to change the spacecraft's flight energy and reduce the fuel consumption required for interplanetary transfer. An ephemeris model was established in the heliocentric J2000.0 ecliptic coordinate system; The planar circular restricted three-body motion model of a spacecraft in a rotating frame is represented as follows: Where r = [x, y], These represent the spacecraft's position and velocity vectors, respectively; μ is the system's mass ratio, μ = m p / (m s +m p ), where m s m is the mass of the sun. p Let r be the mass of planet P; r1 and r2 represent the distances between the spacecraft and the Sun and planet P, respectively; The integral constant of the three-body system, namely the Jacobian 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 spacecraft's motion under the influence of multiple gravitational accelerations; in this planar circular restricted three-body dynamics model, the spacecraft is relative to a mass m s The motion of the Sun is modeled, and multiple perturbations relative to the central body, with mass m, are considered. i The perturbations (i = 1, ..., n) include the Earth, the Moon, Jupiter, Saturn, and Jupiter's moons; in the ecliptic J2000.0 inertial coordinate system centered on the Sun, the spacecraft's motion model is represented as follows: The first term represents the gravitational acceleration of the spacecraft by the central celestial body, while the summation term covers the gravitational interactions between the perturbation body and the spacecraft, as well as between the perturbation body and the central celestial body; r ps In the heliocentric ecliptic J2000.0 inertial coordinate system, the position vector from the Sun to the spacecraft is r. pi Let r be the position vector pointing from the sun to the perturbation body i. si This is the position vector pointing from the spacecraft to the i-th perturbation body; the vector is obtained from the ephemeris table JPL DE440. Step 1.2: Establish a Poincaré map describing the initial state of the spacecraft; By establishing a polar coordinate system centered on planet P, 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 spacecraft and the x-axis of the Sun-planet P center-of-mass rotational system; for a given Jacobian constant C, the spacecraft's position vector r is expressed as... r=[1-μ+r p cosα,r p sinα] T (7) The magnitude of the velocity vector v is calculated by the following formula. Because at the pericenter, the spacecraft's position vector relative to the planet... and velocity vector They are orthogonal; therefore, the velocity vector v is calculated using the flight path angle β. For forward motion, i.e. When the direction of angular momentum is consistent with that of the system, β = α + π / 2; conversely, for retrograde motion, i.e., vector... The direction of angular momentum is opposite to that of the spacecraft system, where β = α - π / 2; then the velocity vector v is expressed as... v=[vcosβ,vsinβ] T (9)。 3. The interplanetary transfer trajectory optimization method based on low-energy travel through a three-body system as described in claim 2, characterized in that: The second step is implemented as follows: Step 2.1: Set the range of variation for polar angle, Jacobian constant and pericentric distance, and discretize them with predetermined step sizes to obtain discrete phase spaces; Once the motion type, such as anterograde 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; placing C within the feasible range [C min C max Discretize α into M points with a step size ΔC within the feasible range [α]. min ,α max The area is discretized into N points with a step size Δα, and r is... p Within the feasible range [r pmin ,r pmax [Within step size Δr] p Discretize into P points, thus obtaining a phase space consisting of M×N×P discrete initial states, where the i-th group of proximal point states is represented 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 in the Sun-planet P center-of-mass rotating frame. Step 2.2: For each discrete point in the phase space, determine whether it corresponds to a low-energy crossing motion. By traversing the discrete phase space, obtain the feasible set of low-energy crossing motions. In the Sun-planet P center-of-mass rotating system, low-energy traversal motion occurs within a disk region centered on planet P and with a radius three times the Hill radius of planet P; if x i For the pericentric state of the low-energy crossing motion at time t0, the following three conditions must be met simultaneously; Condition ①: Inverse integral x i If the reverse trajectory intersects with the boundary of the disk region, it indicates that the spacecraft has entered the planetary system from outside the planetary system, and the next judgment process will be executed. If there is no intersection, then x i The corresponding (r) p ,α,C) i The feasible set U does not belong to low-energy crossing motion; Condition ②: positive integral x i If the positive trajectory intersects with the boundary of the disk region, it indicates that the spacecraft will eventually be able to escape from the planetary system and proceed to the next judgment process; If there is no intersection, then x i The corresponding (r) p ,α,C) i The feasible set U does not belong to low-energy crossing motion; Condition ③: The total number of pericentric points of the spacecraft's trajectory relative to planet P within the disk region is q, where constraint r is satisfied. p <r pmax Let p be the number of pericentric points. If p is greater than or equal to 2, then x i The corresponding (r) p ,α,C) i Up represents the feasible set of low-energy traversal motion; For M×N×P discrete points in the phase space, each discrete point (r) is determined one by one using conditions ①②③. p ,α,C) i Determine whether it belongs to low-energy crossing motion, and thus obtain the feasible set Up of low-energy crossing motion.

4. The interplanetary transfer trajectory optimization method based on low-energy travel of a three-body system as described in claim 3, characterized in that: The method for implementing step three is as follows: Step 3.1: Optimize the transfer trajectory of planet P1 to planet P segment based on the low-energy cross-travel motion of the Sun-Planet P three-body system under the PCRTBP model; The feasible set U for low-energy traversal motion in the Sun-Planet P three-body system p Suppose that the feasible set contains Q discrete initial proximal states, where the j-th state can be represented as (r p ,α,C) j j = 1, 2, 3…Q; its state in the Sun-planet P center-of-mass rotation frame can be represented as x j =[r j ,v j ]; By integrating x in both the inverse and forward directions j , to obtain x j The corresponding low-energy crossing orbit's state relative to the first pericenter of planet P within the disk region is: The state of the last pericentric point is represented as The orbital inclinations of planets P1 and P in the heliocentric inertial frame are very similar, and their eccentricities are close to zero. Therefore, in the Sun-planet P center-of-mass rotation frame, the orbit of P1 is equivalent to a circular orbit centered on the Sun, with a normalized radius of a1. In the heliocentric J2000.0 ecliptic coordinate system, the semi-major axis of planet P1 is smaller than that of planet P. At the pericentric point Applying a proximal maneuver Δv1, the state after the maneuver is: in In the PCRTBP model, inverse integral The backpropagation trajectory S1 is obtained; with the minimum maneuver cost Δv1 as the optimization objective and the constraint that the spacecraft trajectory after maneuvering can intersect with planet P1, an optimization problem is constructed to solve for the maneuver pulse Δv1. As shown in equation (10) In the above formula, constraints This constraint is used to ensure that the backpropagation trajectory S1 intersects with the orbit of planet P1. When the spacecraft rendezvous with planet P1, S1 can be tangent to the orbit of planet P1 in the Sun-planet P center-of-mass rotation frame, thereby reducing spacecraft launch costs and constraining... The spacecraft's orbit is restricted to be tangent to P1's orbit when the spacecraft rendezvous with P1; The optimization variables are the pulse maneuver Δv1 and the back propagation time Δt1, and the optimization objective is to minimize the magnitude of the maneuver Δv1. Solve the optimization problem. The transfer time Δt1 from planet P1 to P in the rotating system, the pulse maneuver magnitude Δv1, and the spacecraft's state when it departs from P1 are obtained. Step 3.2: Based on the spacecraft and planet P 1· By constraining the rendezvous position, the position vector of planet P1 in the rotating frame is obtained. By performing coordinate transformation on the position vector of planet P1, the position state of planet P1 in the inertial frame is obtained. By setting the launch time interval, the Julian date when the spacecraft departs from planet P1 is determined by the position constraint conditions. Because when the spacecraft rendezvouses with planet P1, the state of the rotating system at the center of mass of the Sun-planet P is... Since the spacecraft and planet P1 coincided at the time of their rendezvous, the state of planet P1 in this rotating frame at that moment is: The range of launch time JD0 is [JD 0min JD 0max The state X(JD0) of planet P1 in the heliocentric J2000 ecliptic coordinate system is obtained using ephemeris DE440; the state of planet P1 in the rotating system at JD0 is obtained through coordinate transformation. By constraints Determine the Julian date JD0 when the spacecraft departs from planet P1.

5. The interplanetary transfer trajectory optimization method based on low-energy travel of a three-body system as described in claim 4, characterized in that: Step four is implemented as follows: At the pericentric point Applying a proximal maneuver Δv2, the state after the maneuver is: in In the PCRTBP model, the positive integral The forward propagation trajectory S2 is obtained; with minimizing the maneuver cost Δv2 as the optimization objective and the intersection of the spacecraft's maneuvered trajectory with the orbit of planet P2 as the constraint, an optimization problem is constructed. In the above formula, Δt m Δt2 is the glide time from the first pericenter to the last pericenter in the low-energy flyby orbit, and Δt2 is the transfer time from planet P to planet P2. Let P2 be 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 ephemeris DE440, coordinate transformation is performed; the constraint conditions in equation (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 objective is to minimize the magnitude of the maneuver Δv2; solve the optimization problem. We obtain the transfer time Δt2 from planet P to P2 and the pulse maneuver magnitude Δv2 in the rotating system.

6. The interplanetary transfer trajectory optimization method based on low-energy travel of a three-body system as described in claim 5, characterized in that: Step five is implemented as follows: By combining the low-precision transfer orbits from planet P1 to planet P obtained in step three and from planet P to planet P2 obtained in step four, a low-precision transfer orbit is obtained from planet P1, through the low-energy crossing of the planet P system, to planet P2. 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, where JD1 = JD0 + Δt1, JD2 = JD1 + Δt m JD3 = JD2 + Δt2; Since the state of the spacecraft in the rotating frame at the first pericenter of the low-energy crossing orbit and JD2 are known, the state of the first pericenter in the heliocentric J2000.0 ecliptic frame can be obtained through coordinate transformation. positive integral It is possible to obtain the state of the last pericenter of the low-energy traversal trajectory. JD2 = JD1 + Δt' m , Δt' m It is Δt m Corrections under high-fidelity ephemeris; constructing an optimization problem for solving the corrected maneuvers Δv1' and Δv'2. As shown in equation (12); Where Δt1' and Δt'2 are the transfer times from planet P1 to P and from planet P to P2, respectively, and 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 optimization problems. The initial values ​​are: The optimization objective is to minimize the cost J of the maneuver. Δv1' and Δv'2 are the pericentric maneuvers applied at the first and last pericentric points relative to the planet in the low-energy cross-orbit trajectory, respectively. The pericentric maneuver pulse Δv1 of the low-precision transfer orbit from planet P1 to P obtained in step three and the pericentric maneuver pulse Δv2 of the low-precision transfer orbit from planet P to P2 obtained in step four are used as the initial values ​​for optimization; constraints. This ensures that the spacecraft can rendezvous with planet P1 at time JD0 = JD1 - Δt1'; constraints This ensured that the spacecraft was in JD3=JD1+Δt' m At time +Δt'2, it can intersect with planet P2, where The state of the spacecraft after performing the maneuver Δv1' The position vector in the heliocentric J2000.0 ecliptic coordinate system after inverse integration of Δt1'. The state of the spacecraft after performing maneuver Δv'2 The position vector in the heliocentric J2000.0 ecliptic coordinate system after positive integration of Δt'2. and Let P1 and P2 be the position vectors of planets P1 and P2 in the heliocentric J2000.0 ecliptic coordinate system at the corresponding times; solve the optimization problem. The launch date JD0, the transition durations for different segments, Δt1', Δt'2, and Δt'' are obtained. m And the magnitudes of the pericentric maneuvers, Δv1' and Δv'2.

7. The interplanetary transfer trajectory optimization method based on low-energy travel through a three-body system as described in claim 3, characterized in that: Optimization problem The solution is obtained using the fmincon function from the MATLAB Optimization Toolbox. Optimization problem The solution is obtained using the fmincon function from the MATLAB Optimization Toolbox. Optimization problem The solution is obtained using the fmincon function from the MATLAB Optimization Toolbox.

8. A method for optimizing interplanetary transfer orbits based on low-energy travel through a three-body system, as described in claims 1, 2, 3, 4, 5, 6, or 7, characterized in that: The process also includes step six: based on the high-precision transfer orbit from planet P1 to planet P obtained in step five, the spacecraft performs pulse maneuvers at the corresponding time. Under the constraints of the given transfer start and end states, the spacecraft's flight energy is changed by fully utilizing the three-body orbital dynamics, reducing the fuel consumption required for the planet P1-P2 transfer. Based on 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 rather than escaping with the gravitational assistance of planet P, the spacecraft can fly over the same planetary system multiple times, increasing the spacecraft's opportunities to detect the planetary system. The phase relationship between planets P, P1, and P2 is adjusted by utilizing the time delay caused by the spacecraft being temporarily captured by planet P within the planetary system. The transfer window of the interplanetary orbit is expanded based on the adjusted phase relationship, increasing the spacecraft's opportunities for interplanetary detection.

Images