Solar system margin detection high-precision impulsive transfer orbit optimization method

Abstract

The application discloses a solar system marginal exploration high-precision impulse transfer orbit optimization method and belongs to the technical field of deep space exploration. The method aims at the problem that the existing conic curve splicing model neglects the planetary gravity influence ball in dynamics process, leading to insufficient model fidelity and poor high-precision correction convergence, and proposes a transfer orbit optimization model fusing MGA-SOI-DSM, explicitly modeling the hyperbolic orbit evolution process of the probe in the planetary influence ball, and realizing the continuous splicing of the orbit of the heliocentric section and the planetary section. Further, the influence ball radius homotopy continuation strategy is introduced, so that the optimization problem is smoothly transitioned from the simplified model to the complete model, and the solving stability is effectively improved. On this basis, the segmented shooting method is adopted to correct each section of the orbit under the high-precision multi-body dynamics model, and the consistency of the key node state is ensured. The application can quickly obtain the whole-process high-precision impulse transfer orbit satisfying the task constraints, and significantly improves the orbit design precision and convergence.

Description

Technical Field

[0001] This invention belongs to the field of deep space exploration technology, specifically relating to a high-precision pulse transfer orbit optimization method for exploring the edge of the solar system. Background Technology

[0002] With the continuous development of deep space exploration technology, mission objectives are gradually expanding from interplanetary exploration to the more distant edge of the solar system. For exploration missions at distances of tens to hundreds of astronomical units (AU) from the heliocenter, efficiently constructing transfer orbits that meet mission constraints has become one of the cutting-edge issues in the field of orbit design.

[0003] Due to launch capacity limitations, probes typically require multiple Gravity Assist (MGA) missions to accumulate energy for long-distance transfers. However, multiple MGA missions significantly increase the dimensionality of decision variables in the orbit design problem, resulting in a high-dimensional, highly nonlinear, and multimodal parameter space. Furthermore, orbit design must comprehensively satisfy multiple constraints, including flight time, terminal spatial location (distance and orientation), deep-space maneuver velocity increments, and launch conditions, further increasing the complexity of the optimization problem.

[0004] Current mainstream methods are mostly based on the MGA or MGA-DSM (Multiple Gravity Assist with Deep Space Maneuvers) model and employ the patched conics method for orbit design. Within this framework, the motion of the probe within the Sphere of Influence (SOI) is typically treated as an instantaneous process, with the gravitational pull effect characterized only by abrupt changes in the velocity vector, effectively simplifying the SOI to a point mass. This simplification fails to explicitly characterize the hyperbolic orbital evolution within the SOI during the Earth launch phase and each gravitational pull maneuver. While reducing computational complexity, the resulting orbital solutions exhibit systematic deviations from the real multibody dynamics environment. This leads to poor convergence and high correction costs when performing orbital corrections under high-precision orbital dynamics models (e.g., considering multibody perturbations), making them unsuitable as effective initial values ​​for high-precision optimization or target acquisition calculations.

[0005] Therefore, there is an urgent need for an orbit design method that can balance computational efficiency and dynamic consistency, while maintaining global search capability and improving the physical fidelity of the model, so as to provide a high-precision rapid transfer orbit design scheme for solar system edge exploration missions. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a high-precision pulse transfer orbit optimization method for solar system boundary exploration. By constructing an MGA-SOI-DSM model that continuously splices hyperbolic orbits within the planetary gravitational influence sphere (SOI) with heliocentric transfer orbits, and introducing a SOI radius homotopy extension strategy, a high-precision segmented target correction method for transfer orbits is proposed. This achieves integrated optimization design of high-precision, high-fidelity, and fast-convergence pulse transfer orbits throughout the entire process in solar system boundary exploration missions.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A high-precision pulse transfer orbit optimization method for solar system boundary exploration includes:

[0009] Step S1: Given the constraints of the solar system boundary exploration mission and the leverage flight sequence, construct a high-precision orbital dynamics model that includes gravitational perturbations from multiple celestial bodies;

[0010] Step S2: Establish a transfer trajectory optimization model that considers multi-body leverage and deep space maneuvering, use the differential evolution algorithm for global search, and combine it with the interior point method for local fine optimization to obtain the initial transfer trajectory solution;

[0011] Step S3: Based on the dynamic process within the planetary gravitational influence sphere, establish a transfer orbit optimization model that integrates multi-body leverage, gravitational influence sphere and deep space maneuvering. Use the homotopy extension strategy to gradually expand the radius of the gravitational influence sphere. Using the initial transfer orbit solution as the initial value, combine global and local optimization methods to iteratively solve the problem and obtain an optimized transfer orbit solution that satisfies the boundary continuity condition of the gravitational influence sphere.

[0012] Step S4: Under the high-precision orbit dynamics model, using the optimized transfer orbit solution as the initial value, the trajectory at each stage is successively corrected using the target shooting method to ensure the consistency of the state of key event nodes and obtain a high-precision transfer orbit that satisfies the mission constraints throughout the entire process.

[0013] Furthermore, in step S1, the constraints of the solar system boundary exploration mission are that the probe's heliocentric distance, ecliptic longitude, and ecliptic latitude at the target time meet the range requirements corresponding to the solar system boundary region; the constructed high-precision orbital dynamics model adopts the heliocentric ecliptic inertial coordinate system and considers the gravitational perturbations of the eight planets and the moon.

[0014] Furthermore, in step S2, the transfer orbit optimization model considering multi-body glide and deep-space maneuver is constructed based on the conic section splicing principle, equating planetary glide flight to an instantaneous process, with the probe's heliocentric position remaining unchanged before and after the glide; the deep-space maneuver is set in the heliocentric transfer arc between two adjacent glides, and no deep-space maneuver is applied during the flight towards the edge of the solar system after the last glide; the differential evolution algorithm is used to perform a global search on the transfer orbit optimization model considering multi-body glide and deep-space maneuver; the result of the global search is used as the initial value, and the interior point method is used for local fine optimization to obtain the initial transfer orbit solution that satisfies the constraints.

[0015] Furthermore, in step S3, an optimized transfer orbit model integrating multi-body leverage, gravitational influence sphere, and deep-space maneuvering is established. By explicitly modeling the hyperbolic orbit of the probe within the planetary gravitational influence sphere and combining it with precise planetary ephemeris data, the transfer orbits of the probe in the Earth launch segment, the interplanetary transfer segment, the transfer segment within the planetary influence sphere, and the transfer segment to the edge region of the solar system after leaving the last planet are obtained, and the continuous splicing of each orbit segment is achieved.

[0016] Furthermore, in step S3, the homotopy extension strategy is as follows: using the initial transfer orbit solution as the initial value, the radius of the gravitational influence sphere of each planet is scaled in the initial stage, and then the radius of the gravitational influence sphere is gradually restored to the actual scale during the iteration process, so that the optimization problem smoothly transitions from a simplified model to a complete model. Under each homotopy step, the optimized solution under the gravitational influence sphere radius corresponding to the current step is used as the initial value of the next step. The differential evolution algorithm is used for global search, and the interior point method is combined for local fine optimization, gradually approximating until the optimized transfer orbit solution under the actual gravitational influence sphere scale is obtained.

[0017] Furthermore, in step S4, the key event nodes include the probe entering the boundary node of the planetary gravitational influence sphere, leaving the boundary node of the planetary gravitational influence sphere, and the deep space maneuver node.

[0018] Furthermore, in step S4, the specific method of successively correcting the trajectory at each stage using the target-shooting method is as follows: taking the optimized transfer trajectory solution as the initial value, the Earth launch segment is first corrected by adjusting the perigee velocity vector of the probe to ensure the consistency of its state when leaving the Earth's influence sphere; then, the trajectories of the interplanetary transfer, the transfer within the planetary influence sphere, and the transfer segment from the last planet to the edge of the solar system are corrected in sequence. When adjusting the first few deep-space maneuvers, the consistency of the state at key event nodes is used as a constraint; when adjusting the last deep-space maneuver, the goal is to ensure that the consistency of the state at key event nodes and the heliocentric distance and direction parameters of the probe at the target time meet the constraint conditions. Through target-shooting optimization, a high-precision transfer trajectory that meets the high-precision multibody dynamics constraints throughout the entire process is gradually obtained.

[0019] Furthermore, the final high-precision transfer orbit obtained throughout the entire process is a multi-body transfer orbit that satisfies the constraints of heliocentric distance, ecliptic longitude, and ecliptic latitude in the solar system boundary exploration mission under a high-precision orbital dynamics model.

[0020] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for optimizing high-precision pulse transfer orbits for solar system boundary exploration.

[0021] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for optimizing high-precision pulse transfer orbits for solar system boundary exploration.

[0022] The beneficial effects of this invention are as follows:

[0023] Significantly improves orbit modeling fidelity: A transfer orbit optimization model integrating MGA-SOI-DSM was constructed. For the first time, hyperbolic orbit dynamics modeling within the planetary gravitational influence sphere was explicitly introduced into the traditional conic section splicing framework, achieving continuous and consistent splicing of the heliocentric transfer segment and the planetary leverage segment. Compared to the traditional method of simplifying the influence sphere to a point mass, this invention can more realistically characterize the dynamic evolution of the probe near the planet, fundamentally eliminating the systematic bias caused by model simplification.

[0024] To effectively improve the convergence of subsequent high-precision orbit corrections, a homotopy extension strategy for the influence sphere radius is introduced. By gradually expanding the influence sphere radius from zero to the actual scale, the optimization problem smoothly transitions from a simplified model to a complete model. This strategy uses the orbit solution under the low-precision model as the initial value, guiding the solution process to gradually approach the high-fidelity solution under the MGA-SOI-DSM model. This provides a good initial value guess for subsequent high-precision orbit corrections, effectively avoiding optimization divergence problems caused by model mutations, and significantly improving the stability and convergence of the solution process.

[0025] Achieving rapid, high-precision trajectory design throughout the entire process: A segmented target-based correction method is proposed, constrained by the consistency of key node states from "entering the influence sphere—leaving the influence sphere—reaching the deep-space maneuver point." Under a high-precision multibody dynamics model, each trajectory segment is successively corrected to ensure the continuous consistency of states at key event nodes, ultimately obtaining a high-precision transfer trajectory that satisfies multibody dynamics constraints throughout the entire process. This method balances global search capability with local convergence accuracy, enabling the rapid acquisition of engineering-usable high-precision trajectory solutions with reasonable computational cost.

[0026] It has good engineering applicability and scalability: This invention does not depend on a specific flight sequence or propulsion method, and can be flexibly applied to solar system edge exploration missions with different planetary lever combinations and terminal constraints, providing a general technical solution for the orbit design of future ultra-long-range deep space exploration missions. Attached Figure Description

[0027] Figure 1 This is a flowchart of a high-precision pulse transfer orbit optimization method for solar system boundary exploration according to the present invention;

[0028] Figure 2 This is a schematic diagram of the transfer orbit optimization model integrating MGA-SOI-DSM according to an embodiment of the present invention;

[0029] Figure 3 This is a schematic diagram of the optimized high-precision pulse transfer orbit for exploring the edge of the solar system, taking the Earth-Jupiter-Saturn-nose tip flight sequence as an example. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] This invention proposes a high-precision pulse transfer orbit optimization method for solar system boundary exploration. The core of this method lies in the MGA-SOI-DSM (Multiple Gravity Assist with Sphere of Influence and Deep Space Maneuvers) model. Based on the traditional MGA-DSM framework, it introduces hyperbolic orbital dynamics modeling within the sphere of gravitational influence (SOI), enabling continuous splicing of orbital states under different central bodies inside and outside the SOI. Simultaneously, a homotopy extension strategy is employed, gradually expanding the SOI radius from zero to the actual scale, smoothly transitioning the optimization problem from a simplified model to a complete model. This guides the solution results to gradually approximate the orbital solution under the MGA-SOI-DSM model, effectively improving the stability and convergence of the solution process. Furthermore, a high-precision orbital target-shooting correction method based on a multibody dynamics model is proposed. With the goal of minimizing the state error at key event nodes, segmented target-shooting achieves full-process orbital refinement, ultimately forming a high-precision integrated transfer orbit design method for solar system boundary exploration missions.

[0032] like Figure 1 As shown, the method specifically includes:

[0033] Step S1: Given the constraints of the solar system boundary exploration mission and the leverage flight sequence, construct a high-precision orbital dynamics model that includes gravitational perturbations from multiple celestial bodies, providing a unified dynamic basis for subsequent orbit optimization and correction;

[0034] Step S2: Establish a transfer trajectory optimization model that considers multi-body leverage and deep space maneuver (MGA-DSM), use the differential evolution algorithm (DE) for global search, and combine it with the interior-point method for local fine optimization to obtain the initial transfer trajectory solution;

[0035] Step S3: Based on the dynamic processes within the planetary gravitational influence sphere (SOI), a transfer orbit optimization model integrating MGA-SOI-DSM is established. A homotopy extension strategy is used to progressively expand the SOI radius. Using the initial transfer orbit solution obtained in Step S2 as the initial value, global and local optimization methods are combined for iterative solution to obtain an optimized transfer orbit solution that satisfies the SOI boundary continuity condition.

[0036] Step S4: Under the high-precision orbital dynamics model, using the optimized transfer trajectory solution obtained in step S3 as the initial value, the trajectory at each stage is successively corrected by the target shooting method to ensure the consistency of the state of key event nodes (SOI entry and exit points and deep space maneuver points) and obtain a high-precision transfer trajectory that meets the mission constraints throughout the entire process.

[0037] Furthermore, step S1 includes the following steps:

[0038] First, the constraints of the solar system boundary exploration mission are that the probe's heliocentric distance, ecliptic longitude, and ecliptic latitude at the target time must meet the range requirements corresponding to the solar system boundary region; the establishment of a unified reference coordinate system includes: the heliocentric ecliptic inertial frame (HEI), the planetary central ecliptic inertial frame, and the B-plane coordinate system.

[0039] The HEI coordinate system is defined as follows: with the Sun's center of mass as the origin, the X-axis points towards the mean vernal equinox at epoch J2000.0, the Z-axis is perpendicular to the mean ecliptic plane and points towards the North Celestial Pole, and the Y-axis is determined by the right-hand rule.

[0040] The planetary center ecliptic inertial coordinate system is aligned with the axes of the HEI, except that the origin of the coordinate system is shifted to the corresponding planetary center of mass.

[0041] The B-plane coordinate system is defined as follows: with the target planet's center of mass as the origin, the X-axis points in the direction of the hyperbolic residual velocity vector when the probe enters the SOI, the Y-axis points in the direction of the vector obtained by the cross product of the X-axis and the normal to the planet's orbital plane, and the Z-axis forms a right-handed coordinate system with the X-axis and Y-axis.

[0042] A high-precision heliocentric orbital dynamics model considering the gravitational perturbations of the eight planets and the Moon is constructed, and its equations of motion are as follows:

[0043] (1)

[0044] in, , and are the position vectors of the probe, the p-th planet, and the moon in the HEI coordinate system, respectively; , and Let be the gravitational constants of the Sun, the p-th planet, and the Moon, respectively, with the superscript · indicating the second derivative. This represents the modulus of a vector.

[0045] In this embodiment of the invention, the glide path sequence is pre-set based on the actual energy requirements and target direction of the solar system boundary exploration mission. As shown in the following embodiments, starting from Earth, the probe passes through Jupiter and Saturn in sequence for glide path borrowing, with the final target being the nose region of the solar system boundary. This sequence utilizes the large mass and suitable positional distribution of Jupiter and Saturn, gradually increasing the probe's heliocentric orbit energy through two planetary glide paths, enabling it to reach the solar system boundary region at a long distance, in a high ecliptic latitude or a specific ecliptic longitude direction, under the constraints of limited launch energy and deep-space maneuver speed increments. The choice of glide path sequence is not limited to this; it can be flexibly adjusted according to the target direction, mission window, and launch energy, such as using an Earth-Jupiter-Uranus-Neptune sequence or other combinations. The method of this invention has good versatility and scalability.

[0046] Furthermore, step S2 includes the following steps:

[0047] A solar system boundary exploration transfer trajectory optimization model considering multi-body glide and deep space maneuver (MGA-DSM) is constructed. Based on the conic section splicing principle, this model equates the planetary glide process to an instantaneous process, where the probe's heliocentric position vector remains unchanged before and after the glide, while the heliocentric velocity vector undergoes an instantaneous jump. Simultaneously, a deep space maneuver (DSM) is considered between any two adjacent glide attempts. Based on two-body dynamics orbit recursion and Lambert's problem solving, and combined with B-plane parameters to characterize the state changes before and after the glide, the position and velocity vectors before and after the DSM and the glide can be obtained, allowing for the calculation of the corresponding velocity increments and the construction of a complete multi-segment transfer trajectory solution.

[0048] For missions exploring the edge of the solar system, the objective is to reach a region of space that meets distance and orientation constraints at a given epoch, rather than to rendezvous with a specific planet. Therefore, after the final glide flight, no deep-space maneuvers are performed; instead, a heliocentric two-body orbit is directly calculated to reach the target time. Let the number of glide objects be m; then the optimization problem contains 4m + 4 decision variables, which together constitute the decision vector. .in For the launch time, , and These represent the magnitude of the residual velocity of the escape hyperbola, ecliptic longitude, and ecliptic latitude, respectively. This represents the transfer time coefficient between two adjacent celestial bodies that utilize gravity. This represents the time coefficient for deep-space maneuvering between two adjacent celestial bodies that utilize different gravitational pull. This indicates the radius of gravity of different celestial bodies that provide leverage. This represents the B-plane angle for different celestial bodies that provide leverage. The constraint condition is that the detector is at the target time... heliocentric distance Yellow Classic He Huang Wei The preset interval constraints are met. Based on this, and with the goal of minimizing the sum of all deep-space maneuver velocity increments throughout the mission, the transfer trajectory optimization model is established as follows:

[0049] (2)

[0050] in, Let be the objective function. Indicates the first The magnitude of the speed increment during deep space maneuvers; This indicates that within the MGA-DSM model framework, the decision vector... Nonlinear dynamic relationships mapped to velocity increments and terminal states; , , , and These represent the lower limit of the heliocentric distance, the lower limit of ecliptic longitude, the upper limit of ecliptic longitude, the lower limit of ecliptic latitude, and the upper limit of ecliptic latitude corresponding to the outer regions of the solar system.

[0051] In solving the optimization problem, a differential evolution algorithm is used for global search to obtain an initial solution with good feasibility. Based on this, an interior point method is introduced to perform local fine-tuning, thereby obtaining the initial transfer trajectory solution under the heliocentric two-body dynamic model. The methods used are conventional algorithms for those skilled in the art and will not be elaborated further here.

[0052] Furthermore, step S3 includes the following steps:

[0053] Considering the dynamic processes within the planetary gravitational influence sphere (SOI), a transfer orbit optimization model integrating multi-body leverage-SOI-DSM (MGA-SOI-DSM) is constructed, such as... Figure 2 As shown, a unified description and continuous splicing of the heliocentric two-body transfer orbit and the hyperbolic orbit within the sphere affected by planetary gravity are achieved.

[0054] First, a model of the Earth launch phase is constructed. The probe moves along a hyperbolic escape trajectory within the Earth's SOI, assuming... The time detector is located at the perigee position of a hyperbolic orbit, given a perigee radius of... Select the orbital inclination angle in the geocentric ecliptic inertial coordinate system. Longitude of ascending node Perigeal argument and the magnitude of the hyperbola's residual velocity As an optimization variable, the semi-major axis is calculated based on the hyperbolic orbital relationship. ( (representing the gravitational constant) and eccentricity Thus, the equation of the hyperbolic orbit is established. f represents the true anomaly angle in the hyperbolic orbit.

[0055] By setting in the hyperbolic orbit equation ( (Based on the radius of the Earth's influence sphere), the true anomaly angle when the probe reaches the boundary of the Earth's SOI can be obtained. And the flight time required for the probe to move from perigee to the SOI boundary. Among them, the hyperbolic near point angle This allows us to determine the moment when the probe reaches the Earth's SOI boundary. ,as well as The position vector of the time detector relative to the Earth and velocity vector By combining precise ephemeris data, the heliocentric position vector of Earth at the same moment can be obtained. and the corresponding velocity vector This leads to the conversion of the detector's... The heliocentric position vector at time and velocity vector .

[0056] Subsequently, the process was recursively advanced to the [number]th ... The time of the i-th deep space maneuver (it should be noted that there is a one-to-one correspondence between the i-th deep space maneuver and the i-th leveraging celestial body) Obtain the heliocentric position vector at the moment of maneuver. and the heliocentric velocity vector at the instant before the maneuver .in, Indicates that the probe left the first The SOI boundary of the leveraging celestial body until reaching the first The transfer time between the SOI boundaries of each leveraging celestial body Indicates the detector at the The transfer time within a single SOI (Self-Propelled Object) is different from that in the MGA-DSM model. ,use This represents the deep space maneuver time coefficient in the MGA-SOI-DSM model. The probe reaches the... The moment when leveraging the SOI boundary of a celestial body is Assuming the first The radius of the sphere influenced by the influence of a celestial body. The ecliptic longitude and ecliptic latitude of the detector at the SOI boundary of this celestial body are respectively and Then, at this moment, the position vector of the probe relative to the celestial body that is being used is .therefore, The heliocentric position vector of the time detector is ,in This is the heliocentric position vector of the celestial body at the same moment (obtained from precise ephemeris).

[0057] Next, according to and and transfer time By solving the Lambert problem, we can obtain the detector's speed from the first... The deep-space maneuver continued until reaching the... The heliocentric two-body trajectory, obtained by leveraging the SOI boundary process of a celestial body, thus yields the first... Instantaneous velocity vector after maneuvering at the sub-deep space moment And the probe reached the The heliocentric velocity vector at the boundary of the SOI (Solar Injection Object) Therefore, the detector's first Sub-deep space maneuver speed increment is The hyperbolic residual velocity of the probe at the boundary of the SOI (Solar Orbital Intrusion) object. ,in This is the heliocentric velocity of the lever object (obtained from precise ephemeris) when the probe reaches the SOI boundary. and The hyperbolic orbital elements of the probe, which are influenced by celestial bodies, can be obtained through conversion. and orbital equations ,make The true anterior angle of the detector at the point where it leaves the SOI boundary is obtained. And influencing the flight time within the sphere ,in This allows us to determine the moment when the detector leaves the SOI boundary. And the position vector of the probe relative to the celestial body at that moment. and velocity vector Thus, the detector's position is determined. The heliocentric position vector at time and velocity vector ,in, and These are the heliocentric position vector and velocity vector of the celestial body that are being used for propulsion. (Obtained from precise ephemeris).

[0058] Finally, based on the probe's position and velocity vectors obtained above, the same solution process and calculation methods are used to sequentially calculate the trajectories for each subsequent deep-space maneuver, the pre-flyaway transfer phase, and the flight phase within the influence sphere, until the probe leaves the SOI of the last flyaway object. Afterward, the orbit is extrapolated to the target time, and the probe's heliocentric distance and orientation parameters are checked to ensure they meet mission constraints. Through this method, the consistency between the probe's heliocentric transfer trajectory and its trajectory within the influence sphere of the flyaway object in terms of time, position, and velocity is achieved, thereby improving the accuracy of the overall orbit modeling.

[0059] Based on the above modeling process, the transfer orbit optimization model integrating MGA-SOI-DSM is established as shown below. For models containing... For this mission involving leveraging flight, the model has a total of 4m+5 decision variables, and the corresponding decision vector is:

[0060] .

[0061] The transfer orbit optimization model is as follows:

[0062] (3)

[0063] in, Represents the decision vector under the MGA-SOI-DSM model framework. Nonlinear dynamic relationships mapped to velocity increments and terminal states.

[0064] During the optimization process, the transfer trajectory solution obtained based on the MGA-DSM model was used as the initial solution for the MGA-SOI-DSM model. However, the two models have fundamental differences in their definitions of transfer time: in the MGA-DSM model, the transfer time for each segment... Defined as the flight time of the probe between the positions of the center of mass on two adjacent days; while in the MGA-SOI-DSM model, the transition time for each segment... Defined as the flight time of the probe from the boundary of the initial planet's gravitational influence sphere (SOI) to the boundary of the target planet's SOI, excluding the probe's motion time within the SOI. This difference will lead to significant time skew when the SOI scale is large, making it difficult to directly convert the initial solution parameters provided by the MGA-DSM model into MGA-SOI-DSM model parameters. This will hinder optimization initiation and may also reduce optimization convergence.

[0065] To address this, a homotopy extension strategy is introduced to improve the optimization process: in the initial stage, the SOI radii of each planet are scaled to construct a simplified problem closer to the MGA-DSM model; subsequently, during the iteration process, the SOI radii are gradually restored to the actual scale, allowing the optimization problem to smoothly transition from the simplified model to the complete model. At each homotopy step, a differential evolution algorithm is used for global search, combined with an interior point method for local fine-tuning. Through this stepwise approximation process, the optimized transfer orbit solution corresponding to the actual SOI scale is finally obtained.

[0066] Furthermore, step S4 includes the following steps:

[0067] Using the optimized transfer orbit solution obtained from the MGA-SOI-DSM model as the initial solution, target-based corrections were sequentially applied to each orbital segment under a high-precision multibody dynamics model. First, the Earth launch segment was corrected by adjusting the probe's perigee velocity vector to ensure its state upon leaving the Earth's SOI under the high-precision dynamics model was consistent with the corresponding state in the optimized transfer orbit solution. Then, the orbit was integrated to the moment of the first deep-space maneuver, and this maneuver was adjusted for the first time to ensure the probe's state upon entering the target planet's SOI under the high-precision dynamics model was consistent with the state in the optimized transfer orbit solution. Based on this, a second adjustment was made to the maneuver to further constrain the consistency of its state upon leaving the target planet's SOI. Finally, a third adjustment was made to ensure the consistency of its state upon reaching the next DSM moment.

[0068] According to the above strategy, the first m-1 deep space maneuvers are adjusted sequentially, and the corresponding orbit segments are corrected by targeted shots. For the m-th deep space maneuver, in addition to the first and second adjustments according to the above strategy, a third adjustment is made with the target that the heliocentric distance and direction parameters of the probe at the target time satisfy the constraint conditions in equation (3), and the orbit of the transfer segment to the edge region of the solar system after leaving the last planetary influence sphere is corrected by targeted shots.

[0069] Through the above segmented target correction process, a high-precision multi-body glide transfer trajectory that satisfies multibody dynamics constraints is finally obtained.

[0070] Example:

[0071] refer to Figure 3 Taking, for example, a mission launched from Earth that, after receiving gravitational pull from Jupiter and Saturn, finally reaches the tip of the solar system's edge:

[0072] Step S1: Given the constraints of the solar system boundary exploration, the probe at the target time... heliocentric distance Yellow Classic He Huang Wei Satisfying equation (2), where the lower limit of the heliocentric distance of the solar system boundary region in the direction of the nose tip. Lower limit of ecliptic longitude Upper limit of ecliptic longitude Huang Wei lower limit Yellow latitude upper limit The given propulsion sequence is: Earth starts – Jupiter propels – Saturn propels – reaches the tip of the solar system's edge. A high-precision heliocentric orbital dynamics model considering the gravitational perturbations of the eight planets and the Moon is constructed. The gravitational constants of the Sun, the eight planets, and the Moon in the equations of motion are taken as follows: , , , , , , , , and .

[0073] Step S2: Establish a transfer orbit optimization model considering MGA-DSM. The range of values ​​for the optimization variables is given based on the probe's Earth launch time. The magnitude of the remaining velocity of the escape hyperbola Yellow Classic He Huang Wei Earth-Jupiter transfer time Jupiter-Saturn transit time Deep space maneuver time coefficient , leverage radius , plane B angle , Based on the above optimization model and input conditions, a differential evolution algorithm is used for global search to obtain an initial solution with good feasibility. Under this initial solution, the heliocentric distance of the probe at the target time is 82.3649 AU, and the ecliptic longitude and latitude are 254.3493° and 3.9617°, respectively, both satisfying the constraints. The total velocity increment during flight is 2.4432 km / s. Based on this, the interior point method is introduced to carry out local fine optimization, thereby obtaining the initial transfer trajectory solution under the heliocentric two-body dynamic model. The heliocentric distance of the probe at the target moment corresponding to this transfer orbit solution is 80.1955 AU, with ecliptic longitude and latitude of 256.3837° and 1.4076° respectively, both satisfying the constraints. The total velocity increment during the flight is... km / s.

[0074] Step S3: Considering the dynamic processes within the planetary gravitational influence sphere (SOI), construct a transfer orbit optimization model that integrates multi-body leverage-gravitational influence sphere-deep space maneuver (MGA-SOI-DSM), such as... Figure 2 As shown, a unified description and continuous stitching of the heliocentric and planetary orbits are achieved. First, a transfer orbit optimization model integrating MGA-SOI-DSM is established. Launch time With transfer orbit solution The corresponding time is consistent, escape The range of values ​​for is the transfer orbit solution. Neighborhood of relevant parameters The range of values ​​for the escape hyperbolic trajectory element is: , , Earth-Jupiter transfer time The range of values ​​for is the transfer orbit solution. Neighborhood of relevant parameters Jupiter-Saturn transit time The range of values ​​for is the transfer orbit solution. Neighborhood of relevant parameters Earth-Jupiter transfer deep space maneuver time coefficient Jupiter-Saturn transfer deep space maneuver time coefficient The longitude of the ecliptic when the probe enters Jupiter He Huang Wei The ecliptic longitude of the planet when the probe enters Saturn He Huang Wei Based on the aforementioned transfer orbit optimization model, using a homotopy step size of 1 / 1000 of the radius of the gravitational influence sphere, the SOI radii of the gravitational influence spheres for Jupiter and Saturn's gravitational pull are progressively expanded from zero to the full real scale (Jupiter 48,182,823.822 km, Saturn 54,569,596.582 km). At each SOI scale, a differential evolution algorithm is used for global search, combined with interior point method for local fine optimization. The optimization result of the current stage is used as the initial value for the next stage. Through this homotopy extension iterative process, the optimized transfer orbit solution under the real SOI scale is finally obtained. The heliocentric distance of the probe target at the time corresponding to this transfer orbit solution is 85.0956 AU, and the ecliptic longitude and latitude are 253.9387° and 4.4557°, respectively, both of which satisfy the constraint conditions. The total velocity increment during the flight process is 0.0033 km / s.

[0075] Step S4: Using the optimized transfer trajectory solution obtained from the MGA-SOI-DSM model as the initial value, the target-shooting iterative correction is performed sequentially on each orbital segment under the high-precision multibody dynamics model, resulting in the following: First, during the Earth launch phase, the probe needs to apply a pulse velocity increment of 0.0011 km / s at perigee to ensure that its position and velocity state when leaving the Earth's gravitational influence sphere are consistent with the calculated results of the optimized transfer trajectory solution. Second, to ensure that the orbital state of the probe when reaching the second deep-space maneuver point under the high-precision dynamics model is consistent with the results of the optimized transfer trajectory solution, a velocity increment of 0.0419 km / s needs to be applied at the moment of the first deep-space maneuver. Finally, to ensure that the heliocentric distance and direction parameters at the target moment satisfy the constraints shown in equation (3), a velocity increment of 0.1511 km / s also needs to be applied at the moment of the second deep-space maneuver.

[0076] Through the above-described segmented target-firing iterative correction process, a multi-body glide transfer orbit for solar system boundary exploration in the nose-tip direction, satisfying all constraints under a high-precision multibody dynamics model, was finally obtained. Figure 3 As shown, the corresponding total pulse velocity increment is 0.1941 km / s. That is, after sequentially passing through Earth for launch, Jupiter for gravity assist, and Saturn for gravity assist, the probe finally accurately reaches the nose region of the solar system's edge (the figure shows curves or coordinates of the transfer orbit, deep-space maneuver point, Earth, Jupiter, Saturn, launch time position, and target time position, respectively, using curves of different colors). The entire trajectory remains continuous and smooth at each key node, demonstrating the effectiveness of the MGA-SOI-DSM-integrated transfer orbit optimization model and homotopy extension strategy, as well as the good convergence performance of the segmented target correction method under a high-precision multibody dynamics model. This invention provides a fast, reliable, and high-precision integrated design method for pulse transfer orbits for solar system edge exploration missions.

[0077] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for optimizing high-precision pulse transfer orbits for solar system boundary exploration.

[0078] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned method for optimizing high-precision pulse transfer orbits for solar system boundary exploration.

[0079] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing a high-precision impulsive transfer orbit for a solar system margin exploration, characterized in that, include: Step S1: Given the constraints of the solar system boundary exploration mission and the leverage flight sequence, construct a high-precision orbital dynamics model that includes gravitational perturbations from multiple celestial bodies; Step S2: Establish a transfer trajectory optimization model that considers multi-body leverage and deep space maneuvering, use the differential evolution algorithm for global search, and combine it with the interior point method for local fine optimization to obtain the initial transfer trajectory solution; Step S3: Based on the dynamic process within the planetary gravitational influence sphere, establish a transfer orbit optimization model that integrates multi-body leverage, gravitational influence sphere and deep space maneuvering. Use the homotopy extension strategy to gradually expand the radius of the gravitational influence sphere. Using the initial transfer orbit solution as the initial value, combine global and local optimization methods to iteratively solve the problem and obtain an optimized transfer orbit solution that satisfies the boundary continuity condition of the gravitational influence sphere. Step S4: Under the high-precision orbit dynamics model, using the optimized transfer orbit solution as the initial value, the trajectory at each stage is successively corrected using the target shooting method to ensure the consistency of the state of key event nodes and obtain a high-precision transfer orbit that satisfies the mission constraints throughout the entire process.

2. The method of claim 1, wherein, In step S1, the constraints of the solar system boundary exploration mission are that the probe's heliocentric distance, ecliptic longitude, and ecliptic latitude at the target time meet the range requirements corresponding to the solar system boundary region; the constructed high-precision orbital dynamics model adopts the heliocentric ecliptic inertial coordinate system and considers the gravitational perturbations of the eight planets and the moon.

3. The high-precision pulse transfer orbit optimization method for solar system boundary exploration according to claim 1, characterized in that, In step S2, the transfer orbit optimization model considering multi-body glide and deep-space maneuver is constructed based on the conic section splicing principle, equating planetary glide flight to an instantaneous process, with the probe's heliocentric position remaining unchanged before and after the glide. The deep-space maneuver is set in the heliocentric transfer arc between two adjacent glides, and no deep-space maneuver is applied during the flight towards the edge of the solar system after the last glide. The differential evolution algorithm is used to perform a global search on the transfer orbit optimization model considering multi-body glide and deep-space maneuver. The result of the global search is used as the initial value, and the interior point method is used for local fine optimization to obtain the initial transfer orbit solution that satisfies the constraints.

4. The high-precision pulse transfer orbit optimization method for solar system boundary exploration according to claim 1, characterized in that, In step S3, an optimized transfer orbit model is established that integrates multi-celestial body leverage, gravitational influence sphere, and deep space maneuvering. By explicitly modeling the hyperbolic orbit of the probe within the planetary gravitational influence sphere and combining it with precise planetary ephemeris data, the transfer orbits of the probe in the Earth launch segment, the interplanetary transfer segment, the transfer segment within the planetary influence sphere, and the transfer segment to the edge region of the solar system after leaving the last planet are obtained, and the continuous splicing of each orbit segment is achieved.

5. The high-precision pulse transfer orbit optimization method for solar system boundary exploration according to claim 1, characterized in that, In step S3, the homotopy extension strategy is as follows: using the initial transfer orbit solution as the initial value, the radius of the gravitational influence sphere of each planet is scaled in the initial stage, and then the radius of the gravitational influence sphere is gradually restored to the actual scale during the iteration process, so that the optimization problem smoothly transitions from a simplified model to a complete model. Under each homotopy step, the optimized solution under the gravitational influence sphere radius corresponding to the current step is used as the initial value of the next step. The differential evolution algorithm is used for global search, and the interior point method is combined for local fine optimization, gradually approximating until the optimized transfer orbit solution under the actual gravitational influence sphere scale is obtained.

6. The high-precision pulse transfer orbit optimization method for solar system boundary exploration according to claim 1, characterized in that, In step S4, key event nodes include the probe entering the boundary node of the planet's gravitational influence sphere, leaving the boundary node of the planet's gravitational influence sphere, and the deep space maneuver node.

7. The high-precision pulse transfer orbit optimization method for solar system boundary exploration according to claim 1, characterized in that, In step S4, the specific method of successively correcting the trajectory at each stage using the target-shooting method is as follows: taking the optimized transfer trajectory solution as the initial value, the Earth launch segment is first corrected by adjusting the perigee velocity vector of the probe to ensure the consistency of its state when leaving the Earth's influence sphere; then, the trajectories of the interplanetary transfer, the transfer within the planetary influence sphere, and the transfer segment from the last planet to the edge of the solar system are corrected in sequence. When adjusting the first few deep-space maneuvers, the consistency of the state at key event nodes is used as a constraint; when adjusting the last deep-space maneuver, the goal is to ensure that the consistency of the state at key event nodes and the heliocentric distance and direction parameters of the probe at the target time meet the constraint conditions. Through target-shooting optimization, a high-precision transfer trajectory that meets the high-precision multibody dynamics constraints throughout the entire process is gradually obtained.

8. The high-precision pulse transfer orbit optimization method for solar system boundary exploration according to claim 1, characterized in that, The final high-precision transfer orbit obtained throughout the entire process is a multi-body transfer orbit that satisfies the constraints of heliocentric distance, ecliptic longitude, and ecliptic latitude in the solar system boundary exploration mission under a high-precision orbital dynamics model.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the high-precision pulse transfer orbit optimization method for solar system boundary exploration as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the high-precision pulse transfer orbit optimization method for solar system boundary exploration as described in any one of claims 1-8.

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