A method for jointly reconstructing a lunar mission rocket trajectory and a spacecraft orbit

Abstract

The application discloses a method for jointly reconstructing a moon-exploring mission rocket trajectory and a spaceship orbit, which comprises the following steps: S1, after a thrust drop fault occurs in a third flight section of a carrier rocket, judging whether to continue to execute a moon-racing mission; S2, if the execution is continued, determining an initial equivalent start time and initial transfer orbit parameters under a current fault condition based on an orbit perigee equivalent conversion method; S3, obtaining new transfer orbit parameters that satisfy orbit around the moon constraints and match a time of a transfer between the earth and the moon; S4, solving a reconstructed trajectory of the rocket and corresponding actual entry point states and an actual entry time; and S5, calculating a transfer time from an orbit perigee corresponding to the actual entry point states to the actual entry point. After the thrust drop fault occurs in the carrier rocket, the rocket flight trajectory and the spaceship transfer orbit between the earth and the moon can be quickly and cooperatively reconstructed on line, so that the spaceship can still enter the orbit around the moon according to the mission requirements under the fault condition.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, specifically to a method for jointly reconstructing the trajectory of a rocket and the orbit of a spacecraft in a lunar exploration mission. Background Technology

[0002] In lunar exploration missions, the first step is to use a launch vehicle to send the spacecraft into a pre-set Earth-Moon transfer orbit. Among various failure modes, a decrease in propulsion system thrust is one of the most common non-fatal failures. From a guidance and control perspective, how to rationally utilize the rocket's remaining payload capacity and replan the flight trajectory online after such a failure to send the spacecraft into a feasible Earth-Moon transfer orbit is a key capability for improving the reliability and autonomy of lunar exploration missions. Online ballistic-orbit joint planning and guidance reconfiguration technology, as an effective means to achieve this goal, has become an important development direction for future intelligent launch vehicles, sparking extensive research. However, unlike low Earth orbit missions, deep space exploration missions require spacecraft not only to survive after a failure but also to complete the mission of flying to a specific target celestial body (such as the Moon). This necessitates that the launch vehicle's failure reconfiguration must fully consider its complex impact on the spacecraft's subsequent transfer orbit. Because of the continuous relative motion between the Earth and the Moon, simple trajectory replanning may send the rocket into a new orbit, but it cannot guarantee that the Earth-Moon transfer process will still be feasible after the spacecraft separates from that orbit, or that it can form a lunar orbit that meets the mission requirements at the predetermined time.

[0003] Currently, research on online mission reconfiguration after launch vehicle failures mainly focuses on low Earth orbit missions. For example, related methods aim to send spacecraft into their original target orbit or a degraded rescue orbit (such as a parking orbit) after a failure. These studies emphasize rapid replanning and guidance of the rocket trajectory itself, without incorporating the characteristics of the spacecraft's subsequent deep space transfer orbit, especially the spatiotemporal dynamic coupling relationship of the Earth-Moon system, into a unified guidance reconfiguration framework. On the other hand, in the field of Earth-Moon transfer orbit design, many studies have focused on the optimization and characteristic analysis of the orbit itself, such as using conic section splicing and overlapping conic section methods for preliminary orbit design. However, these studies usually assume that the starting point (entry point) of the transfer orbit is predetermined and ideal, falling within the scope of offline mission planning.

[0004] In summary, the shortcomings of existing technologies are as follows: 1. Fault reconstruction methods for near-Earth missions do not consider the spatiotemporal constraints caused by the relative motion of celestial bodies in deep-space transfer missions, and the reconstruction results cannot guarantee the feasibility of subsequent lunar missions. 2. Online reconstruction of rocket trajectories and design of spacecraft transfer orbits are usually two separate processes. When a fault occurs, how to quickly and collaboratively determine a "joint optimal" orbit that is both reachable by the faulty rocket and ensures the successful completion of the subsequent Earth-Moon transfer based on the rocket's real-time remaining capacity is still a blank area of ​​research. 3. After a fault, how the reconstructed orbital entry point (position and time) of the rocket specifically affects the subsequent Earth-Moon transfer process, and how to dynamically search for and lock a suitable transfer orbit based on this, lacks a systematic solution. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the present invention aims to provide a method for the joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions. This method can reconstruct the rocket flight trajectory and spacecraft Earth-Moon transfer orbit online, quickly, and collaboratively after a launch vehicle experiences a thrust reduction failure, so as to ensure that the spacecraft can still enter lunar orbit as required by the mission under failure conditions.

[0006] To achieve the objectives of this invention, the following solution is adopted: A method for jointly reconstructing the trajectory of a lunar exploration mission rocket and the orbit of a spacecraft includes the following steps: S1. After a thrust reduction failure occurs during the third stage of the launch vehicle, determine whether to continue the lunar mission based on the rocket's status and remaining payload capacity at the time of the failure. S2. If execution continues, determine the initial equivalent departure time and initial transfer orbit parameters under the current fault conditions based on the orbit perigee equivalent conversion method. S3. Based on the initial equivalent departure time and initial transfer orbit parameters, call the transfer orbit search method to obtain new transfer orbit parameters that satisfy the lunar orbit constraints and match the Earth-Moon transfer time. S4. Using the new transfer orbit parameters as the target orbit, call the rocket trajectory reconstruction method to solve for the reconstructed trajectory of the rocket and the corresponding actual orbit insertion point state and actual orbit insertion time. S5. Calculate the transfer time from the orbital perigee corresponding to the actual orbital entry point state to the actual orbital entry point, and determine whether the equivalent departure condition is met based on the actual orbital entry time. S6. If not satisfied, update the equivalent departure time and return to step S3 for iteration; if satisfied, output the joint reconstruction result, including the reconstructed rocket trajectory and the spacecraft's Earth-Moon transfer orbit that satisfies the time matching.

[0007] Furthermore, in step S2, the orbital perigee equivalent transformation method includes: The Earth-Moon transfer motion of the spacecraft starting from its actual orbital insertion point is equivalently converted into the motion of the spacecraft starting from its orbital perigee. Among them, the equivalent departure time of orbital perigee Determined according to the following formula: In the formula, The actual orbital insertion time is mentioned. The orbital transfer time from the orbital perigee to the actual orbital entry point is calculated using Kepler's equations of motion based on the orbital elements at the actual entry point.

[0008] Further, in step S3, the transfer trajectory search method is a time-matching search method based on the overlapping conic section method, including: S3.1. Based on the current equivalent departure time and lunar orbit parameters, estimate the entry time into the lunar center orbit; S3.2. Use the overlapping conic section method to calculate the Earth-Moon transfer time and transfer orbit parameters; S3.3 Determine whether the deviation between the estimated lunar orbit entry time and the current equivalent departure time plus the Earth-Moon transfer time meets the convergence condition; S3.4 If not satisfied, update the estimated lunar orbit entry time and repeat steps S3.2 to S3.3 until convergence, to obtain the transfer orbit parameters that satisfy the time matching.

[0009] Furthermore, in step S4, the rocket trajectory reconstruction method is a trajectory reconstruction method based on sequential convex optimization, including: S4.1 Establish a rocket trajectory optimization model with the minimum fuel consumption as the performance index, which includes the first flight stage, the glide stage, and the second flight stage of the third stage; S4.2 Set the initial reference trajectory, and perform convex approximation and discretization on the dynamic equations and terminal trajectory constraints in the optimization model to form a convex optimization subproblem; S4.3 Iteratively solve the convex optimization subproblem: In each iteration, construct and solve the convex subproblem based on the current reference trajectory to obtain the optimized trajectory. Then update the reference trajectory with the optimized trajectory until the solution converges, and finally output the reconstructed trajectory that satisfies the terminal trajectory constraint.

[0010] Furthermore, the thrust reduction failure is a non-fatal failure caused by a decrease in engine flow rate per second, which occurs during the first or second startup phase of the third stage of the rocket.

[0011] Furthermore, in step S5, the method for determining whether the equivalent starting condition is met is as follows: Calculate the actual orbit insertion time Subtract the transfer time from the orbital perigee to the actual orbital insertion point. The value of is the equivalent start time set in this iteration. Compare; If the absolute deviation between the two is less than the preset convergence threshold, it is determined that the equivalent starting condition is met.

[0012] Furthermore, the overlapping conic section method includes the following steps: Based on the relative motion relationship between the Earth and the Moon and introducing a pseudo-state sphere, an orbital model of the Earth-centered two-body segment is constructed inside the pseudo-state sphere, and an orbital model of the Moon-centered two-body segment is constructed outside the pseudo-state sphere. The position and velocity of the pseudo-state point are solved by iterative algorithm, so that the orbit models of the geocentric two-body segment and the lunar two-body segment meet the continuity conditions of position and velocity at the boundary of the pseudo-state sphere, and the two orbit segments are smoothly spliced. Based on the smoothly stitched orbit, the state parameters of the transfer orbit at perigee and the total transfer time from perigee to the lunar center orbit entry point are calculated by reverse calculation.

[0013] Furthermore, the convexity approximation and discretization processing in step S4.2 are achieved by performing the following operations on the dynamic equations in the rocket trajectory optimization model: A first-order Taylor expansion of the dynamic equations is performed at a given reference trajectory to achieve a linearized convexity approximation. A first-order discretization-preserving method is used to transform the continuous dynamic equations after convexity approximation into the dynamic equations of a discrete linear system.

[0014] Furthermore, the lunar orbit constraints include the lunar distance and orbital inclination. The Earth-Moon transfer time matching condition refers to the condition that after the spacecraft undergoes Earth-Moon transfer motion from the equivalent departure time, it can reach the lunar center orbit entry point that satisfies the lunar orbit constraints at a predetermined time.

[0015] Furthermore, the method for joint reconstruction of rocket trajectory and spacecraft orbit in lunar exploration missions is applicable to lunar exploration missions that use the Hohmann transfer method for Earth-Moon transfer.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention fundamentally solves the mission coupling problem caused by the relative motion between the Earth and the Moon. Addressing the deficiency of existing fault reconstruction methods in not considering the spatiotemporal dynamics of deep space transfer missions, this invention introduces an "orbital perigee equivalent conversion method." This method converts the complex Earth-Moon transfer motion at the spacecraft's orbital insertion point into an equivalent motion originating from the orbital perigee, thereby establishing a clear spatiotemporal mapping relationship between the rocket trajectory (orbital insertion point and time) and the spacecraft orbit (subsequent Earth-Moon transfer). This enables a systematic analysis and assurance of the feasibility of subsequent lunar missions after rocket failure, overcoming the inherent drawback of existing near-Earth orbit reconstruction strategies potentially leading to mission failure when directly applied to lunar exploration missions.

[0017] 2. This invention achieves true integrated optimization of rocket trajectory and spacecraft orbit. It abandons the traditional model of separating trajectory reconstruction and orbit design, creatively proposing a sequential iterative joint reconstruction framework. By cyclically executing the two sub-problems of "orbit search" and "trajectory reconstruction," and using the "equivalent launch condition" as the convergence criterion, it ultimately outputs a joint scheme that can be achieved by a failed rocket and ensures the spacecraft accurately enters the target lunar orbit. This maximizes the overall mission benefit under limited remaining payload capacity and significantly improves the probability of mission success in the event of a failure.

[0018] 3. This invention ensures both the speed and engineering practicality of online reconfiguration. Addressing the stringent computational speed requirements of fault handling, this invention employs efficient algorithms in key stages. In the orbit search subproblem, the overlapping conic section method based on pseudo-state theory is applied for rapid design and analysis of the Earth-Moon transfer orbit, significantly improving computational efficiency while maintaining sufficient accuracy. In the ballistic reconfiguration subproblem, the complex non-convex trajectory optimization problem is transformed and efficiently solved using the Sequential Convex Optimization (SCP) method. Simulation verification shows that this joint reconfiguration scheme can complete calculations within seconds, meeting the requirements of online real-time guidance for launch vehicles.

[0019] 4. This invention enhances the autonomous survivability and mission adaptability of launch vehicles. After experiencing non-fatal malfunctions such as thrust reduction, this invention enables launch vehicles to no longer passively enter a rescue orbit or abandon their mission, but instead possess the advanced capability to autonomously make decisions and continue executing their original deep space exploration mission. This transforms the launch vehicle from a traditional program-guided + contingency plan mode to one with online intelligent planning and reconfiguration capabilities. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method for joint reconstruction of rocket trajectory and spacecraft orbit in a lunar exploration mission, as described in this embodiment of the invention. Figure 2 This is a schematic diagram (a) illustrating the effect of departure time deviation on lunar orbit parameters in an embodiment of the present invention; Figure 3 This is a schematic diagram (b) illustrating the effect of departure time deviation on lunar orbit parameters in an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the equivalent substitution of the spacecraft's Earth-Moon transfer motion in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the equivalent starting conditions and Earth-Moon transfer motion conditions in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the problem decomposition of rocket trajectory-spacecraft orbit joint reconstruction in an embodiment of the present invention; Figure 7 This is a schematic diagram of the overlapping conic section method in an embodiment of the present invention; Figure 8 This is a schematic diagram illustrating the overlapping conic section method and the calculation of the transfer time in an embodiment of the present invention; Figure 9 This is a schematic diagram of time-matching track search in an embodiment of the present invention; Figure 10 This is a flowchart of the time-matching track search process in an embodiment of the present invention; Figure 11 This is a schematic diagram of the overall scheme for joint reconfiguration of rocket trajectory and spacecraft orbit in an embodiment of the present invention; Figure 12 This is a schematic diagram (a) showing the comparison between the reconstructed trajectory and the reference trajectory in an embodiment of the present invention; Figure 13 This is schematic diagram b, showing the comparison between the reconstructed trajectory and the reference trajectory in an embodiment of the present invention. Figure 14 This is a schematic diagram (c) showing the comparison between the reconstructed trajectory and the reference trajectory in an embodiment of the present invention. Figure 15 This is a schematic diagram of the reconstructed trajectory in an embodiment of the present invention; Figure 16 This is a schematic diagram of the reconstructed trajectory in an embodiment of the present invention; Figure 17 This is a schematic diagram of the reconstructed trajectory in an embodiment of the present invention; Figure 18 This is a schematic diagram of the reconstructed trajectory in an embodiment of the present invention; Figure 19 This is a schematic diagram of the reconstructed trajectory in an embodiment of the present invention; Figure 20 This is a schematic diagram of the reconstructed trajectory in an embodiment of the present invention; Figure 21 This is a schematic diagram of the reconstructed trajectory g in an embodiment of the present invention; Figure 22 This is a schematic diagram of the reconstructed trajectory h in an embodiment of the present invention; Figure 23This is a schematic diagram illustrating the reconstructed Earth-Moon transfer motion results in an embodiment of the present invention; Figure 24 This is a schematic diagram of the iterative process of the transfer orbit search method in an embodiment of the present invention; Figure 25 This is a schematic diagram (b) illustrating the iterative process of the transfer orbit search method in an embodiment of the present invention; Figure 26 This is a schematic diagram (c) illustrating the iterative process of the transfer orbit search method in an embodiment of the present invention; Figure 27 This is a schematic diagram (d) illustrating the iterative process of the transfer orbit search method in an embodiment of the present invention; Figure 28 This is a schematic diagram of the iterative process of the transfer orbit search method in an embodiment of the present invention; Figure 29 This is a schematic diagram of the iterative process of the transfer orbit search method in an embodiment of the present invention; Figure 30 This is a schematic diagram of the iterative process of the transfer orbit search method in an embodiment of the present invention; Figure 31 This is a schematic diagram of the iterative process of rocket trajectory reconstruction in an embodiment of the present invention; Figure 32 This is a schematic diagram (b) illustrating the iterative process of the rocket trajectory reconstruction problem in an embodiment of the present invention; Figure 33 This is a schematic diagram (c) illustrating the iterative process of the rocket trajectory reconstruction problem in an embodiment of the present invention; Figure 34 This is a schematic diagram (d) illustrating the iterative process of the rocket trajectory reconstruction problem in an embodiment of the present invention; Figure 35 This is a schematic diagram of the iterative process of rocket trajectory reconstruction in an embodiment of the present invention; Figure 36 This is a schematic diagram of the iterative process of rocket trajectory reconstruction in an embodiment of the present invention. Detailed Implementation

[0021] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0022] like Figure 1 As shown in the figure, this invention provides a method for jointly reconstructing the trajectory of a lunar exploration mission rocket and the orbit of a spacecraft, including the following steps: S1. After a thrust reduction failure occurs during the third stage of the launch vehicle, determine whether to continue the lunar mission based on the rocket's status and remaining payload capacity at the time of the failure.

[0023] S2. If execution continues, the initial equivalent departure time and initial transfer orbit parameters under the current fault conditions are determined based on the orbit perigee equivalent conversion method.

[0024] S3. Based on the initial equivalent departure time and initial transfer orbit parameters, call the transfer orbit search method to obtain new transfer orbit parameters that satisfy the lunar orbit constraints and match the Earth-Moon transfer time.

[0025] S4. Using the new transfer orbit parameters as the target orbit, call the rocket trajectory reconstruction method to solve for the reconstructed trajectory of the rocket and the corresponding actual orbit insertion point state and actual orbit insertion time.

[0026] S5. Calculate the transfer time from the orbital perigee corresponding to the actual orbital entry point state to the actual orbital entry point, and determine whether the equivalent departure condition is met based on the actual orbital entry time.

[0027] S6. If not satisfied, update the equivalent departure time and return to step S3 for iteration; if satisfied, output the joint reconstruction result, including the reconstructed rocket trajectory and the spacecraft's Earth-Moon transfer orbit that satisfies the time matching.

[0028] The method for joint reconstruction of rocket trajectory and spacecraft orbit in lunar exploration missions according to embodiments of the present invention will be further described in detail below.

[0029] This invention addresses the trajectory replanning technology for three-and-a-half-stage launch vehicles, designed to enable continued missions to specific target planets while maintaining survivability in the event of rocket malfunctions. Considering safety requirements, for malfunctions occurring in the first and second stages of flight, which typically involve halting the lunar exploration mission and placing the rocket in a rescue parking orbit to await rescue, this invention considers malfunctions occurring during the third stage of flight. At this stage, the rocket is already in a vacuum environment, ready to send the spacecraft to a suitable Earth-Moon transfer entry point to perform subsequent lunar missions. For the third-stage flight, this project considers thrust reduction malfunctions caused by a decrease in engine flow rate per second. This decrease in flow rate per second is equivalent to having remaining fuel available while the total impulse remains constant, resulting in a longer fuel burn time despite a decrease in apparent acceleration. Various common Earth-Moon transfer methods are available, such as the Hohmann transfer method with two-pulse orbital maneuvers, the transfer method based on the invariant manifold of the Earth-Moon L1 point, and the weakly stable boundary transfer method. For lunar exploration missions, although the latter two transfer methods are more energy-efficient than the Hohmann transfer method, considering constraints such as flight time, safety, and reliability, and in order to reduce the time astronauts spend in space, this invention still uses the Hohmann transfer method to plan the Earth-Moon transfer orbit after a rocket failure.

[0030] In this embodiment, the specific details of the modeling of the rocket's third-stage flight process in the case of a non-fatal failure of the propulsion system are as follows: This invention considers a scenario where a rocket experiences a thrust reduction during engine activation in the third stage of flight. The third-stage flight process consists of three phases: the first stage, the glide phase, and the second stage. The engines are activated at the initial moments of the first and second stages. The scenario of engine failure during the second stage activation is slightly simpler than the scenario of engine failure during the first stage activation, as only the second stage remains. Furthermore, the scenario of engine failure during the first stage activation encompasses the scenario of engine failure during the second stage activation. Therefore, this invention performs trajectory reconstruction problem modeling and analysis for the scenario of engine failure during the first stage activation, considering the second stage activation failure as a special case of the aforementioned problem.

[0031] Furthermore, the equations of motion for the rocket during the three-stage flight process are as follows: The third-stage rocket flight occurs in a vacuum environment, therefore the influence of the atmosphere on the rocket's motion does not need to be considered. The primary task of the first stage of the third stage is to place the rocket into the parking orbit. The coasting stage is a non-powered flight stage, primarily aimed at adjusting for a suitable Earth-Moon transfer entry point. The primary task of the second stage of the third stage is to place the rocket into the Earth-Moon transfer orbit. During the third-stage flight, the rocket is mainly affected by thrust and Earth's gravity. This project considers a thrust reduction fault caused by a decrease in engine flow rate per second. A decrease in flow rate per second is equivalent to having remaining fuel available while the total impulse remains constant, resulting in a longer fuel burn time despite a decrease in apparent acceleration. To describe the fault situation, a percentage of remaining thrust is introduced into the mass differential equation and the inference calculation equations. The differential equations of motion for the rocket's center of mass under launch inertia (first and second stages) are as follows: in, Represents the position vector of the rocket. Represents the rocket's velocity vector. Indicates the mass of the rocket, , , These represent thrust amplitude, total flow rate per second, and engine specific impulse, respectively. The acceleration due to gravity at sea level. The direction of thrust. This is the gravitational acceleration vector.

[0032] During the unpowered gliding phase, the rocket is only affected by Earth's gravity, and its kinematics are as follows: Further analysis of constraints at each stage: Based on the above, the three-stage flight process of the rocket can be divided into three consecutive flight phases. Therefore, the starting state of the next phase is the ending state of the previous phase. The superscripts 1, 2, and 3 represent the state information of the first flight phase, the glide phase, and the second flight phase of the third stage, respectively, while the subscripts 0 and f represent the starting and ending state information of each phase.

[0033] For the first flight segment of the third stage, its starting state is determined by the state at the moment the rocket's third-stage first flight failure occurs: in, The moment the malfunction occurred during flight. , , This represents the position, velocity vector, and remaining mass at the moment the flight malfunction occurs.

[0034] The terminal point of the first stage of flight 3 needs to meet the conditions for entering the parking track. The parking track is a circular track, constrained by its semi-major axis, with the track inclination angle near the nominal reference value, and the eccentricity restricted to an interval near 0. Therefore, the track constraints determined by the terminal point state of the first stage of flight 3 are as follows: in The number of track elements (semi-major axis, eccentricity, track inclination, perigee argument, ascending node longitude) indicates the parking track. This indicates the conversion relationship between position / velocity and orbital elements. The constraint interval representing the number of track elements for parking is determined by the constraint conditions. The specific form is as follows: in, and These represent the semi-major axis of the nominal parking rail and the rail inclination angle, respectively. and These represent the permissible ranges for the semi-major axis and the track inclination angle, respectively. This represents the maximum permissible value for eccentricity.

[0035] For the taxiing segment, its starting point state is the same as the ending point state of the first flight segment of the third stage, and its ending point state is the same as the starting point state of the second flight segment of the third stage. In addition, considering the pre-cooling preparation for two engine ignitions, the taxiing period must meet flight time constraints: in and These represent the upper and lower limits of the flight time during the taxiing segment.

[0036] For the second phase of the third stage, the primary mission of the lunar rocket is to adjust the appropriate Earth-Moon transfer entry point, send the spacecraft into the Earth-Moon transfer orbit, and ensure that the spacecraft achieves the desired lunar orbit parameters at the appropriate lunar center orbit entry time. Based on the above mission requirements, the rocket's terminal state should meet the following constraints: in, Represents the set of orbital elements, with subscripts. These represent the Earth-Moon transfer orbit and the lunar orbit, respectively. This indicates the moment the spacecraft entered the lunar core. This represents the mapping relationship between the spacecraft's Earth-Moon transfer motion from its entry point into the Earth-Moon transfer orbit to its entry point into the lunar orbit. Due to the relative motion between the Earth and the Moon, the spacecraft's Earth-Moon transfer motion depends not only on its entry point position and velocity, but also on the relative position and velocity of its entry point. It is also related to the spacecraft's orbital insertion time (the departure time of the Earth-Moon transfer). Related.

[0037] Furthermore, consider the analysis and constraint transformation of the rocket trajectory reconstruction problem in the subsequent motion of the spacecraft: Unlike near-Earth orbit missions, lunar missions culminate in the spacecraft entering lunar orbit. Therefore, the rocket failure reconfiguration problem introduces complex and difficult-to-analyze constraints on the spacecraft's Earth-Moon transfer motion (9). As analyzed above, due to the relative motion between the Earth and the Moon, considering the subsequent Earth-Moon transfer motion of the spacecraft, even if the spacecraft can depart from the predetermined injection point in the event of a failure, different departure times will still lead to changes in the subsequent Earth-Moon transfer motion, thus causing differences in the spacecraft's lunar orbit entry time and lunar orbit parameters. Taking the nominal operating condition spacecraft departing from the nominal injection point at the nominal time as an example, considering the deviation of the departure time and the unchanged arrival time at the Moon, the final lunar orbit near-moon distance and orbital inclination deviations are related to the deviation of the departure time as follows: Figure 2 and Figure 3 As shown, the greater the deviation in departure time, the greater the deviation in lunar orbital parameters.

[0038] However, in the event of a malfunction, even if the rocket enters its intended orbit, its entry point and time will likely change. To achieve the predetermined lunar orbit parameters, the spacecraft's Earth-Moon transfer time needs to be adjusted accordingly, thus affecting the entry time into the lunar center orbit. The changes; under severe fault conditions, the rocket enters the predetermined orbit. Due to the large variation in the orbit insertion time, the relative motion relationship between the Earth and the Moon may make it impossible to form the desired lunar orbit parameters even if the Earth-Moon transfer motion time of the spacecraft is adjusted. The complexity and coupled spatiotemporal relationship of the above-mentioned multiple variables make it difficult to specifically analyze the spacecraft's Earth-Moon transfer motion constraint condition (9), which greatly increases the complexity of the rocket trajectory reconstruction problem under the fault condition of the lunar mission.

[0039] In order to analyze the impact of rocket power failure leading to extended flight time on the constraints of the Earth-Moon transfer motion, this invention proposes an Earth-Moon transfer motion analysis method based on the equivalent transformation of orbital perigee. This method establishes a spatiotemporal mapping relationship and unifies the rocket's orbital entry point, orbital entry time and lunar center orbit entry time in the constraint condition equation (9) into the expression of orbital parameters and the equivalent departure time of perigee, thereby realizing the dimensionality reduction of complex coupling relationships.

[0040] like Figure 4 As shown, the entry time of the spacecraft into the lunar orbit under the known nominal operating conditions. Spacecraft orbit insertion time The travel time of the spacecraft's Earth-Moon transfer The three satisfy the following constraints: Based on the true anomaly angle of the orbital insertion point, the orbital transfer time between the perigee and the insertion point can be calculated using Kepler's equations of motion. Equation (10) can be restated to the following form: in, The equivalent departure time at the orbital perigee, in the form of, This is the transfer time from the perigee of the orbit to the entry point of the lunar orbit at the center.

[0041] Equation (11) equivalently describes the Earth-Moon transfer motion of the spacecraft from the orbit insertion point as: at the equivalent departure time Starting from the orbital perigee, passing through The Earth-Moon transition over time, in the same The moment of arrival at the lunar orbit entry point. This equation equivalently transforms the subsequent Earth-Moon transfer motion after the entry point into the subsequent Earth-Moon transfer motion after the perigee. Simultaneously, the orbital perigee can be equivalently represented as transfer orbit parameters, thus constructing a spatiotemporal mapping relationship between the entry orbit perigee and the Earth-Moon transfer motion. Therefore, the Earth-Moon transfer motion constraint in the equation can be expressed as a constraint condition for the spatiotemporal information of the orbital perigee through an equivalent transformation relationship: like Figure 5 As shown, equations (12) and (13) explain the spatiotemporal relationship that the rocket's entry point and orbit should satisfy with the spacecraft's Earth-Moon transfer motion from two dimensions. First, the rocket's entry time needs to satisfy the equivalent launch condition (12), that is, the difference between the entry time and the transfer time from the perigee to the entry point is equal to the equivalent launch time. Second, the transfer orbit the rocket enters needs to satisfy the Earth-Moon transfer matching condition (13), that is, the spacecraft can form the desired lunar orbit constraint by starting from the perigee at the equivalent launch time and undergoing Earth-Moon transfer motion.

[0042] Given the nominal launch time and orbit of the rocket under standard operating conditions, the equivalent launch time of the nominal orbit can be calculated. In the event of a malfunction, if the rocket still chooses to enter the original orbit, the equivalent launch condition can be determined based on the launch time and the reconfigured launch point. If it is, it means that the spacecraft can continue the Earth-Moon transfer motion from the equivalent launch point. Otherwise, in order for the spacecraft to continue the transfer motion between the perigee and the reconfigured launch point, the equivalent launch time of the orbit needs to be changed. At the same time, the change of the equivalent launch time will affect the lunar orbit parameters formed along the current orbit, and a new transfer orbit that satisfies the lunar orbit constraints and the Earth-Moon transfer motion constraints needs to be searched.

[0043] Therefore, as Figure 6 As shown, the joint reconfiguration problem of rocket trajectory and spacecraft orbit can be decomposed into a rocket trajectory reconfiguration problem upon entering the orbit and a transfer orbit search problem satisfying corresponding constraints. By iteratively and sequentially solving these problems until the equivalent start conditions are met, for the rocket, a trajectory connecting the equivalent start point and the reconfigured entry point can be obtained; for the spacecraft, a lunar transfer orbit connecting the reconfigured entry point to the lunar center orbit entry point and satisfying the desired lunar orbit constraint can be obtained. Based on the above analysis, the joint reconfiguration problem of trajectory and orbit under rocket failure conditions in a lunar mission is decomposed into two simplified subproblems. For the first problem, a trajectory optimization problem with minimum fuel consumption as the performance index is established, and a sequential convex optimization method is used for rapid solution. For the second problem, an orbit search method satisfying both the lunar orbit constraint and the lunar transfer constraint is designed using the overlapping conic section method.

[0044] In this embodiment, the specific details of the calculation method for the feasible Earth-Moon transfer orbit and the corresponding transfer time are as follows: The key to the two sub-problems mentioned above lies in quickly and accurately searching for feasible Earth-Moon transfer orbits that meet the relevant lunar orbit constraints and calculating the corresponding Earth-Moon transfer times. To address these requirements, given some orbital constraints and the target orbit requirements, the overlapping conic section method can obtain the corresponding Earth-Moon transfer orbits, Earth-Moon transfer times, and return the corresponding spacecraft-rocket separation point status information.

[0045] In the preliminary design of the Earth-Moon transfer orbit, the spliced ​​conic section method is often used as an approximate analysis method. Its basic idea is to introduce the concept of a gravitational sphere, dividing the Earth-Moon transfer orbit into two segments: a geocentric Keplerian conic section and a lunar-centric Keplerian conic section, thus transforming the three-body problem into a two-body problem. The advantage of this method is that the calculations are all algebraic operations, resulting in fast computation speed. However, because the spliced ​​conic section method neglects the influence of lunar gravity in the geocentric conic section and the influence of Earth's gravity in the lunar-centric conic section, it introduces a significant path error.

[0046] The overlapping conic section method, based on pseudo-state theory, differs from the traditional splicing conic section method in that it calculates both the geocentric and lunar conic sections within the same time period simultaneously and superimposes them according to certain criteria to obtain an approximate solution for the Earth-Moon transfer orbit. When applied to the preliminary calculation and simulation of the Earth-Moon transfer orbit, this method can reduce errors by more than 80% compared to the splicing conic section method, while maintaining computational simplicity and speed.

[0047] Furthermore, the overlapping conic section method and the calculation of the transition time: The overlapping conic section method applied to the preliminary design problem of the Earth-Moon transfer orbit is characterized by its application range covering the entire Earth-Moon transfer orbit, starting at the perigee state of the transfer orbit, and ending at the state where the spacecraft performs lunar braking deceleration at the end of the transfer orbit. This section presents a rapid calculation method for the Earth-Moon transfer orbit. The preliminary design problem of the Earth-Moon transfer orbit is a separated two-point boundary value problem, that is, given some orbital constraints and target orbit requirements, while other components are unknowns.

[0048] To reduce the complexity of rapid solutions, the preliminary design of the Earth-Moon transfer orbit should consider the main orbital constraints while temporarily ignoring secondary constraints. The main constraints considered in this section are as follows: (1) Lunar orbit constraint: including lunar orbital altitude and orbital inclination These two constraints can be obtained based on the design values ​​of the nominal track.

[0049] (2) Orbital plane orientation constraints: From the perspective of reducing spacecraft energy, the angle between the transfer orbit and the lunar orbit plane should be as small as possible. However, since the transfer orbit starts from the Earth parking orbit, which is limited by launch time and launch site, it usually does not coincide with the lunar orbit plane. If orbital plane change maneuvers are performed on the Earth parking orbit, the required energy will be extremely large. Therefore, the scheme of the Earth-Moon transfer orbit being coplanar with the Earth parking orbit is adopted here.

[0050] (3) Orbital perigee constraint: orbital altitude at perigee Track inclination and speed These three constraints can be obtained from the aforementioned ship-rocket separation point.

[0051] Figure 7 This is a schematic diagram of the overlapping conic section method. The pseudo-state sphere is the sphere influenced by the moon's gravity, and its radius is set. It is 35 times the radius of the moon.

[0052] The specific steps for calculating the transition time using the overlapping conic section method are as follows, and the detailed process is as follows: Figure 8 As shown: (1) Given the time of lunar arrival The lunar position vector is obtained from the lunar ephemeris. and velocity vector and with The initial value of the position vector of the pseudo-state inside the auxiliary variable, i.e. .

[0053] (2) Considering only the two-body effect of Earth's gravity, the known constraints of the starting point of the transfer orbit ( , and Using the conservation equation (14) and energy conservation equation (15) of the geocentric two-body segment, the velocity at the pseudo-state of the inner point of the auxiliary variable is solved. .

[0054] in, It is the polar unit vector of the geocentric equatorial inertial frame.

[0055] (3) Transform the velocity vector of the inner pseudo-state point of the auxiliary variable into the lunar coordinate system, and introduce the auxiliary motion between the inner pseudo-state point and the pseudo-state sphere. Define the projection point of the auxiliary motion on the pseudo-state sphere as the outer pseudo-state point. Assume that the auxiliary motion is uniform linear motion. Therefore, the velocity vector of the outer pseudo-state in the lunar coordinate system can be obtained according to Equation (16). .

[0056] (4) Based on the converted velocity vector Maintaining lunar orbital inclination No change, adjust the longitude of the ascending node. This makes the unit normal vector of the lunar orbital plane obtained from equation (17) and vertical: in This is the transformation matrix from the lunar perihelion coordinate system to the lunar translation coordinate system.

[0057] (5) Solve the pseudo-state problem, considering only the gravitational two-body effect of the moon. In the lunar coordinate system, according to the velocity vector of the outer pseudo-state point obtained in step (3), and position size (radius of pseudo-state sphere) ) and the lunar distance of the near-lunar deceleration braking point The magnitude of the velocity at the lunar deceleration braking point can be obtained from the orbital energy formula. As shown in the formula: (6) The velocity vector of the outer pseudo-state point obtained in step (3) and the unit normal vector of the lunar orbital plane obtained in step (4) Define the following two unit vectors: Obviously Perpendicular to Both are within the lunar orbital plane formed by the final state of their transfer orbits; therefore... This can be represented as a linear combination of these two vectors, as shown in the following equation: scalar and They are respectively: (7) Considering only the gravitational two-body effect of the moon, in the lunar coordinate system, the velocity vector of the outer pseudo-state point obtained according to steps (3) and (6) is... and position vector And the lunar distance of the near-lunar deceleration braking point and speed magnitude The time taken to transition from the outer pseudo-state point to the lunar deceleration braking point can be calculated using the Kepler time-of-flight formula. Therefore, the timing of the outer pseudo-state point can be determined. As shown in the following formula.

[0058] (8) In the lunar coordinate system, the velocity vector of the outer pseudo-state point obtained according to steps (3), (6) and (7) Position vector and the timing of the outer pseudo-state point Considering that the auxiliary motion is uniform linear motion, we can obtain the new position vector of the pseudo-state point inside the auxiliary variable in the lunar coordinate system. Based on the position vector of the moon... This allows us to obtain the new position vector of the pseudo-state point inside the auxiliary variable in the geocentric coordinate system, as shown in the following equation.

[0059] (9) If , If the given value is a small amount, the calculation process ends. Otherwise, use... replace Return to step (2) and repeat steps (2)-(9) until the requirements are met.

[0060] (10) The iteration ends, and the position and velocity vector of the appropriate pseudo-state point are found. and By again utilizing the dynamic laws of the geocentric two-body segment, the orbital perigee state can be obtained. and and transfer time .

[0061] Furthermore, a time-matching trajectory search method: After changing the perigee time, the subsequent Earth-Moon transfer motion along the original transfer trajectory changes, which may prevent the formation of the desired lunar orbit parameters. Therefore, the original lunar center orbit entry time that forms the desired lunar orbit parameters is also unusable, and it is necessary to re-search for the Earth-Moon transfer trajectory and the lunar center orbit entry time. In the calculation of the transfer time using the overlapping conic section method, the conic section method can obtain the specific transfer trajectory parameters and transfer time based on the lunar center orbit entry time and the perigee information of the transfer trajectory. According to the analysis of the rocket's three-stage flight process modeling for non-fatal failures of the propulsion system, it is necessary to obtain a transfer trajectory that can form the desired lunar orbit parameters and satisfy the time matching of equation (11) after the perigee is changed. The conic section method can obtain the transfer time based on the lunar center orbit entry time, so it can solve the corresponding perigee time. By iterating the lunar center orbit to lunar time and calling the overlapping conic section method, the solved perigee time corresponds to the updated equivalent departure time, and thus the transfer trajectory satisfying equations (11) and (13) is obtained. The specific calculation steps are as follows, and the schematic diagram is shown below. Figure 9 As shown, the flowchart is as follows Figure 10 As shown: (1) The set of transfer orbit parameters that satisfy equations (11) and (13) is known. Its value can be obtained from the nominal operating conditions or the results of the last orbit search. Update perigee time. First, assuming the subsequent Earth-Moon transfer time remains unchanged, we obtain an initial guess for the estimated lunar orbit entry time. ; (2) Based on the estimated lunar orbit entry time and lunar orbital parameters The Earth-Moon transfer time was calculated using the overlapping conic section method. and transfer orbit parameters ; (3) Calculate the deviation between the estimated lunar orbit entry time minus the Earth-Moon transfer time and the perigee time. Determine if the deviation is less than the set convergence condition. If yes, proceed to step (4); otherwise, update the estimated lunar orbit entry time. Proceed to step (2); (4) Obtain a new set of Earth-Moon transfer orbit parameters that satisfy the lunar orbit constraints and the Earth-Moon transfer motion constraints (11) and (13). .

[0062] In this embodiment, the rocket trajectory reconstruction method based on sequence convex optimization is described in detail below: Based on the above analysis, the joint reconstruction problem of rocket trajectory and spacecraft orbit is transformed into solving two simplified problems. Among the feasible methods for calculating the Earth-Moon transfer orbit and corresponding transfer time, the orbit search method obtains the time-matched transfer orbit, which is used as the target orbit of the rocket trajectory. Taking fuel efficiency as the performance index, the nonlinear terms of the problem modeling part in the modeling of the rocket's third-stage flight process in the non-fatal failure of the propulsion system are approximated by convexity and combined with sequential convex optimization to solve the rocket trajectory reconstruction problem.

[0063] Furthermore, the problem of reconstructing the original non-convex rocket trajectory into the target orbit: Based on the above analysis, the constraints (9) of the rocket trajectory-spacecraft orbit joint reconstruction problem can be separated. In order to ensure the rational use of rocket fuel, with fuel efficiency as the performance index, and combined with the analysis of the constraints at each stage, the rocket trajectory reconstruction problem can be modeled as follows: Furthermore, the convexity and discretization of dynamic constraints: Problem (24) is a continuous non-convex optimization problem. For the dynamic equations, a first-order Taylor linear approximation and a first-order preserved discretization method are used to make them convex and discretized.

[0064] Given a reference trajectory , The dynamics (kinematics of the taxiing phase) of level three flight can be abstracted into the following form: in, .

[0065] Since we are considering a free-time problem, the time domain of the system dynamics needs to be considered from... , Transform into , that is to say ,but: Performing a first-order Taylor expansion of equation (26) with respect to the reference trajectory, we obtain: in, The flight time for each flight phase is represented by a coefficient matrix in the form of: The first-order preserved discretization method is used to discretize the convex dynamic equation (27). The main idea of ​​the first-order preserved discretization method is to parameterize the control variables as piecewise linear functions and derive the discrete dynamic equation based on the knowledge of linear systems. Specifically, the selected... discrete points The control variables have the following forms: in, , .

[0066] Substituting equation (29) into the convexized dynamic equation yields a linear time-varying system: Based on the fundamental theory of linear systems, the discrete dynamic equations are obtained as follows: The coefficient matrix is ​​defined as follows: in, Let be the state transition matrix of a linear time-varying system, satisfying the following properties: By combining numerical integration methods, such as the classic Runge-Kutta method, the corresponding coefficient matrix can be calculated, thus yielding the discrete dynamic constraint equations. For the unpowered coasting segment, the discrete dynamic constraint equations are as follows: Remove control items .

[0067] Furthermore, the convexity of the orbital insertion constraints: Problem (24) includes orbital insertion constraints for both the parking track and the transfer track, which can be expanded into the following specific form: Given a reference trajectory , A first-order Taylor expansion of equation (34) yields its linear approximation: Furthermore, the problem of discretized rocket trajectory reconstruction entering the target orbit and the sequential convexization algorithm are discussed. Given the number of discrete points for a three-stage primary flight, a taxiing phase flight, and a three-stage secondary flight. , Thus, the discrete convex subproblem form of problem (24) can be obtained (36).

[0068] The algorithm flow for sequence convexization is given below: Initialization steps: Set the number of discrete points for each flight phase. (in (Corresponding to the first flight segment, taxiing segment, and second flight segment of the third stage, respectively), setting the initial reference trajectory. (Including state variables, control variables, and time), set the maximum number of iterations. And set the parameters for the iterative convergence criterion. ( ); Initialize the current iteration number k to 1.

[0069] Iterative solution steps: Before the number of iterations k exceeds... Under the given conditions, repeat the following process: Iteration count update: Let .

[0070] Constructing a convex sub-problem: Based on the current k-th iteration reference trajectory The original nonlinear optimization problem is approximated by convexity, and corresponding convex optimization subproblems are constructed.

[0071] Solving the convex subproblem: Use the interior point method to solve the convex subproblem and obtain the optimized trajectory under the current iteration. .

[0072] Calculate the iterative residual: Calculate the residual Δx between the current optimized trajectory and the reference trajectory, which is defined as follows: .

[0073] Update the reference trajectory: Adjust the optimized trajectory Set as the reference trajectory for the next iteration, i.e. .

[0074] Convergence criterion: If the calculated residuals If the algorithm converges, the iteration is terminated; otherwise, the next iteration continues.

[0075] When the iteration terminates due to convergence or reaching the maximum number of iterations, the final optimized trajectory obtained is the desired rocket reconfiguration trajectory.

[0076] in, Trust region constraints are used to ensure the effectiveness of the problem after linearization.

[0077] Furthermore, the overall scheme for the joint reconfiguration of the lunar trajectory and orbit: A predetermined transfer orbit is selected as the target orbit. The rocket reconfiguration trajectory problem under fault conditions is solved, and the transfer time between the reconfiguration insertion point and the perigee is calculated. If the equivalent launch condition is met, it means that the reconfiguration insertion point into which the rocket sends the spacecraft can continue the predetermined Earth-Moon transfer motion. Otherwise, the equivalent launch time is updated, and a new transfer orbit satisfying the lunar orbit constraint and the Earth-Moon transfer constraint is searched. This new transfer orbit is used as the target orbit, and the rocket reconfiguration trajectory problem under fault conditions is solved again. This process is repeated sequentially until the reconfiguration insertion point and the reconfiguration transfer orbit satisfy the equivalent launch condition. Finally, a rocket trajectory and spacecraft orbit satisfying the lunar orbit constraint and matching the rocket-spacecraft motion and the Earth-Moon transfer are obtained. The specific flowchart is shown below. Figure 11 As shown, the rocket trajectory reconstruction problem is solved using the rocket trajectory reconstruction method based on the above-mentioned sequence convex optimization, while the problem satisfying the lunar orbit constraint and the Earth-Moon transfer orbit constraint is solved using the above-mentioned method for calculating the feasible Earth-Moon transfer orbit and the corresponding transfer time.

[0078] In this embodiment, the specific content of the numerical simulation analysis is as follows: Furthermore, the simulation conditions are set as follows: This invention considers a failure scenario where one engine shuts down during the second startup, using a self-designed typical three-and-a-half-stage rocket configuration. The simulation was conducted in a Matlab, x86, Windows 11 environment, with an Intel(R) Xeon(R) W-11855M CPU @ 3.20GHz, and ECOS was used to solve the rocket trajectory reconstruction convexity problem.

[0079] Table 1 Target orbit parameters Furthermore, simulation results under the condition of a third-stage secondary flight failure: For the fault condition where one engine shuts down during the second-stage restart of the third stage, when the remaining flow rate is 0.65, the rocket trajectory-spacecraft orbit joint reconstruction algorithm converges after three sequential iterations of solving the rocket trajectory reconstruction problem and two iterations of searching for feasible orbits for the Earth-Moon transfer, with an algorithm time of 0.1285s.

[0080] Reconstructing the trajectory's distance from the Earth's center, velocity magnitude, and mass consumption, for example... Figures 12 to 14 As shown, the results of reconstructing the ballistic variables are as follows: Figures 15 to 22 As shown, the thrust component changes smoothly, meeting the rocket's attitude control requirements. In the event of a malfunction, the lunar transfer motion of the spacecraft after the rocket sends it into its original orbit and after reconfiguring its orbit is as follows: Figure 23 As shown, the reconstructed orbit is closer to the Moon.

[0081] As shown in Table 2, under the aforementioned fault conditions, the rocket entered a new reconfiguration orbit by extending its flight time by approximately 449 seconds. The delayed arrival time to the moon after spacecraft separation was 100 seconds, which was less than the extended flight time. This indicates that the algorithm can correct the deviation in the spacecraft's arrival time to the moon caused by the extended flight time of the rocket by adjusting the corresponding insertion orbit. The final lunar distance and lunar orbit inclination of the spacecraft were 329.22 km and 92.33 degrees, respectively, which were close to the set lunar orbit parameters, proving the feasibility of the Earth-Moon transfer orbit obtained by using the conic section method.

[0082] For the transfer orbit search method satisfying both lunar orbit constraints and Earth-Moon transfer motion constraints, the equivalent launch condition deviation after the first rocket trajectory reconstruction is 82.28 s. After updating the equivalent launch time of the perigee, this deviation value is used as the initial value for the transfer orbit search method. The first orbit search algorithm converges after 4 iterations. After using the result of the first orbit search as the target orbit to solve the trajectory reconstruction problem, the equivalent launch condition deviation is 1.01 s. The time matching degree between the rocket-spacecraft motion and the Earth-Moon transfer motion is relatively high, so the first orbit search converges after only 2 iterations. The changes in the Earth-Moon transfer feasibility condition deviation, equivalent Earth-Moon transfer time, and transfer orbit elements with the number of iterations are as follows: Figures 24 to 30 As shown. The equivalent starting conditions and orbital elements for the rocket trajectory reconstruction problem change with the number of iterations, as shown in the figure. Figures 31 to 36 As shown.

[0083] Table 2 Reconstructed Flight Time and Reconstructed Orbit Results The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for jointly reconstructing the trajectory of a rocket and the orbit of a spacecraft in a lunar exploration mission, characterized in that, Includes the following steps: S1. After a thrust reduction failure occurs during the third stage of the launch vehicle, determine whether to continue the lunar mission based on the rocket's status and remaining payload capacity at the time of the failure. S2. If execution continues, determine the initial equivalent departure time and initial transfer orbit parameters under the current fault conditions based on the orbit perigee equivalent conversion method. S3. Based on the initial equivalent departure time and initial transfer orbit parameters, call the transfer orbit search method to obtain new transfer orbit parameters that satisfy the lunar orbit constraints and match the Earth-Moon transfer time. S4. Using the new transfer orbit parameters as the target orbit, call the rocket trajectory reconstruction method to solve for the reconstructed trajectory of the rocket and the corresponding actual orbit insertion point state and actual orbit insertion time. The rocket trajectory reconstruction method is a trajectory reconstruction method based on sequential convex optimization, including: S4.1 Establish a rocket trajectory optimization model with the minimum fuel consumption as the performance index, which includes the first flight stage, the glide stage, and the second flight stage of the third stage; S4.2 Set the initial reference trajectory, and perform convex approximation and discretization on the dynamic equations and terminal trajectory constraints in the optimization model to form a convex optimization subproblem; The convexity approximation and discretization are achieved by performing the following operations on the dynamic equations in the rocket trajectory optimization model: performing a first-order Taylor expansion on the dynamic equations at a given reference trajectory to achieve linearized convexity approximation; and using a first-order discretization-preserving method to convert the continuous dynamic equations after convexity approximation into discrete linear system dynamic equations. S4.3 Iteratively solve the convex optimization subproblem: In each iteration, construct and solve the convex optimization subproblem based on the current reference trajectory to obtain the optimized trajectory. Then update the reference trajectory with the optimized trajectory until the solution converges, and finally output the reconstructed trajectory that satisfies the terminal trajectory constraint. S5. Calculate the transfer time from the orbital perigee corresponding to the actual orbital entry point state to the actual orbital entry point, and determine whether the equivalent departure condition is met based on the actual orbital entry time. S6. If not satisfied, update the equivalent departure time and return to step S3 for iteration; if satisfied, output the joint reconstruction result, including the reconstructed rocket trajectory and the spacecraft's Earth-Moon transfer orbit that satisfies the time matching.

2. The method for joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions according to claim 1, characterized in that, In step S2, the orbital perigee equivalent transformation method includes: The Earth-Moon transfer motion of the spacecraft starting from its actual orbital insertion point is equivalently converted into the motion of the spacecraft starting from its orbital perigee. Among them, the equivalent departure time of orbital perigee Determined according to the following formula: In the formula, The actual orbital insertion time is mentioned. The orbital transfer time from the orbital perigee to the actual orbital entry point is calculated using Kepler's equations of motion based on the orbital elements at the actual entry point.

3. The method for joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions according to claim 1, characterized in that, In step S3, the transfer trajectory search method is a time-matching search method based on the overlapping conic section method, including: S3.

1. Based on the current equivalent departure time and lunar orbit parameters, estimate the entry time into the lunar center orbit; S3.

2. Use the overlapping conic section method to calculate the Earth-Moon transfer time and transfer orbit parameters; S3.3 Determine whether the deviation between the estimated lunar orbit entry time and the current equivalent departure time plus the Earth-Moon transfer time meets the convergence condition; S3.4 If not satisfied, update the estimated lunar orbit entry time and repeat steps S3.2 to S3.3 until convergence, to obtain the transfer orbit parameters that satisfy the time matching.

4. The method for joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions according to claim 1, characterized in that, The thrust reduction fault is a non-fatal fault caused by a decrease in engine flow rate per second, which occurs during the first or second startup phase of the third stage of the rocket.

5. The method for joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions according to claim 1, characterized in that, In step S5, the method for determining whether the equivalent starting condition is met is as follows: Calculate the actual orbit insertion time Subtract the transfer time from the orbital perigee to the actual orbital insertion point. The value of is the equivalent start time set in the current iteration when returning to step S3 for iteration. Compare; If the absolute deviation between the two is less than the preset convergence threshold, it is determined that the equivalent starting condition is met.

6. The method for joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions according to claim 3, characterized in that, The overlapping conic section method includes the following steps: Based on the relative motion relationship between the Earth and the Moon and introducing a pseudo-state sphere, an orbital model of the Earth-centered two-body segment is constructed inside the pseudo-state sphere, and an orbital model of the Moon-centered two-body segment is constructed outside the pseudo-state sphere. The position and velocity of the pseudo-state point are solved by iterative algorithm, so that the orbit models of the geocentric two-body segment and the lunar two-body segment meet the continuity conditions of position and velocity at the boundary of the pseudo-state sphere, and the two orbit segments are smoothly spliced. Based on the smoothly stitched orbit, the state parameters of the transfer orbit at perigee and the total transfer time from perigee to the lunar center orbit entry point are calculated by reverse calculation.

7. The method for joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions according to claim 1, characterized in that, The lunar orbit constraints include the lunar distance and orbital inclination. The Earth-Moon transfer time matching condition refers to the ability of a spacecraft to reach the lunar center orbit entry point that satisfies the lunar orbit constraints after undergoing Earth-Moon transfer motion from the equivalent departure time.

8. The method for joint reconstruction of rocket trajectory and spacecraft orbit for lunar exploration missions according to claim 1, characterized in that, The method for joint reconstruction of rocket trajectory and spacecraft orbit in lunar exploration missions is applicable to lunar exploration missions that use the Hohmann transfer method for Earth-Moon transfer.

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