Time-optimal spacecraft attitude trajectory planning method and system under time-varying constraint

Abstract

The invention provides a time-optimal spacecraft attitude trajectory planning method and system under time-varying constraint, and the method comprises the steps: determining a time-varying constraint forbidden zone, judging whether the time-varying constraint forbidden zone can be avoided at the same time, and carrying out the avoidance processing and time domain planning, so as to achieve the purpose that an aircraft completes a task in the shortest time. The method comprises the specific steps of determining the positions of time-varying constraint forbidden zones before a task starts, judging whether the time-varying constraint forbidden zones can be avoided at the same time or not, performing simultaneous avoiding processing on the time-varying constraint forbidden zones which can be avoided at the same time, performing different-time avoiding processing on the time-varying constraint forbidden zones which cannot be avoided at the same time, and finally completing the task with the optimal time. According to the invention, the aircraft can safely and efficiently complete tasks in the shortest time.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft attitude control, and more particularly, to a method and system for time-optimal spacecraft attitude trajectory planning under time-varying constraints. Background Art

[0002] In the field of spacecraft attitude control, it is crucial to ensure that the spacecraft can effectively avoid various time-varying constraint no-go zones during mission execution. These time-varying constraint no-go zones may include communication blind spots formed due to the occlusion of the Earth or other celestial bodies, as well as other areas that must be avoided due to mission requirements or safety considerations. Traditional spacecraft attitude trajectory planning methods often struggle to adapt to these dynamically changing constraint conditions, resulting in sub-optimal trajectories that may not complete the mission in the shortest time or pose safety risks when avoiding time-varying constraint no-go zones.

[0003] In the process of implementing the embodiments of the present invention, the inventors found that there are at least the following problems or defects in the prior art: existing planning methods often lack the ability to adapt to the dynamic changes of time-varying constraint no-go zones, resulting in the inability to achieve optimal time efficiency and safety in practical applications; at the same time, the avoidance handling of multiple time-varying constraint no-go zones is not flexible enough, making it difficult to meet multiple avoidance conditions simultaneously, thus limiting the flexibility and effectiveness of spacecraft attitude trajectory planning. Summary of the Invention

[0004] The present invention provides a method and system for time-optimal spacecraft attitude trajectory planning under time-varying constraints.

[0005] In a first aspect of the present invention, a method for time-optimal spacecraft attitude trajectory planning under time-varying constraints is provided, including: Step S1: Determine the time-varying constraint no-go zones before the mission starts; Step S2: Determine whether the time-varying constraint no-go zones can be avoided simultaneously. If yes, proceed to step S3; if no, proceed to step S4; Step S3: Spacecraft attitude trajectory planning under time-varying constraints; simultaneously avoid the time-varying constraint no-go zone problems that can be avoided simultaneously in step S2, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-go zones, so that the aircraft completes the mission in the shortest time; Step S4: Spacecraft attitude trajectory planning under time-varying constraints; perform non-simultaneous avoidance processing on the time-varying constraint no-go zone problems that cannot be avoided simultaneously in step S2, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-go zones, so that the aircraft completes the mission in the shortest time.

[0006] Further, step S1 includes: Step S101. Determine the position of the time-varying constraint no-go zone. According to the mission requirements, determine the position of the time-varying constraint no-go zone. If the pointing to the time-varying constraint no-go zone is not within the observation arc segment, end; if the pointing to the time-varying constraint no-go zone is within the observation arc segment, proceed to the next step; Step S102. Define the time-varying no-go zone. Define the time-varying constraint no-go zone according to the on-orbit position change of the pointing to the time-varying constraint no-go zone; the time-varying constraint no-go zone includes a time-varying elliptical no-go zone with an elliptical cone shape and a time-varying spherical no-go zone with a spherical cone shape; where the time-varying elliptical no-go zone is:

[0007] where represents the distance from the observer to the time-varying constraint no-go zone, is the reference distance, is the eccentricity, is the angle, is the reference angle; The time-varying spherical no-go zone is:

[0008] where represents the distance from the observer to the time-varying constraint no-go zone.

[0009] Furthermore, in step S2, the following method is used to determine whether the time-varying constraint no-go zones can be avoided simultaneously: If the major-axis foci of any two time-varying constraint no-go zones are different, then the points of any two time-varying constraint no-go zones can be avoided simultaneously; If the major-axis foci of any two time-varying constraint no-go zones are the same but the minor-axis foci are different, then the points of any two time-varying constraint no-go zones cannot be avoided simultaneously.

[0010] Furthermore, step S3 specifically includes the following steps: Step S301. Determine the known conditions, including the observation arc segment and the time-varying constraint no-go zone; Step S302. Construct the time-varying elliptical no-go zone under the known conditions; Assume that the major and minor axis foci of any two time-varying constraint no-go zones with an elliptical cone shape among N time-varying constraint no-go zones are at the same place, and at the start of the arc segment, the pointing points to any one of the time-varying constraint no-go zones, and at the end of the arc segment, the pointing points to another on-orbit position of the time-varying constraint no-go zone, and the focal lengths of any two elliptical cones among the N time-varying constraint no-go zones are different, and the cone center coordinates of the elliptical cone at each moment are known, and the lengths of the major and minor axes of the ellipse, convert the time-varying elliptical no-go zone into an elliptical cone for solution; the cone center is:

[0011] where, is the time; ; is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse; Then the equation of the ellipse to be solved is:

[0012] Step S303: Solve using the convex optimization algorithm; construct the optimization objective function:

[0013] where, represents the time length of the execution arc segment, represents that during the time of the execution arc segment of the actuator, is the initial state of the motion trajectory, is the final state of the motion trajectory; The constraint function is:

[0014]

[0015]

[0016] where, is the initial state, is the final state, is the major semi - axis of the ellipse, is the minor semi - axis of the ellipse, and respectively represent the minimum spatial spacing that the motion trajectory needs to satisfy and the maximum displacement that the aircraft can achieve.

[0017] Furthermore, in step S302, the ellipse is transformed into an elliptic cone for solution, which is specifically obtained through the following method: Since the center of the elliptic cone is known and the lengths of the major semi - axis and minor semi - axis of the ellipse are fixed, the trajectory points on the conical surface and the trajectory points of the ellipse can be determined; therefore, judging whether there is an intersection between the motion trajectory points in the elliptic cone and the points of the ellipse can be obtained by judging whether the intersection of the circle at the bottom of the elliptic cone and the ellipse intersects; thus, the trajectory constraint problem is transformed into whether the trajectory points intersect with the circle at the bottom of the cone.

[0018] Furthermore, in step S303, the sphere is transformed into a spherical cone for solution, which is specifically obtained through the following method: Since the center of the spherical cone is known and the radius of the sphere is fixed, the trajectory points on the conical surface and the sphere can be determined; therefore, judging whether there is an intersection between the motion trajectory points in the spherical cone and the intersection of the sphere can be obtained by judging whether the intersection of the vertex of the spherical cone and the sphere intersects; thus, the trajectory constraint problem is transformed into whether the distance from the vertex to the sphere is less than the radius of the sphere.

[0019] Furthermore, step S4 includes: When the observation arc segment starts, the centers of all time-varying constraint no-fly zones are located on the straight line where the arc segment is located, but the cone vertices are at the on-orbit positions outside the observation arc segment. Then, after processing through step S3, the time-domain planning of the trajectory points and the time-varying constraint no-fly zones is carried out.

[0020] Furthermore, in step S303, the method for obtaining the intersection points is as follows: At each moment , the equation of the circle at the bottom of the cone is:

[0021] where is the initial state, is the final state, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse, and respectively represent the minimum spatial distance that the motion trajectory needs to satisfy and the maximum displacement that the aircraft can achieve; Judge whether the trajectory points satisfy the cone vertex constraint. If they do, the trajectory points at this moment are inside the elliptical cone. Otherwise, the trajectory points are outside the elliptical cone; within the arc segment time, through the above judgment, if the trajectory points are inside the cone, it means that all points of any cone are inside the cone; if any point of any cone is not inside the cone, it means that there is at least one point not inside the cone; that is, the motion trajectory at this moment and the cone cannot form an intersection; Represent whether the trajectory points are inside the cone as a dual problem:

[0022]

[0023]

[0024] where

[0025] where represents the distance from the observer to the time-varying constraint no-fly zone, and , represents the distance from the observer to the time-varying constraint no-fly zone, and is the constraint condition; The trajectory points that satisfy the constraint condition are obtained by solving .

[0026] Furthermore, step S3 also includes the following steps: Step S304: For the trajectory points obtained by solving in step S303, perform the avoidance verification of the time-varying constraint no-fly zone; This step involves the trajectory points Compare with the equations of the time-varying elliptical no-go zone and the time-varying spherical no-go zone to verify whether the trajectory points meet the avoidance requirements; if the trajectory points meet the avoidance requirements of all time-varying constraint no-go zones, it is considered that the avoidance is successful, otherwise the trajectory points need to be adjusted; Step S305: If the avoidance verification in step S304 fails, adjust the trajectory points; dynamically adjust the trajectory points according to the changes of the time-varying constraint no-go zones to meet the avoidance requirements; the adjustment can include changing the position, speed or acceleration of the trajectory points until all avoidance conditions are met; Step S306: Re-perform the avoidance verification in step S304 on the adjusted trajectory points until the optimal trajectory that meets the avoidance requirements of all time-varying constraint no-go zones is found.

[0027] In the second aspect of the present invention, a time-optimal spacecraft attitude trajectory planning system under time-varying constraints is provided, including: A constraint no-go zone determination module for determining the time-varying constraint no-go zones before the start of the mission; A judgment module for judging whether the time-varying constraint no-go zones can be avoided simultaneously; A first planning module for simultaneously avoiding the problems of time-varying constraint no-go zones that can be avoided simultaneously, and performing time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-go zones, so that the aircraft can complete the mission in the shortest time; A second planning module for non-simultaneously avoiding the problems of time-varying constraint no-go zones that cannot be avoided simultaneously, and performing time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-go zones, so that the aircraft can complete the mission in the shortest time.

[0028] According to the above embodiments of the present invention, at least the following beneficial effects are achieved: By comprehensively considering the dynamic characteristics of the time-varying constraint no-go zones, the method can effectively plan the attitude trajectory of the spacecraft, so that while avoiding the time-varying constraint no-go zones, the mission can be completed in the shortest time. This method can improve the safety and mission execution efficiency of the spacecraft in a complex environment, and reduce the time delay and resource waste caused by improper avoidance.

[0029] In addition, through accurate time-domain planning and convex optimization algorithms, the method can flexibly handle the problems of time-varying constraint no-go zones that can be avoided simultaneously and those that cannot be avoided simultaneously, so as to find the optimal spacecraft attitude trajectory on the premise of meeting all avoidance requirements. This method can ensure the stability and reliability of the spacecraft during the mission execution process, and at the same time reduce the risks brought by improper avoidance, providing a strong guarantee for the safe operation of the spacecraft. Description of the Drawings

[0030] By reading the following detailed description with reference to the accompanying drawings, the above and other objects, features, and advantages of the exemplary embodiments of the present invention will become readily understandable. In the drawings, several embodiments of the present invention are shown by way of illustration and not limitation, wherein: Figure 1 It is a schematic flowchart of a time-optimal spacecraft attitude trajectory planning method under time-varying constraints provided by an embodiment of the present invention; Figure 2 It is a schematic structural diagram of a time-optimal spacecraft attitude trajectory planning system under time-varying constraints provided by an embodiment of the present invention; Figure 3 It schematically shows a schematic structural diagram of an electronic device according to an embodiment of the present invention. Detailed Embodiments

[0031] The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are given only to enable those skilled in the art to better understand and then implement the present invention, and not to limit the scope of the present invention in any way. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to be able to convey the scope of the present invention fully to those skilled in the art.

[0032] Those skilled in the art know that the embodiments of the present invention can be implemented as a system, device, equipment, method, or computer program product. Therefore, the present invention can be specifically implemented in the following forms, namely: completely hardware, completely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.

[0033] It should be noted that any number of elements in the drawings is for illustration and not limitation, and any naming is only for distinction and does not have any limiting meaning.

[0034] Next, refer to Figure 1 , Figure 1 It is a schematic flowchart of a time-optimal spacecraft attitude trajectory planning method under time-varying constraints provided by an embodiment of the present invention. As Figure 1 shown, a time-optimal spacecraft attitude trajectory planning method 100 under time-varying constraints includes: Step S1, determine the time-varying constraint no-go zone before the mission starts; Step S2, determine whether the time-varying constraint no-go zones can be avoided simultaneously. If yes, go to step S3; if no, go to step S4; Step S3, spacecraft attitude trajectory planning under time-varying constraints: perform simultaneous avoidance processing on the time-varying constraint no-go zone problems that can be avoided simultaneously in step S2, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-go zones, so that the aircraft completes the mission in the shortest time; Step S4: Spacecraft attitude trajectory planning under time-varying constraints; deal with the problem of time-varying constraint no-go zones that cannot be avoided simultaneously in step S2 by non-simultaneous avoidance, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-go zones, so that the aircraft can complete the task in the optimal time.

[0035] It should be noted that in the step of determining the time-varying constraint no-go zones before the start of the mission, we first need to identify and define those areas that may be encountered during the spacecraft's mission execution and whose positions and shapes change with time. These areas may include communication blind zones formed by the occlusion of the Earth or other celestial bodies, as well as other areas that must be avoided due to mission requirements or safety considerations. The time-varying constraint no-go zones refer to the areas whose positions and shapes change with time and need to be dynamically avoided.

[0036] Specifically, the process of determining the position of the time-varying constraint no-go zones includes analyzing mission requirements and observation data to determine the specific positions of these no-go zones. For example, if the pointing time-varying constraint no-go zone is not within the observation arc, no further processing is required; if it is within the observation arc, the shape and size of the no-go zone need to be defined. When defining the time-varying no-go zones, according to the position change of the pointing time-varying constraint no-go zone in orbit, a time-varying elliptical no-go zone with an elliptical cone shape and a time-varying spherical no-go zone with a spherical cone shape can be defined. These shapes can be accurately described by mathematical formulas. For example, the formula for the time-varying elliptical no-go zone is:

[0037] where represents the distance from the observer to the time-varying constraint no-go zone, is the reference distance, is the eccentricity, is the angle, is the reference angle.

[0038] Preferably, in the process of determining the time-varying constraint no-go zones, we can use advanced observation technologies and data processing algorithms to improve the accuracy of the no-go zone positions and shapes. For example, machine learning algorithms can be used to predict the future position and shape changes of the time-varying constraint no-go zones, so as to plan avoidance strategies in advance.

[0039] Furthermore, for the definition of the time-varying spherical no-go zone, it can be determined by the distance from the observer to the time-varying constraint no-go zone, and this distance can be set according to the specific requirements and safety standards of the mission. Through these precise definitions and predictions, it can be ensured that the spacecraft can effectively avoid the time-varying constraint no-go zones during mission execution and guarantee the smooth completion of the mission.

[0040] In some embodiments, step S1 includes: Step S101. Determine the position of the time-varying constraint no-go zone. According to the mission requirements, determine the position of the time-varying constraint no-go zone. If the pointing to the time-varying constraint no-go zone is not within the observation arc segment, end; if the pointing to the time-varying constraint no-go zone is within the observation arc segment, proceed to the next step; Step S102. Define the time-varying no-go zone. Define the time-varying constraint no-go zone according to the on-orbit position change of the pointing to the time-varying constraint no-go zone; the time-varying constraint no-go zone includes a time-varying elliptical no-go zone with an elliptical cone shape and a time-varying spherical no-go zone with a spherical cone shape; where the time-varying elliptical no-go zone is:

[0041] where represents the distance from the observer to the time-varying constraint no-go zone, is the reference distance, is the eccentricity, is the angle, is the reference angle; The time-varying spherical no-go zone is:

[0042] where represents the distance from the observer to the time-varying constraint no-go zone.

[0043] It should be noted that the first step of this method involves determining the position of the time-varying constraint no-go zone before the mission starts. This requires us to identify those time-varying constraint no-go zones that may exist within the spacecraft's observation arc segment according to the specific mission requirements. The observation arc segment refers to the specific area that the spacecraft needs to observe or pass through during the mission execution, while the time-varying constraint no-go zone refers to those areas whose positions and shapes change with time and need to be avoided to ensure the safe execution of the mission.

[0044] Specifically, the process of determining the position of the time-varying constraint no-go zone includes analyzing the spacecraft's mission requirements and observation data to determine the specific positions of these no-go zones. If the pointing to the time-varying constraint no-go zone is not within the observation arc segment, no further processing is required; if it is within the observation arc segment, the next step is to define the shape and size of the time-varying no-go zone.

[0045] More specifically, when defining the time-varying no-go zone, a time-varying elliptical no-go zone with an elliptical cone shape and a time-varying spherical no-go zone with a spherical cone shape can be defined according to the on-orbit position change of the pointing to the time-varying constraint no-go zone. These shapes can be accurately described by mathematical formulas. For example, the formula for the time-varying elliptical no-go zone is:

[0046] where represents the distance from the observer to the time-varying constraint no-go zone, is the reference distance, is the eccentricity, is the angle, is the reference angle.

[0047] Preferably, in the process of determining the time-varying constraint no-go zone, we can use advanced observation techniques and data processing algorithms to improve the accuracy of the no-go zone's position and shape. For example, machine learning algorithms can be adopted to predict the future position and shape changes of the time-varying constraint no-go zone, so as to plan the avoidance strategy in advance. In addition, for the definition of the time-varying spherical no-go zone, it can be determined by the distance from the observer to the time-varying constraint no-go zone This distance can be set according to the specific requirements of the mission and safety standards. Through these precise definitions and predictions, it can be ensured that the spacecraft can effectively avoid the time-varying constraint no-go zone during the mission execution, guaranteeing the smooth completion of the mission.

[0048] In some embodiments, step S2 determines whether the time-varying constraint no-go zones can be simultaneously avoided by the following method: If the major-axis foci of any two time-varying constraint no-go zones are different, then the points of any two time-varying constraint no-go zones can be simultaneously avoided; If the major-axis foci of any two time-varying constraint no-go zones are the same, but the minor-axis foci are different, then the points of any two time-varying constraint no-go zones cannot be simultaneously avoided.

[0049] It should be noted that this step involves determining whether the time-varying constraint no-go zones can be simultaneously avoided. Simultaneous avoidance here means that when the spacecraft plans its trajectory, it can find a path so that all time-varying constraint no-go zones can be avoided, without the need to avoid each no-go zone separately. The major-axis focus and minor-axis focus refer to the geometric characteristics of these regions when defining the time-varying elliptical no-go zone and the time-varying spherical no-go zone, and they are the key parameters determining the shape and position of the no-go zone.

[0050] Specifically, the method for determining whether the time-varying constraint no-go zones can be simultaneously avoided includes checking whether the major-axis foci and minor-axis foci of any two time-varying constraint no-go zones are the same. If the major-axis foci of any two time-varying constraint no-go zones are different, it means that their avoidance paths will not conflict with each other, so they can be simultaneously avoided. On the contrary, if the major-axis foci are the same but the minor-axis foci are different, it means that at least one no-go zone's avoidance path conflicts with other no-go zones, so they cannot be simultaneously avoided. The judgment of these foci can be determined through geometric analysis and mathematical calculations, and the specific parameter settings need to be determined according to the actual observation data and mission requirements.

[0051] Preferably, in the process of determining whether the time-varying constraint no-go zones can be simultaneously avoided, computer-aided design (CAD) software or professional trajectory planning software can be used to assist in the analysis. These software can automatically calculate the foci of each time-varying constraint no-go zone according to the input parameters and geometric models, and judge whether they can be simultaneously avoided.

[0052] Furthermore, optimization algorithms can be considered to find possible avoidance paths that can minimize the trajectory adjustment of the spacecraft while satisfying all avoidance conditions, thereby improving the planning efficiency and mission success rate.

[0053] In some embodiments, step S3 specifically includes the following steps: Step S301: Determine the known conditions including the observation arc segment and the time-varying constraint no-go zone; Step S302: Construct a time-varying elliptical no-go zone under the known conditions; Assume that the major and minor axis foci of any two time-varying constraint no-go zones in the shape of elliptical cones among N time-varying constraint no-go zones are at the same location, and at the start of the arc segment, the direction points to any one of the time-varying constraint no-go zones, and at the end of the arc segment, the direction points to another on-orbit position of the time-varying constraint no-go zone, and the focal lengths of any two elliptical cones among N time-varying constraint no-go zones are different, and the cone center coordinates of the elliptical cone at each moment are known, and the lengths of the major and minor axes of the ellipse, convert the time-varying elliptical no-go zone into an elliptical cone for solution; The cone center is:

[0054] Where, is time; ; is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse; Then the equation for solving the ellipse is:

[0055] Step S303: Solve using the convex optimization algorithm; Construct the optimization objective function:

[0056] Where, represents the time length of the execution arc segment, represents the actuator within the time of the execution arc segment, is the initial state of the motion trajectory, is the final state of the motion trajectory; The constraint function is:

[0057]

[0058]

[0059] Where, is the initial state, is the final state, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse, and respectively represent the minimum spatial distance that the motion trajectory needs to satisfy and the maximum displacement that the aircraft can achieve.

[0060] It should be noted that this step details how to perform spacecraft attitude trajectory planning when the time-varying constraint no-fly zones can be simultaneously avoided. The time-varying elliptical no-fly zone and the time-varying spherical no-fly zone involved here are two specific shapes of time-varying constraint no-fly zones, and their positions and sizes change with time and need to be considered in the planning. Time-domain planning refers to planning the trajectory of the spacecraft in the time dimension to ensure that the spacecraft can be in the correct position at a specific time point.

[0061] Specifically, the steps include determining known conditions, such as the observation arc segment and the time-varying constraint no-fly zone, and then constructing the time-varying elliptical no-fly zone under these known conditions. In this process, we assume that the foci of the major and minor axes of all time-varying constraint no-fly zones are located at the same position and point to different on-orbit positions at the start and end of the arc segment.

[0062] More specifically, we also need to know the cone center coordinates of the elliptical cone at each moment, as well as the lengths of the major and minor axes of the ellipse. These parameters can be obtained from observation data or predicted through mathematical models. When constructing the optimization objective function, we need to consider the time length of the execution arc segment, as well as the initial state and final state of the actuator's motion trajectory during the execution arc segment.

[0063] Preferably, in order to more precisely construct the time-varying elliptical no-fly zone and solve the optimization objective function, we can use numerical methods and algorithms to handle these complex mathematical problems. For example, numerical integration methods can be used to solve the integral terms in the optimization objective function, and numerical optimization algorithms can be used to find the optimal solution.

[0064] Furthermore, machine learning techniques can also be considered to predict the future state of the time-varying constraint no-fly zone, thereby improving the accuracy and adaptability of the planning. During the solution process, we also need to consider the minimum safety distance that the motion trajectory needs to satisfy and the maximum displacement that the aircraft can achieve, and these parameters can be set according to the design and performance of the aircraft. Through these methods, we can ensure that the spacecraft can complete the task with the optimal time while avoiding the time-varying constraint no-fly zone.

[0065] In some embodiments, in step S302, the conversion of the ellipse into an elliptical cone for solution is specifically obtained through the following method: Since the cone center of the elliptical cone is known and the lengths of the major semi-axis and minor semi-axis of the ellipse are fixed, then through the cone surface trajectory points and the trajectory points of the ellipse can be determined; therefore, determining whether there is an intersection between the motion trajectory points inside the elliptical cone and the points of the ellipse can be obtained by determining whether the intersection of the circle at the bottom of the elliptical cone and the ellipse intersects; thus, the trajectory constraint problem is converted into whether the trajectory points intersect with the circle at the bottom of the cone.

[0066] It should be noted that this step details how to transform a time-varying elliptical no-fly zone into an elliptical cone for solution. Here, the elliptical cone refers to a geometric shape with an elliptical base and a conical side, which can be used to simulate and handle the avoidance problem of the time-varying elliptical no-fly zone. Transformation means converting the geometric characteristics and motion trajectories of the time-varying elliptical no-fly zone into the geometric model of the elliptical cone for mathematical solution.

[0067] Specifically, the process of transforming an ellipse into an elliptical cone for solution involves determining the position of the cone center of the elliptical cone and the lengths of the major and minor semi-axes of the ellipse. These parameters can be obtained by analyzing the observation data of the time-varying elliptical no-fly zone. For example, the cone center can be calculated from time series data, and the lengths of the major and minor semi-axes can be determined according to the maximum and minimum sizes of the elliptical no-fly zone. With these parameters, we can construct the geometric model of the elliptical cone and apply it to the solution of the avoidance problem.

[0068] Preferably, in order to perform the transformation and solution of the elliptical cone more precisely, computer-aided design (CAD) software or professional geometric modeling software can be used to assist this process. These software can automatically construct a three-dimensional model of the elliptical cone based on the input parameters and perform geometric analysis. In addition, numerical optimization methods can also be considered to handle the solution problem of the elliptical cone, such as finding the optimal solution that satisfies all constraint conditions through iterative algorithms.

[0069] Furthermore, in actual operation, the parameter settings of the elliptical cone can also be adjusted according to the dynamic characteristics and mission requirements of the aircraft to achieve a more flexible and adaptable avoidance strategy. Through these methods, we can ensure that the spacecraft completes the mission with the optimal time while avoiding the time-varying elliptical no-fly zone.

[0070] In some embodiments, in step S303, the transformation of the spherical surface into a spherical cone for solution is specifically obtained through the following method: Since the cone center of the spherical cone is known and the spherical radius is fixed, the cone surface trajectory points and the spherical surface can be determined; therefore, determining whether there is an intersection between the motion trajectory points inside the spherical cone and the spherical surface can be obtained by determining whether there is an intersection between the vertex of the spherical cone and the spherical surface; thus, transforming the trajectory constraint problem into whether the distance from the vertex to the spherical surface is less than the spherical radius.

[0071] It should be noted that this step involves the process of transforming a time-varying spherical no-fly zone into a spherical cone for solution. The spherical cone is a geometric shape with a spherical base and a vertex on the opposite side of the center of the sphere, which can be used to simulate and handle the avoidance problem of the time-varying spherical no-fly zone. Transformation means converting the geometric characteristics and motion trajectories of the time-varying spherical no-fly zone into the geometric model of the spherical cone for mathematical solution.

[0072] Specifically, the process of transforming a spherical surface into a spherical cone for solution includes determining the position of the cone center of the spherical cone and the radius of the spherical surface. These parameters can be obtained by analyzing the observation data of the time-varying spherical no-fly zone. For example, the cone center can be calculated from time series data, and the spherical radius can be determined according to the maximum size of the spherical no-fly zone. With these parameters, we can construct the geometric model of the spherical cone and apply it to the solution of the avoidance problem.

[0073] Preferably, in order to more precisely transform and solve the spherical cone, computer-aided design (CAD) software or professional geometric modeling software can be used to assist this process. These software can automatically construct a three-dimensional model of the spherical cone based on the input parameters and perform geometric analysis.

[0074] Furthermore, numerical optimization methods can also be considered to handle the solution problem of the spherical cone, such as finding the optimal solution that satisfies all constraint conditions through iterative algorithms. In actual operation, the parameter settings of the spherical cone can also be adjusted according to the dynamic characteristics and mission requirements of the aircraft to achieve a more flexible and adaptable avoidance strategy. Through these methods, we can ensure that the spacecraft can avoid the time-varying spherical no-fly zone while achieving the time-optimal task completion.

[0075] In some embodiments, step S4 includes: When the observation arc segment starts, if the cone centers of all time-varying constraint no-fly zone cones are located on the straight line where the arc segment is located, but the cone vertices are at the on-orbit positions outside the observation arc segment, then after processing through step S3, the time-domain planning of the trajectory points and the time-varying constraint no-fly zone is performed.

[0076] It should be noted that this step describes the processing method when the cone centers of all time-varying constraint no-fly zone cones are located on the straight line where the arc segment is located, but the cone vertices are at the on-orbit positions outside the observation arc segment when the observation arc segment starts. Here, the observation arc segment refers to the specific orbital area that the spacecraft needs to pass through during the mission, and the cone center and cone vertex refer to the geometric center and the top point of the time-varying constraint no-fly zone cone. The on-orbit position refers to the real-time position of the spacecraft in the orbit.

[0077] Specifically, when the observation arc segment starts, we need to determine whether the cone centers of all time-varying constraint no-fly zone cones are located on the straight line where the arc segment is located, and whether the cone vertices are at the on-orbit positions outside the observation arc segment. This process involves the precise measurement and analysis of the spacecraft orbit data, as well as the detailed definition of the geometric characteristics of the time-varying constraint no-fly zone cone. The parameter settings include determining the position coordinates of the cone center and the position relationship of the cone vertex relative to the arc segment, which can be determined through the orbit parameters of the spacecraft and the geometric model of the time-varying constraint no-fly zone.

[0078] Preferably, to handle this situation more precisely, we can adopt advanced orbit analysis and geometric modeling tools. These tools can help us accurately determine the positions of the cone center and cone vertex and predict their changes over time. In addition, we can also use dynamic programming algorithms to adjust the trajectory points of the spacecraft to ensure that they can avoid the time-varying constraint forbidden zone at any moment within the observation arc.

[0079] Furthermore, in actual operation, we can also consider using machine learning techniques to predict the dynamic changes of the time-varying constraint forbidden zone and adjust the trajectory of the spacecraft in real time to adapt to these changes. Through these methods, we can ensure that the spacecraft can achieve the time-optimal task completion while avoiding the time-varying constraint forbidden zone.

[0080] In some embodiments, in step S303, the method for obtaining the intersection point is as follows: At each moment , the circular equation of the cone bottom is:

[0081] where is the initial state, is the final state, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse, and respectively represent the minimum spatial distance that the motion trajectory needs to satisfy and the maximum displacement that the aircraft can achieve; Judge whether the trajectory point satisfies the cone vertex constraint. If it satisfies, the trajectory point at this moment is inside the elliptical cone; otherwise, the trajectory point is outside the elliptical cone. During the arc time, through the above judgment, if the trajectory point is inside the cone, it means that any point of the cone is inside the cone; if any point of the cone is not inside the cone, it means that there is at least one point not inside the cone; that is, the motion trajectory at this moment and the cone cannot form an intersection. Represent whether the trajectory point is inside the cone as a dual problem:

[0082]

[0083]

[0084] where

[0085] where represents the distance from the observer to the time-varying constraint forbidden zone, and , represents the distance from the observer to the time-varying constraint forbidden zone, and is the constraint condition; obtain the trajectory points that satisfy the constraint condition through solution 。

[0086] It should be noted that this step involves calculating the circular equation of the cone bottom at each moment to determine whether the trajectory point satisfies the cone vertex constraint. The circle at the cone bottom here refers to the circular area formed by the bottom of the time-varying constraint forbidden zone cone, and the trajectory point refers to the expected position of the spacecraft on the planned path. The cone vertex constraint refers to the geometric and spatial restrictions that the spacecraft must comply with when avoiding the time-varying constraint forbidden zone.

[0087] Specifically, the circular equation of the cone bottom at each moment can be calculated by the following formula:

[0088] where, and are the coordinates of the center of the circle, is the radius of the circle. These parameters can be determined according to the geometric characteristics of the time-varying constraint forbidden zone cone and the current position of the spacecraft. Through this equation, we can determine whether the trajectory point of the spacecraft is inside the circle at the cone bottom, so as to determine whether the cone vertex constraint is satisfied.

[0089] Preferably, in order to calculate the circular equation of the cone bottom and judge the trajectory point more precisely, numerical calculation methods and geometric analysis tools can be adopted. These tools can help us quickly and accurately calculate the parameters of the circle at the cone bottom at each moment and judge the position of the trajectory point. In addition, optimization algorithms can also be considered to adjust the trajectory of the spacecraft so that while satisfying the cone vertex constraint, the path length or fuel consumption is minimized.

[0090] Furthermore, in actual operation, the parameter settings of the circle at the cone bottom can also be dynamically adjusted according to the dynamic characteristics and mission requirements of the spacecraft to adapt to mission changes and avoidance requirements. Through these methods, we can ensure that the spacecraft completes the mission with the optimal time while avoiding the time-varying constraint forbidden zone.

[0091] In some embodiments, step S3 further includes the following steps: Step S304: For the trajectory point obtained by solving in step S303, perform the avoidance verification of the time-varying constraint forbidden zone; this step involves comparing the trajectory point with the equations of the time-varying elliptical forbidden zone and the time-varying spherical forbidden zone to verify whether the trajectory point meets the avoidance requirements; if the trajectory point meets the avoidance requirements of all time-varying constraint forbidden zones, it is considered that the avoidance is successful, otherwise the trajectory point needs to be adjusted; Step S305: If the avoidance verification in step S304 fails, adjust the trajectory point; dynamically adjust the trajectory point according to the change of the time-varying constraint forbidden zone , to meet the avoidance requirements; the adjustment may include changing the position, speed, or acceleration of the trajectory points until all avoidance conditions are met; Step S306: Use the adjusted trajectory points to re-perform the avoidance verification in step S304 until an optimal trajectory that meets all time-varying constraint forbidden zone avoidance requirements is found.

[0092] It should be noted that this step describes the process of performing avoidance verification of the time-varying constraint forbidden zone for the obtained trajectory points. Avoidance verification refers to verifying whether the trajectory points of the spacecraft meet all predetermined avoidance requirements to ensure that the spacecraft does not enter any time-varying constraint forbidden zone. A trajectory point refers to the expected position of the spacecraft on the planned path, and a time-varying constraint forbidden zone refers to those areas whose positions and shapes change with time and need to be considered in the planning.

[0093] Specifically, for the obtained trajectory points, we need to compare them with the equations of the time-varying elliptical forbidden zone and the time-varying spherical forbidden zone to verify whether the trajectory points meet the avoidance requirements. This process involves substituting the coordinates of the trajectory points into the mathematical model of the time-varying constraint forbidden zone to check whether all avoidance conditions are met.

[0094] More specifically, if the trajectory points meet all the avoidance requirements of the time-varying constraint forbidden zone, the avoidance is considered successful; if not, the trajectory points need to be adjusted. These adjustments may include changing the position, speed, or acceleration of the trajectory points until all avoidance conditions are met.

[0095] Preferably, in order to perform avoidance verification and adjustment more precisely, computer-aided design (CAD) software or professional trajectory planning software can be used to assist this process. These software can automatically calculate whether the trajectory points are within the time-varying constraint forbidden zone based on the input parameters and geometric models and provide adjustment suggestions.

[0096] Furthermore, optimization algorithms can also be considered to automatically adjust the trajectory points to meet the avoidance requirements while minimizing the impact on the original plan. In actual operation, the avoidance strategy can also be dynamically adjusted according to the dynamic characteristics and mission requirements of the aircraft to adapt to mission changes and avoidance needs. Through these methods, we can ensure that the spacecraft can complete the mission with the optimal time while avoiding the time-varying constraint forbidden zone.

[0097] The above embodiments of the present invention have the following beneficial effects: The method described in the present invention can provide a time-optimal attitude trajectory planning solution for a spacecraft under time-varying constraint conditions. This method can ensure that the spacecraft can efficiently avoid various dynamically changing no-fly zones while maintaining the time efficiency of mission execution. By precisely defining the time-varying constraint no-fly zones and determining whether they can be avoided simultaneously, the avoidance strategy can be optimized, unnecessary trajectory adjustments can be reduced, thereby reducing energy consumption and increasing the success rate of mission execution.

[0098] Furthermore, the technologies described in these claims can dynamically adjust the trajectory points to adapt to the changes in the time-varying constraint no-fly zones, ensuring that the spacecraft always stays on a safe trajectory throughout the mission execution. Through continuous avoidance verification and adjustment, this method can find the optimal trajectory that meets all avoidance requirements, which can enhance the adaptability and flexibility of the spacecraft in a complex space environment and provide solid technical support for the safe and efficient operation of the spacecraft.

[0099] As Figure 2 shown, a time-optimal spacecraft attitude trajectory planning system 200 under time-varying constraints in some embodiments, the system 200 includes: A constraint no-fly zone determination module 201, configured to determine the time-varying constraint no-fly zones before the mission starts; A judgment module 202, configured to judge whether the time-varying constraint no-fly zones can be avoided simultaneously; A first planning module 203, configured to perform simultaneous avoidance processing on the time-varying constraint no-fly zone problems that can be avoided simultaneously, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-fly zones, so that the aircraft can complete the mission under time-optimal conditions; A second planning module 204, configured to perform non-simultaneous avoidance processing on the time-varying constraint no-fly zone problems that cannot be avoided simultaneously, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-fly zones, so that the aircraft can complete the mission under time-optimal conditions.

[0100] It can be understood that the various modules described in the time-optimal spacecraft attitude trajectory planning system 200 under time-varying constraints correspond to the respective steps in the time-optimal spacecraft attitude trajectory planning method described with reference to Figure 1 Therefore, the operations, features, and beneficial effects described above for the time-optimal spacecraft attitude trajectory planning method under time-varying constraints also apply to the time-optimal spacecraft attitude trajectory planning system 200 under time-varying constraints and the modules included therein, and will not be elaborated herein.

[0101] Next, with reference to Figure 3, which shows a schematic structural diagram of a structure 300 of an electronic device suitable for implementing some embodiments of the present invention. The electronic device in some embodiments of the present invention may include, but is not limited to, mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Tablet Computers), PMPs (Portable Multimedia Players), in-vehicle terminals (such as in-vehicle navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Figure 3 The terminal device shown is merely an example and should not impose any limitations on the functions and usage scope of the embodiments of the present invention.

[0102] As Figure 3 shown, the electronic device 300 may include a processing device (such as a central processing unit, a graphics processing unit, etc.) 301, which may perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 302 or the program loaded from the storage device 308 into the random access memory (RAM) 303. In the RAM 303, various programs and data required for the operation of the electronic device 300 are also stored. The processing device 301, the ROM 302, and the RAM 303 are connected to each other through a bus 304. The input / output (I / O) interface 305 is also connected to the bus 304.

[0103] Generally, the following devices may be connected to the I / O interface 305: an input device 306 including, for example, a touch screen, a touchpad, a keyboard, a mouse, a camera, a microphone, an accelerometer, a gyroscope, etc.; an output device 307 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 308 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 309. The communication device 309 may allow the electronic device 300 to communicate with other devices wirelessly or wiredly to exchange data. Although Figure 3 the electronic device 300 with various devices is shown, it should be understood that it is not required to implement or have all the shown devices. Instead, more or fewer devices may be implemented or had. Figure 3 Each block shown in

[0104] Furthermore, the storage medium according to the embodiments of the present application stores program instructions capable of implementing all the above methods. Among them, the program instructions can be stored in the above storage medium in the form of a software product, including several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical discs, or terminal devices such as computers, servers, mobile phones, and tablets.

[0105] The above description is only some preferred embodiments of the present invention and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present invention is not limited to the technical solutions formed by the specific combination of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the technical solutions formed by mutually replacing the above features with the (but not limited to) technical features with similar functions disclosed in the embodiments of the present invention.

Claims

1. A time-optimal spacecraft attitude trajectory planning method under time-varying constraints, characterized in that It includes the following steps: Step S1: Determine the time-varying constraint no-fly zone before the task starts; Step S2: Judge whether the time-varying constraint no-fly zones can be avoided simultaneously. If yes, go to Step S3; if no, go to Step S4; Step S3: Spacecraft attitude trajectory planning under time-varying constraints; simultaneously avoid the problems of time-varying constraint no-fly zones that can be avoided simultaneously in Step S2, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-fly zones, so that the aircraft can complete the task with the optimal time; Step S4: Spacecraft attitude trajectory planning under time-varying constraints; perform non-simultaneous avoidance processing on the problems of time-varying constraint no-fly zones that cannot be avoided simultaneously in Step S2, and perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-fly zones, so that the aircraft can complete the task with the optimal time.

2. The time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to claim 1, characterized in that Step S1 includes: Step S101: Determine the position of the time-varying constraint no-fly zone. According to the task requirements, determine the position of the time-varying constraint no-fly zone. If the pointing to the time-varying constraint no-fly zone is not within the observation arc, end; if the pointing to the time-varying constraint no-fly zone is within the observation arc, go to the next step; Step S102: Define the time-varying no-fly zone. According to the on-orbit position change of the pointing to the time-varying constraint no-fly zone, define the time-varying constraint no-fly zone; the time-varying constraint no-fly zone includes a time-varying elliptical no-fly zone with an elliptical cone shape and a time-varying spherical no-fly zone with a spherical cone shape; among them, the time-varying elliptical no-fly zone is: wherein represents the distance from the observer to the time-varying constraint forbidden area, is the reference distance, is the eccentricity, is the angle, is the reference angle; The time-varying spherical no-go zone is as follows: wherein represents the distance from the observer to the time-varying constraint forbidden area.

3. A method for time-optimal spacecraft attitude trajectory planning under time-varying constraints according to claim 1, characterized in that: Step S2 judges whether the time-varying constraint no-fly zones can be avoided simultaneously by the following method: If the major axis foci of any two time-varying constraint no-fly zones are different, the points of any two time-varying constraint no-fly zones can be avoided simultaneously; If the major axis foci of any two time-varying constraint no-fly zones are the same, but the minor axis foci are different, the points of any two time-varying constraint no-fly zones cannot be avoided simultaneously.

4. A time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to claim 1, characterized in that, Step S3 specifically includes the following steps: Step S301: Determine the known conditions, including the observation arc and the time-varying constraint no-fly zone; Step S302: Construct the time-varying elliptical no-fly zone under the known conditions. Assume that the major and minor axis foci of any two time-varying constraint no-fly zones with an elliptical cone shape among N time-varying constraint no-fly zones are at the same place, and at the start of the arc, the pointing points to any one of the time-varying constraint no-fly zones, and at the end of the arc, the pointing points to another on-orbit position of the time-varying constraint no-fly zone, and the focal lengths of any two elliptical cones among N time-varying constraint no-fly zones are different, and the cone center coordinates of the elliptical cone at each moment are known, and the lengths of the major and minor axes of the ellipse, and convert the time-varying elliptical no-fly zone into an elliptical cone for solution; the cone center is: wherein, is the time; ; is the major semi - axis of the ellipse, is the minor semi - axis of the ellipse; Then the equation for solving the ellipse is: Step S303: Solve using the convex optimization algorithm; construct the optimization objective function: Among them, represents the time length of the execution arc segment, represents that during the time of the actuator executing the arc segment, is the initial state of the motion trajectory, is the final state of the motion trajectory; Constraint function is as follows: Among them, is the initial state, is the final state, is the major semi - axis of the ellipse, is the minor semi - axis of the ellipse, and respectively represent the minimum spatial distance that the movement trajectory needs to satisfy and the maximum displacement that the aircraft can achieve.

5. A method for time-optimal spacecraft attitude trajectory planning under time-varying constraints according to claim 4, characterized in that: In step S302, the conversion of the ellipse into an elliptic cone for solution is specifically obtained through the following method: Since the cone center of the elliptic cone is known and the lengths of the major semi-axis and minor semi-axis of the ellipse are fixed, the trajectory points of the cone surface and the trajectory points of the ellipse can be determined; therefore, determining whether there is an intersection between the moving trajectory points in the elliptic cone and the points of the ellipse can be obtained by determining whether the circle at the bottom of the elliptic cone intersects with the ellipse; Thus, the trajectory constraint problem is transformed into whether the trajectory point intersects with the cone bottom circle.

6. A method for time-optimal spacecraft attitude trajectory planning under time-varying constraints according to claim 4, characterized in that: In step S303, the conversion of the spherical surface into a spherical cone for solution is specifically obtained through the following method: Since the center of the spherical cone is known and the spherical radius is fixed, the cone surface locus points and the spherical surface can be determined; therefore, determining whether there is an intersection between the moving locus points within the spherical cone and the spherical surface can be obtained by judging whether the intersection of the vertex of the spherical cone and the spherical surface intersects; thus, the trajectory constraint problem is transformed into the problem of whether the distance from the vertex to the spherical surface is less than the spherical radius.

7. A time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to claim 1, characterized in that Step S4 includes: When the observation arc segment starts, the centers of all time-varying constraint no-fly zones are located on the line where the arc segment is located, but the cone vertices are at the on-orbit positions outside the observation arc segment. Then, after processing through step S3, the time-domain planning of the trajectory points and the time-varying constraint no-fly zones is carried out.

8. A time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to claim 7, characterized in that, In step S303, the method for obtaining the intersection points is as follows: At each moment , the circular equation of the cone bottom is as follows: Among them, is the initial state, is the final state, is the major semi - axis of the ellipse, is the minor semi - axis of the ellipse, and respectively represent the minimum spatial distance that the motion trajectory needs to satisfy and the maximum displacement that the aircraft can achieve; Judge whether the trajectory points satisfy the cone vertex constraint. If they do, the trajectory points at this moment are inside the elliptical cone; otherwise, the trajectory points are outside the elliptical cone. During the arc segment time, through the above judgment, if the trajectory points are inside the cone, it means that all points of any cone are inside the cone; if the points of any cone are not inside the cone, it means that there is at least one point not inside the cone; that is, the motion trajectory at this moment and the cone cannot form an intersection. Represent whether the trajectory points are inside the cone as a dual problem: Among them, Among them, represents the distance from the observer to the time-varying constraint forbidden area, and , represents the distance from the observer to the time-varying constraint forbidden area, and is the constraint condition; the trajectory points that satisfy the constraint condition are obtained by solving.

9. A time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to claim 4, characterized in that Step S3 further includes the following steps: Step S304: For the trajectory points obtained in step S303 , perform evasion verification for the time-varying constraint no-go zones; this step involves comparing the trajectory points with the equations of the time-varying elliptical no-go zones and the time-varying spherical no-go zones to verify whether the trajectory points meet the evasion requirements; if the trajectory points meet the evasion requirements of all the time-varying constraint no-go zones, it is considered that the evasion is successful, otherwise the trajectory points need to be adjusted; Step S305: If the avoidance verification in step S304 fails, adjust the trajectory points; dynamically adjust the trajectory points according to the change of the time-varying constraint restricted area , so as to meet the avoidance requirements; the adjustment may include changing the position, speed or acceleration of the trajectory points until all avoidance conditions are met; Step S306: Re - perform the avoidance verification of step S304 on the adjusted trajectory points until an optimal trajectory that meets all the requirements for avoiding time - varying constraint restricted areas is found.

10. A time-optimal spacecraft attitude trajectory planning system under time-varying constraints, characterized in that, Including: A no-fly zone determination module for determining the time-varying constraint no-fly zones before the start of the mission; A judgment module for judging whether the time-varying constraint no-fly zones can be avoided simultaneously; A first planning module for simultaneously avoiding the time-varying constraint no-fly zone problems that can be avoided simultaneously, and carrying out time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-fly zones, so that the aircraft completes the mission under the optimal time; A second planning module for non-simultaneously avoiding the time-varying constraint no-fly zone problems that cannot be avoided simultaneously, and carrying out time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint no-fly zones, so that the aircraft completes the mission under the optimal time.

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