A time-optimal spacecraft attitude trajectory planning method and system under time-varying constraints

Abstract

The present invention provides a time-optimal spacecraft attitude trajectory planning method and system under time-varying constraints. The method involves determining time-varying constraint forbidden zones, determining whether they can be avoided simultaneously, performing avoidance processing, and time-domain planning to enable the spacecraft to complete its mission in the shortest possible time. The specific steps include: determining the location of the time-varying constraint forbidden zones before the mission begins; determining whether they can be avoided simultaneously; performing simultaneous avoidance processing for those that can be avoided simultaneously; and performing non-simultaneous avoidance processing for those that cannot be avoided simultaneously, ultimately completing the mission in the most time-optimal manner. This invention ensures that the spacecraft completes its mission safely and efficiently in the shortest possible time.

Description

Technical Field

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

[0002] In the field of spacecraft attitude control, ensuring that spacecraft can effectively avoid various time-varying restricted zones during mission execution is crucial. These restricted zones may include communication blind spots caused by obstructions from 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 constraints, resulting in suboptimal planned trajectories that fail to complete the mission in the shortest possible time, or posing safety risks when avoiding time-varying restricted 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: the existing planning methods often lack the ability to adapt to the dynamic changes of time-varying constraint forbidden areas, resulting in the inability to achieve optimal time efficiency and safety in practical applications; at the same time, the avoidance processing of multiple time-varying constraint forbidden areas is not flexible enough, and it is difficult to meet multiple avoidance conditions at the same time, thereby limiting the flexibility and effectiveness of spacecraft attitude trajectory planning. Summary of the Invention

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

[0005] In a first aspect of the present invention, a time-optimal spacecraft attitude trajectory planning method under time-varying constraints is provided, comprising:

[0006] Step S1: Determine the time-varying constraint restricted area before the task starts;

[0007] Step S2: determine whether the time-varying constraint restricted areas can be avoided simultaneously. If yes, proceed to step S3; if not, proceed to step S4.

[0008] Step S3, spacecraft attitude trajectory planning under time-varying constraints; performing simultaneous avoidance processing on the time-varying constraint forbidden area problem that can be avoided simultaneously in step S2, and performing time domain planning on the processed trajectory points and the trajectory points of the time-varying constraint forbidden area, so that the spacecraft completes the mission in the optimal time;

[0009] Step S4, spacecraft attitude trajectory planning under time-varying constraints; perform different avoidance processing on the time-varying constraint forbidden area problem 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 forbidden area, so that the aircraft can complete the mission under the optimal time.

[0010] Furthermore, step S1 includes:

[0011] Step S101: Determine the location of the time-varying constraint forbidden zone. According to the task requirements, determine the location of the time-varying constraint forbidden zone. If the time-varying constraint forbidden zone is not within the observation arc, then end; if the time-varying constraint forbidden zone is within the observation arc, proceed to the next step.

[0012] Step S102: Define a time-varying restricted zone. Define a time-varying restricted zone based on the position change of the time-varying restricted zone on orbit. The time-varying restricted zone includes a time-varying elliptical restricted zone in the shape of an elliptical cone and a time-varying spherical restricted zone in the shape of a spherical cone. The time-varying elliptical restricted zone is:

[0013]

[0014] in represents the distance from the observer to the time-varying constraint forbidden zone, is the reference distance, is the eccentricity, is the angle, is the reference angle;

[0015] The time-varying spherical restricted area is:

[0016] in represents the distance from the observer to the time-varying constraint forbidden zone.

[0017] Furthermore, step S2 determines whether the time-varying constraint forbidden zone can be avoided simultaneously by the following method: if the long axis focal points of any two time-varying constraint forbidden zones are different, then any two points of the time-varying constraint forbidden zone can be avoided simultaneously;

[0018] If the long axis focus of any two time-varying constraint forbidden zones is the same but the short axis focus is different, then any two points of the time-varying constraint forbidden zones cannot be avoided at the same time.

[0019] Furthermore, step S3 specifically includes the following steps:

[0020] Step S301: Determine known conditions including observation arc segments and time-varying constraint restricted areas;

[0021] Step S302: Construct a time-varying elliptical restricted area under known conditions; assuming that the major and minor axis foci of any two elliptical cones in the N time-varying restricted areas are at the same location, and that the foci at the beginning of the arc point to any one of the time-varying restricted areas, and at the end of the arc point to another on-orbit location of the time-varying restricted area, and that the focal lengths of any two elliptical cones in the N time-varying restricted areas are different, and that the coordinates of the cone center of the elliptical cone at each moment are known, and the lengths of the major and minor axes of the ellipse are known, the time-varying elliptical restricted area is converted into an elliptical cone for solution; the cone center is:

[0022]

[0023] in, For time; ; is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse;

[0024] Then the equation of the ellipse is:

[0025]

[0026] Step S303: solve using a convex optimization algorithm; construct an optimization objective function:

[0027]

[0028] in, Indicates the time length of executing the arc segment, Indicates that the actuator is executing the arc time. is the initial state of the motion trajectory, is the final state of the motion trajectory;

[0029] Constraint Function for:

[0030]

[0031]

[0032]

[0033] in, 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 They represent the minimum spatial spacing that the motion trajectory needs to meet and the maximum displacement that the aircraft can achieve.

[0034] Furthermore, in step S302, the ellipse is converted into an elliptical cone by the following method: Since the center of the elliptical cone is known and the lengths of the major and minor axes of the ellipse are fixed, the cone trajectory point The trajectory points of the ellipse can be determined; therefore, whether there is an intersection between the motion trajectory points in the elliptical cone and the points of the ellipse can be determined by judging whether the intersection of the circle at the bottom of the elliptical cone and the ellipse intersects; thus converting the trajectory constraint problem into whether the trajectory points intersect with the circle at the bottom of the cone.

[0035] Furthermore, in step S303, the sphere is converted into a spherical cone by the following method: Since the center of the spherical cone is known and the radius of the sphere is fixed, the cone trajectory point and the sphere can be determined; therefore, whether there is an intersection between the point of intersection of the motion trajectory point in the spherical cone and the sphere can be determined by judging whether the intersection of the vertex of the spherical cone and the sphere intersects; thus transforming the trajectory constraint problem into a vertex Whether the distance to the sphere is less than the radius of the sphere.

[0036] Furthermore, step S4 includes:

[0037] When the observation arc begins, the cone centers of all time-varying constraint restricted area cones are located on the straight line where the arc segment is located, but the cone apex is at an on-orbit position outside the observation arc segment. Then, it is processed through step S3 and then the time domain planning of the trajectory point and the time-varying constraint restricted area is performed.

[0038] Furthermore, in step S303, the method for obtaining the intersection point is:

[0039] At every moment , the equation of the circle at the base of the cone is:

[0040]

[0041] in, 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 They represent the minimum spatial spacing that the motion trajectory needs to meet and the maximum displacement that the aircraft can achieve;

[0042] Determine whether the trajectory point satisfies the cone vertex constraint. If so, the trajectory point is inside the elliptical cone at this moment, 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 all points of the cone are inside the cone; if any point of the cone is not inside the cone, it means that there is at least one point that is not inside the cone; that is, the motion trajectory at this moment cannot intersect with the cone. Whether the trajectory point is inside the cone is expressed as a dual problem:

[0043]

[0044]

[0045]

[0046] in,

[0047] in, 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; the trajectory points that meet the constraint condition are obtained by solving .

[0048] Furthermore, step S3 further includes the following steps:

[0049] Step S304: For the trajectory points obtained in step S303 , to verify the avoidance of the time-varying constraint restricted area; this step involves the trajectory point Compare with the equations of the time-varying elliptical restricted area and the time-varying spherical restricted area to verify whether the trajectory point meets the avoidance requirements; if the trajectory point meets the avoidance requirements of all time-varying restricted areas, the avoidance is considered successful, otherwise the trajectory point needs to be adjusted;

[0050] Step S305: If the avoidance verification in step S304 fails, the trajectory point is adjusted; the trajectory point is dynamically adjusted according to the changes in the time-varying constraint restricted area. , to meet the avoidance requirements; the adjustment may include changing the position, velocity or acceleration of the trajectory point until all avoidance conditions are met;

[0051] Step S306: Adjust the track points The avoidance verification of step S304 is repeated until the optimal trajectory that meets all the time-varying restricted area avoidance requirements is found.

[0052] In a second aspect of the present invention, a time-optimal spacecraft attitude trajectory planning system under time-varying constraints is provided, comprising:

[0053] The constraint restricted zone determination module is used to determine the time-varying constraint restricted zone before the mission begins;

[0054] A judgment module, used to judge whether the time-varying constraint restricted areas can be avoided simultaneously;

[0055] The first planning module is used to simultaneously avoid the time-varying constraint restricted areas that can be avoided at the same time, and to perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint restricted areas, so that the aircraft can complete the mission in the optimal time;

[0056] The second planning module is used to perform different avoidance processing on the time-varying constraint restricted area problem that cannot be avoided simultaneously, and to perform time domain planning on the processed trajectory points and the trajectory points of the time-varying constraint restricted area, so that the aircraft can complete the mission under the optimal time.

[0057] The above-described embodiments of the present invention have at least the following beneficial effects: By comprehensively considering the dynamic characteristics of time-varying constraint exclusion zones, this method can effectively plan a spacecraft's attitude trajectory, enabling it to avoid time-varying constraint exclusion zones while achieving mission completion in the most optimal time. This method can improve spacecraft safety and mission execution efficiency in complex environments, reducing time delays and resource waste caused by improper avoidance.

[0058] Furthermore, through precise time-domain planning and a convex optimization algorithm, this method can flexibly handle both simultaneously avoidable and non-avoidable time-varying restricted zones, thereby finding the optimal spacecraft attitude trajectory while satisfying all avoidance requirements. This approach ensures the stability and reliability of the spacecraft during its mission, while mitigating the risks associated with improper avoidance, providing a strong guarantee for its safe operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily apparent by reading the following detailed description with reference to the accompanying drawings, in which several embodiments of the present invention are shown by way of example and not limitation, in which:

[0060] Figure 1 A schematic flow chart of a time-optimal spacecraft attitude trajectory planning method under time-varying constraints provided by one embodiment of the present invention;

[0061] Figure 2 A schematic diagram of the structure of a time-optimal spacecraft attitude trajectory planning system under time-varying constraints provided by one embodiment of the present invention;

[0062] Figure 3 The figure schematically shows the structure of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] 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 provided solely to enable those skilled in the art to better understand and implement the present invention, and are not intended to limit the scope of the present invention in any way. Rather, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0064] Those skilled in the art will appreciate that embodiments of the present invention may be implemented as a system, apparatus, device, method, or computer program product. Therefore, the present invention may be implemented in the following forms: entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or in a combination of hardware and software.

[0065] It should be noted that any number of elements in the drawings is for illustration only and not for limitation, and any naming is only for distinction and does not have any limiting meaning.

[0066] Reference below Figure 1 , Figure 1 This is a flow chart of a method for time-optimal spacecraft attitude trajectory planning under time-varying constraints provided by one embodiment of the present invention. Figure 1 As shown, a time-optimal spacecraft attitude trajectory planning method 100 under time-varying constraints includes:

[0067] Step S1: Determine the time-varying constraint restricted area before the task starts;

[0068] Step S2: determine whether the time-varying constraint restricted areas can be avoided simultaneously. If yes, proceed to step S3; if not, proceed to step S4.

[0069] Step S3, spacecraft attitude trajectory planning under time-varying constraints; performing simultaneous avoidance processing on the time-varying constraint forbidden area problem that can be avoided simultaneously in step S2, and performing time domain planning on the processed trajectory points and the trajectory points of the time-varying constraint forbidden area, so that the spacecraft completes the mission in the optimal time;

[0070] Step S4, spacecraft attitude trajectory planning under time-varying constraints; perform different avoidance processing on the time-varying constraint forbidden area problem 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 forbidden area, so that the aircraft can complete the mission under the optimal time.

[0071] It's important to note that when determining time-varying restricted zones before a mission begins, we first need to identify and define areas whose position and shape change over time during the spacecraft's mission. These areas might include communication blind spots caused by obstructions by the Earth or other celestial bodies, as well as other areas that must be avoided due to mission requirements or safety concerns. Time-varying restricted zones are areas whose position and shape change over time and require dynamic avoidance.

[0072] Specifically, the process of determining the location of the time-varying constraint forbidden zone includes analyzing the mission requirements and observation data to determine the specific locations of these forbidden zones. For example, if the pointing time-varying constraint forbidden 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 forbidden zone need to be defined. When defining the time-varying forbidden zone, a time-varying elliptical forbidden zone in the shape of an elliptical cone and a time-varying spherical forbidden zone in the shape of a spherical cone can be defined based on the position change of the pointing time-varying constraint forbidden zone on orbit. These shapes can be accurately described by mathematical formulas. For example, the formula for the time-varying elliptical forbidden zone is:

[0073]

[0074] in represents the distance from the observer to the time-varying constraint forbidden zone, is the reference distance, is the eccentricity, is the angle, is the reference angle.

[0075] Preferably, when determining time-varying restricted zones, we can use advanced observation techniques and data processing algorithms to improve the accuracy of the restricted zone's location and shape. For example, we can use machine learning algorithms to predict the future location and shape of time-varying restricted zones, thereby planning avoidance strategies in advance.

[0076] Furthermore, for the definition of the time-varying spherical restricted area, the distance from the observer to the time-varying restricted area can be This distance can be determined based on 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 restricted area when performing the mission, ensuring the successful completion of the mission.

[0077] In some embodiments, step S1 includes:

[0078] Step S101: Determine the location of the time-varying constraint forbidden zone. According to the task requirements, determine the location of the time-varying constraint forbidden zone. If the time-varying constraint forbidden zone is not within the observation arc, then end; if the time-varying constraint forbidden zone is within the observation arc, proceed to the next step.

[0079] Step S102: Define a time-varying restricted zone. Define a time-varying restricted zone based on the position change of the time-varying restricted zone on orbit. The time-varying restricted zone includes a time-varying elliptical restricted zone in the shape of an elliptical cone and a time-varying spherical restricted zone in the shape of a spherical cone. The time-varying elliptical restricted zone is:

[0080]

[0081] in represents the distance from the observer to the time-varying constraint forbidden zone, is the reference distance, is the eccentricity, is the angle, is the reference angle;

[0082] The time-varying spherical restricted area is:

[0083] in represents the distance from the observer to the time-varying constraint forbidden zone.

[0084] It's important to note that the first step in this method involves determining the locations of time-varying constraint exclusion zones before the mission begins. This requires identifying those time-varying constraint exclusion zones that may exist within the spacecraft's observation arc, based on the specific mission requirements. The observation arc refers to the specific area that the spacecraft needs to observe or pass through during the mission, while time-varying constraint exclusion zones are areas whose location and shape change over time and must be avoided to ensure safe mission execution.

[0085] Specifically, the process of determining the locations of time-varying constraint exclusion zones involves analyzing the spacecraft's mission requirements and observational data to determine their specific locations. If the time-varying constraint exclusion zone is not within the observation arc, no further processing is required. If it is within the observation arc, the next step is to define the shape and size of the time-varying exclusion zone.

[0086] More specifically, when defining a time-varying restricted zone, we can define a time-varying elliptical restricted zone with an elliptical cone shape and a time-varying spherical restricted zone with a spherical cone shape, based on the position change of the time-varying restricted zone on orbit. These shapes can be accurately described by mathematical formulas. For example, the formula for the time-varying elliptical restricted zone is:

[0087]

[0088] in represents the distance from the observer to the time-varying constraint forbidden zone, is the reference distance, is the eccentricity, is the angle, is the reference angle.

[0089] Preferably, in the process of determining the time-varying restricted zone, we can use advanced observation techniques and data processing algorithms to improve the accuracy of the restricted zone position and shape. For example, we can use machine learning algorithms to predict the future position and shape changes of the time-varying restricted zone, so as to plan the avoidance strategy in advance. In addition, for the definition of the time-varying spherical restricted zone, we can use the distance from the observer to the time-varying restricted zone to calculate the distance between the observer and the time-varying restricted zone. This distance can be determined based on 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 restricted area when performing the mission, ensuring the successful completion of the mission.

[0090] In some embodiments, step S2 determines whether the time-varying constraint forbidden zone can be avoided simultaneously by the following method: if the long axis focal points of any two time-varying constraint forbidden zones are different, then any two points of the time-varying constraint forbidden zone can be avoided simultaneously;

[0091] If the long axis focus of any two time-varying constraint forbidden zones is the same but the short axis focus is different, then any two points of the time-varying constraint forbidden zones cannot be avoided at the same time.

[0092] It's important to note that this step involves determining whether the time-varying constraint exclusion zones can be avoided simultaneously. Simultaneous avoidance here means that the spacecraft, when planning its trajectory, can find a path that avoids all time-varying constraint exclusion zones, without having to evade each one separately. The major and minor axis focal points refer to the geometric properties of the time-varying elliptical and spherical exclusion zones when defining them. They are key parameters that determine the shape and location of the exclusion zones.

[0093] Specifically, the method for determining whether time-varying constraint forbidden zones can be avoided simultaneously includes checking whether the major and minor axis focal points of any two time-varying constraint forbidden zones are the same. If the major axis focal points of any two time-varying constraint forbidden zones are different, it means that their avoidance paths do not conflict with each other, and thus they can be avoided simultaneously. Conversely, if the major axis focal points are the same but the minor axis focal points are different, it means that the avoidance path of at least one of the forbidden zones conflicts with the other forbidden zones, and therefore cannot be avoided simultaneously. The determination of these focal points can be determined through geometric analysis and mathematical calculations, and the specific parameter settings need to be determined based on actual observation data and mission requirements.

[0094] Preferably, computer-aided design (CAD) software or specialized trajectory planning software can be used to assist in the analysis of whether time-varying constraint exclusion zones can be simultaneously avoided. Based on input parameters and geometric models, these software programs can automatically calculate the focal points of each time-varying constraint exclusion zone and determine whether they can be simultaneously avoided.

[0095] Furthermore, it is also possible to consider using optimization algorithms to find possible avoidance paths that can minimize the spacecraft's trajectory adjustments while satisfying all avoidance conditions, thereby improving planning efficiency and mission success rate.

[0096] In some embodiments, step S3 specifically includes the following steps:

[0097] Step S301: Determine known conditions including observation arc segments and time-varying constraint restricted areas;

[0098] Step S302: Construct a time-varying elliptical restricted area under known conditions; assuming that the major and minor axis foci of any two elliptical cones in the N time-varying restricted areas are at the same location, and that the foci at the beginning of the arc point to any one of the time-varying restricted areas, and at the end of the arc point to another on-orbit location of the time-varying restricted area, and that the focal lengths of any two elliptical cones in the N time-varying restricted areas are different, and that the coordinates of the cone center of the elliptical cone at each moment are known, and the lengths of the major and minor axes of the ellipse are known, the time-varying elliptical restricted area is converted into an elliptical cone for solution; the cone center is:

[0099]

[0100] in, For time; ; is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse;

[0101] Then the equation of the ellipse is:

[0102]

[0103] Step S303: solve using a convex optimization algorithm; construct an optimization objective function:

[0104]

[0105] in, Indicates the time length of executing the arc segment, Indicates that the actuator is executing the arc time. is the initial state of the motion trajectory, is the final state of the motion trajectory;

[0106] Constraint Function for:

[0107]

[0108]

[0109]

[0110] in, 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 They represent the minimum spatial spacing that the motion trajectory needs to meet and the maximum displacement that the aircraft can achieve.

[0111] It's important to note that this step details how to plan a spacecraft's attitude trajectory, assuming that time-varying constraint exclusion zones can be avoided simultaneously. The time-varying elliptical and spherical exclusion zones mentioned here are two specific types of time-varying constraint exclusion zones. Their position and size vary over time and must be accounted for in planning. Temporal planning involves planning a spacecraft's trajectory over time to ensure it is in the correct position at a specific point in time.

[0112] Specifically, the steps include determining known conditions, such as the observation arc and the time-varying constraint exclusion zone, and then constructing the time-varying elliptical exclusion zone under these known conditions. In this process, we assume that the major and minor axis foci of all time-varying constraint exclusion zones are located at the same position and point to different on-orbit locations at the beginning and end of the arc.

[0113] More specifically, we also need to know the coordinates of the cone center of the ellipse at each moment, as well as the lengths of the major and minor axes of the ellipse. These parameters can be obtained from observational data or predicted using mathematical models. When constructing the optimization objective function, we need to consider the duration of the arc execution and the initial and final states of the actuator's trajectory during the arc execution time.

[0114] Preferably, in order to more accurately construct the time-varying elliptical exclusion zone and solve the optimization objective function, numerical methods and algorithms can be used to handle these complex mathematical problems. For example, numerical integration methods can be used to solve the integral term in the optimization objective function, and numerical optimization algorithms can be used to find the optimal solution.

[0115] Furthermore, machine learning techniques can be used to predict the future state of time-varying constraint exclusion zones, thereby improving planning accuracy and adaptability. During the solution process, we also need to consider the minimum safe distance that the trajectory must meet and the maximum displacement that the spacecraft can achieve. These parameters can be set based on the design and performance of the spacecraft. Through these methods, we can ensure that the spacecraft achieves the optimal time for mission completion while avoiding time-varying constraint exclusion zones.

[0116] In some embodiments, in step S302, the ellipse is converted into an elliptical cone by the following method: since the center of the elliptical cone is known, the lengths of the major and minor axes of the ellipse are fixed, the cone trajectory point The trajectory points of the ellipse can be determined; therefore, whether there is an intersection between the motion trajectory points in the elliptical cone and the points of the ellipse can be determined by judging whether the intersection of the circle at the bottom of the elliptical cone and the ellipse intersects; thus converting the trajectory constraint problem into whether the trajectory points intersect with the circle at the bottom of the cone.

[0117] It's important to note that this step details how to convert a time-varying elliptical exclusion zone into an elliptical cone for solution. An elliptical cone, here, is a geometric shape with an elliptical base and conical sides. This shape can be used to simulate and address the problem of circumventing a time-varying elliptical exclusion zone. The conversion involves converting the geometric characteristics and motion trajectory of the time-varying elliptical exclusion zone into an elliptical cone geometric model for mathematical solution.

[0118] Specifically, the process of converting an ellipse into an elliptical cone involves determining the location of the cone's center and the lengths of its major and minor axes. These parameters can be obtained by analyzing observational data of time-varying elliptical exclusion zones. For example, the cone's center can be calculated from time series data, while the lengths of its major and minor axes can be determined based on the maximum and minimum dimensions of the elliptical exclusion zone. Using these parameters, we can construct a geometric model of the elliptical cone and apply it to solving circumvention problems.

[0119] Preferably, to more accurately transform and solve the elliptical cone, computer-aided design (CAD) software or specialized geometric modeling software can be used to assist in this process. These software programs can automatically construct a three-dimensional model of the elliptical cone based on the input parameters and perform geometric analysis. Furthermore, numerical optimization methods can be considered to solve the elliptical cone problem, such as using an iterative algorithm to find the optimal solution that satisfies all constraints.

[0120] Furthermore, in actual operations, the parameters of the elliptical cone can be adjusted according to the dynamic characteristics of the spacecraft and mission requirements to achieve a more flexible and adaptable avoidance strategy. Through these methods, we can ensure that the spacecraft achieves the optimal time to complete the mission while avoiding the time-varying elliptical exclusion zone.

[0121] In some embodiments, in step S303, the spherical surface is converted into a spherical cone by the following method: Since the center of the spherical cone is known and the radius of the spherical surface is fixed, the cone trajectory point and the sphere can be determined; therefore, whether there is an intersection between the point of intersection of the motion trajectory point in the spherical cone and the sphere can be determined by judging whether the intersection of the vertex of the spherical cone and the sphere intersects; thus transforming the trajectory constraint problem into a vertex Whether the distance to the sphere is less than the radius of the sphere.

[0122] It's important to note that this step involves converting the time-varying spherical exclusion zone into a spherical cone for solution. A spherical cone is a geometric shape with a spherical base and a vertex on the opposite side of the sphere's center. This shape can be used to simulate and address the problem of circumventing a time-varying spherical exclusion zone. The conversion involves transforming the geometric characteristics and motion trajectory of the time-varying spherical exclusion zone into a spherical cone geometric model for mathematical solution.

[0123] Specifically, the process of converting a sphere into a spherical cone involves determining the location of the cone's center and the radius of the sphere. These parameters can be obtained by analyzing observational data from a time-varying spherical restricted area. For example, the cone's center can be calculated from time series data, while the radius can be determined based on the maximum size of the restricted area. Using these parameters, we can construct a geometric model of the spherical cone and apply it to solving avoidance problems.

[0124] Preferably, in order to more accurately transform and solve the spherical cone, computer-aided design (CAD) software or professional geometric modeling software can be used to assist in this process. These software can automatically construct a three-dimensional model of the spherical cone based on the input parameters and perform geometric analysis.

[0125] Furthermore, numerical optimization methods can be considered to solve the spherical cone problem, for example, by using iterative algorithms to find the optimal solution that satisfies all constraints. In practice, the spherical cone's parameters can be adjusted based on the spacecraft's dynamic characteristics and mission requirements to achieve a more flexible and adaptable avoidance strategy. These methods can ensure that the spacecraft achieves the optimal time-to-mission while avoiding the time-varying spherical exclusion zone.

[0126] In some embodiments, step S4 includes:

[0127] When the observation arc begins, the cone centers of all time-varying constraint restricted area cones are located on the straight line where the arc segment is located, but the cone apex is at an on-orbit position outside the observation arc segment. Then, it is processed through step S3 and then the time domain planning of the trajectory point and the time-varying constraint restricted area is performed.

[0128] It should be noted that this step describes how to handle the situation where, at the beginning of an observation arc, the cone centers of all time-varying constraint exclusion zone cones lie on the line of the arc, but the cone apex lies at an on-orbit position outside the observation arc. The observation arc here refers to the specific orbital region that the spacecraft must traverse during its mission, while the cone center and cone apex refer to the geometric center and apex of the time-varying constraint exclusion zone cones. The on-orbit position refers to the spacecraft's real-time position in orbit.

[0129] Specifically, at the beginning of an observation arc, we need to determine whether the centers of all time-varying constraint exclusion zone cones lie on the line along which the arc lies, and whether the cone vertices are at on-orbit locations outside the observation arc. This process requires precise measurement and analysis of spacecraft orbital data, as well as detailed definition of the geometric characteristics of the time-varying constraint exclusion zone cones. Parameter setting involves determining the coordinates of the cone centers and the positional relationship of the cone vertices relative to the arc. These can be determined using the spacecraft's orbital parameters and the geometric model of the time-varying constraint exclusion zone.

[0130] To more accurately handle this situation, we can employ advanced trajectory analysis and geometric modeling tools. These tools can help us precisely determine the locations of the cone center and apex and predict their evolution over time. Furthermore, we can employ dynamic programming algorithms to adjust the spacecraft's trajectory points to ensure they avoid the time-varying constraint exclusion zone at any moment within the observation arc.

[0131] Furthermore, in actual operations, machine learning techniques can be used to predict the dynamic changes of time-varying constraint exclusion zones and adjust the spacecraft's trajectory in real time to adapt to these changes. Through these methods, we can ensure that the spacecraft achieves the optimal time for mission completion while avoiding time-varying constraint exclusion zones.

[0132] In some embodiments, in step S303, the method for obtaining the intersection point is:

[0133] At every moment , the equation of the circle at the base of the cone is:

[0134]

[0135] in, 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 They represent the minimum spatial spacing that the motion trajectory needs to meet and the maximum displacement that the aircraft can achieve;

[0136] Determine whether the trajectory point satisfies the cone vertex constraint. If so, the trajectory point is inside the elliptical cone at this moment, 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 all points of the cone are inside the cone; if any point of the cone is not inside the cone, it means that there is at least one point that is not inside the cone; that is, the motion trajectory at this moment cannot intersect with the cone. Whether the trajectory point is inside the cone is expressed as a dual problem:

[0137]

[0138]

[0139]

[0140] in,

[0141] in, 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; the trajectory points that meet the constraint condition are obtained by solving .

[0142] It's important to note that this step involves calculating the equation of the circle at the base of the cone at each moment in time to determine whether the trajectory point satisfies the cone vertex constraint. The cone base circle here refers to the circular area formed by the bottom of the time-varying constraint exclusion zone, while the trajectory point refers to the desired position of the spacecraft on the planned path. The cone vertex constraint refers to the geometric and spatial restrictions that the spacecraft must adhere to when circumventing the time-varying constraint exclusion zone.

[0143] Specifically, the circle equation of the cone base at each moment can be calculated using the following formula:

[0144]

[0145] in, and are the coordinates of the circle center, is the radius of the circle. These parameters can be determined based on the geometric properties of the time-varying restricted area cone and the current position of the spacecraft. Using this equation, we can determine whether the spacecraft's trajectory point lies within the cone base circle, thereby determining whether the cone vertex constraint is satisfied.

[0146] To more accurately calculate the cone base circle equation and determine the trajectory points, numerical calculation methods and geometric analysis tools can be used. These tools can help quickly and accurately calculate the cone base circle parameters at each moment and determine the location of the trajectory points. Furthermore, optimization algorithms can be considered to adjust the spacecraft's trajectory to minimize path length or fuel consumption while satisfying the cone vertex constraints.

[0147] Furthermore, in actual operation, the cone base circle parameters can be dynamically adjusted based on the spacecraft's dynamic characteristics and mission requirements to adapt to mission changes and avoidance needs. Through these methods, we can ensure that the spacecraft achieves the optimal time for mission completion while avoiding time-varying restricted areas.

[0148] In some embodiments, step S3 further includes the following steps:

[0149] Step S304: For the trajectory points obtained in step S303 , to verify the avoidance of the time-varying constraint restricted area; this step involves the trajectory point Compare with the equations of the time-varying elliptical restricted area and the time-varying spherical restricted area to verify whether the trajectory point meets the avoidance requirements; if the trajectory point meets the avoidance requirements of all time-varying restricted areas, the avoidance is considered successful, otherwise the trajectory point needs to be adjusted;

[0150] Step S305: If the avoidance verification in step S304 fails, the trajectory point is adjusted; the trajectory point is dynamically adjusted according to the changes in the time-varying constraint restricted area. , to meet the avoidance requirements; the adjustment may include changing the position, velocity or acceleration of the trajectory point until all avoidance conditions are met;

[0151] Step S306: Adjust the track points The avoidance verification of step S304 is repeated until the optimal trajectory that meets all the time-varying restricted area avoidance requirements is found.

[0152] It's important to note that this step describes the process of verifying the time-varying constraint exclusion zones for the solved trajectory points. Avoidance verification verifies that the spacecraft's trajectory points meet all predefined avoidance requirements, ensuring that the spacecraft does not enter any time-varying constraint exclusion zones. Trajectory points are the expected positions of the spacecraft along the planned path, while time-varying constraint exclusion zones are areas whose position and shape change over time and must be accounted for in planning.

[0153] Specifically, for each solved trajectory point, we need to compare it with the equations for the time-varying elliptical and spherical restricted zones to verify whether the trajectory point meets the avoidance requirements. This process involves substituting the coordinates of the trajectory point into the mathematical model of the time-varying restricted zone and checking whether all avoidance conditions are met.

[0154] More specifically, if the trajectory point meets the avoidance requirements of all time-varying constraint exclusion zones, the avoidance is considered successful; if not, the trajectory point needs to be adjusted. These adjustments may include changing the position, velocity, or acceleration of the trajectory point until all avoidance conditions are met.

[0155] Preferably, for more precise avoidance verification and adjustment, computer-aided design (CAD) software or specialized trajectory planning software can be used to assist in this process. Based on the input parameters and geometric model, these software can automatically calculate whether the trajectory points are within the time-varying constraint exclusion zone and provide adjustment suggestions.

[0156] Furthermore, optimization algorithms can be used to automatically adjust trajectory points to meet avoidance requirements while minimizing impact on the original plan. In practice, the avoidance strategy can be dynamically adjusted based on the dynamic characteristics of the spacecraft and mission requirements to adapt to changing missions and avoidance needs. These methods can ensure that the spacecraft achieves optimal mission completion while avoiding time-varying restricted areas.

[0157] The aforementioned embodiments of the present invention have the following beneficial effects: The method described herein can provide a time-optimal attitude trajectory planning solution for a spacecraft under time-varying constraints. This method ensures that the spacecraft can efficiently avoid various dynamically changing forbidden zones during mission execution while maintaining time efficiency. By precisely defining time-varying forbidden zones and determining whether they can be avoided simultaneously, avoidance strategies can be optimized, unnecessary trajectory adjustments can be reduced, thereby lowering energy consumption and improving mission success rates.

[0158] Furthermore, the techniques described in these claims can dynamically adjust trajectory points to accommodate changes in time-varying restricted zones, ensuring that the spacecraft remains on a safe trajectory throughout the mission. Through continuous avoidance verification and adjustment, this method can find the optimal trajectory that meets all avoidance requirements, enhancing the adaptability and flexibility of spacecraft in complex space environments and providing solid technical support for the safe and efficient operation of spacecraft.

[0159] like Figure 2 As shown, in some embodiments, a time-optimal spacecraft attitude trajectory planning system 200 under time-varying constraints includes:

[0160] A constraint forbidden zone determination module 201 is used to determine a time-varying constraint forbidden zone before a task starts;

[0161] A judgment module 202 is used to judge whether the time-varying constraint restricted areas can be avoided simultaneously;

[0162] The first planning module 203 is used to simultaneously avoid the time-varying restricted areas that can be avoided simultaneously, and to perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying restricted areas, so that the aircraft can complete the mission in the optimal time;

[0163] The second planning module 204 is used to perform different avoidance processing on the time-varying constraint forbidden zone problem that cannot be avoided simultaneously, and perform time domain planning on the processed trajectory points and the trajectory points of the time-varying constraint forbidden zone, so that the aircraft can complete the mission in the optimal time.

[0164] It is understandable that the modules recorded in the time-optimal spacecraft attitude trajectory planning system 200 under time-varying constraints are similar to those in the reference Figure 1 The steps in the time-optimal spacecraft attitude trajectory planning method under time-varying constraints described above correspond to each other. Therefore, the operations, features, and beneficial effects described above for the time-optimal spacecraft attitude trajectory planning method under time-varying constraints are also applicable to the time-optimal spacecraft attitude trajectory planning system 200 under time-varying constraints and the modules included therein, and will not be repeated here.

[0165] Reference below Figure 3, which shows a schematic structural diagram of an electronic device structure 300 suitable for implementing some embodiments of the present invention. The electronic devices in some embodiments of the present invention may include, but are 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 (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 3 The terminal device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0166] like Figure 3 As shown, electronic device 300 may include a processing device (e.g., a central processing unit, a graphics processing unit, etc.) 301, which can perform various appropriate actions and processes based on programs stored in a read-only memory (ROM) 302 or programs loaded from a storage device 308 into a random access memory (RAM) 303. RAM 303 also stores various programs and data required for the operation of electronic device 300. Processing device 301, ROM 302, and RAM 303 are interconnected via a bus 304. An input / output (I / O) interface 305 is also connected to bus 304.

[0167] Typically, 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 by wire to exchange data. Figure 3 The electronic device 300 is shown with various devices, but it should be understood that it is not required to implement or possess all of the devices shown. More or fewer devices may be implemented or possessed instead. Figure 3 Each block shown in the figure may represent one device, or may represent multiple devices as needed.

[0168] Furthermore, the storage medium of the embodiment of the present application stores program instructions that can implement all the above methods, wherein the program instructions can be stored in the above storage medium in the form of a software product, including a number of instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, or a terminal device such as a computer, server, mobile phone, or tablet.

[0169] The above descriptions merely illustrate some preferred embodiments of the present invention and the underlying technical principles. Those skilled in the art should understand that the scope of the invention encompassed by the embodiments of the present invention is not limited to technical solutions formed by specific combinations of the aforementioned technical features. It also encompasses other technical solutions formed by any combination of the aforementioned technical features or their equivalents, without departing from the aforementioned inventive concept. For example, a technical solution formed by replacing the aforementioned features with (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 by: The following steps are involved: Step S1: Determine the time-varying constraint restricted area before the task starts; Step S2: determine whether the time-varying constraint restricted areas can be avoided simultaneously. If yes, proceed to step S3; if not, proceed to step S4. Step S3, spacecraft attitude trajectory planning under time-varying constraints; performing simultaneous avoidance processing on the time-varying constraint forbidden area problem that can be avoided simultaneously in step S2, and performing time domain planning on the processed trajectory points and the trajectory points of the time-varying constraint forbidden area, so that the spacecraft completes the mission in the optimal time; Step S4, spacecraft attitude trajectory planning under time-varying constraints; performing different avoidance processing on the time-varying constraint forbidden zone problem that cannot be avoided simultaneously in step S2, and performing time domain planning on the processed trajectory points and the trajectory points of the time-varying constraint forbidden zone, so that the spacecraft completes the mission in the optimal time; Step S2 determines whether the time-varying constraint forbidden zone can be avoided simultaneously by the following method: if the long axis focal points of any two time-varying constraint forbidden zones are different, then any two points of the time-varying constraint forbidden zone can be avoided simultaneously; If the long axis focus of any two time-varying restricted zones is the same but the short axis focus is different, then any two points in the time-varying restricted zones cannot be avoided at the same time; Step S3 specifically includes the following steps: Step S301: Determine known conditions including observation arc segments and time-varying constraint restricted areas; Step S302: Construct a time-varying elliptical restricted area under known conditions; assuming that the major and minor axis foci of any two elliptical cones in the N time-varying restricted areas are at the same location, and that the foci at the beginning of the arc point to any one of the time-varying restricted areas, and at the end of the arc point to another on-orbit location of the time-varying restricted area, and that the focal lengths of any two elliptical cones in the N time-varying restricted areas are different, and that the coordinates of the cone center of the elliptical cone at each moment are known, and the lengths of the major and minor axes of the ellipse are known, the time-varying elliptical restricted area is converted into an elliptical cone for solution; the cone center is: in, For time; ; is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse; Then the equation of the ellipse is: Step S303: solve using a convex optimization algorithm; construct an optimization objective function: in, Indicates the time length of executing the arc segment, Indicates that the actuator is executing the arc time. is the initial state of the motion trajectory, is the final state of the motion trajectory; Constraint Function for: in, is the initial state of the motion trajectory, is the final state of the motion trajectory, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse; In step S302, the ellipse is converted into an elliptical cone by the following method: Since the center of the elliptical cone is known and the lengths of the major and minor axes of the ellipse are fixed, the cone trajectory points are obtained by The trajectory points of the ellipse can be determined; therefore, whether the motion trajectory points in the elliptical cone intersect with the points of the ellipse can be determined by judging whether the intersection of the circle at the bottom of the elliptical 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; Step S4 includes: When the observation arc begins, the cone centers of all time-varying constraint forbidden zone cones are located on the straight line where the arc segment is located, but the cone apex is at an on-orbit position outside the observation arc segment. Then, after processing it through step S3, the time domain planning of the trajectory point and the time-varying constraint forbidden zone is performed; Step S3 further includes the following steps: Step S304: For the trajectory points obtained in step S303 , to verify the avoidance of the time-varying constraint restricted area; this step involves the trajectory point Compare with the equations of the time-varying elliptical restricted area and the time-varying spherical restricted area to verify whether the trajectory point meets the avoidance requirements; if the trajectory point meets the avoidance requirements of all time-varying restricted areas, the avoidance is considered successful, otherwise the trajectory point needs to be adjusted; Step S305: If the avoidance verification in step S304 fails, the trajectory point is adjusted; the trajectory point is dynamically adjusted according to the changes in the time-varying constraint restricted area. , to meet the avoidance requirements; the adjustment may include changing the position, velocity or acceleration of the trajectory point until all avoidance conditions are met; Step S306: Adjust the track points The avoidance verification of step S304 is repeated until the optimal trajectory that meets all the time-varying restricted area avoidance requirements is found.

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 location of the time-varying constraint forbidden zone. According to the task requirements, determine the location of the time-varying constraint forbidden zone. If the time-varying constraint forbidden zone is not within the observation arc, then end; if the time-varying constraint forbidden zone is within the observation arc, proceed to the next step. Step S102: Define a time-varying restricted zone. Define a time-varying restricted zone based on the position change of the time-varying restricted zone on orbit. The time-varying restricted zone includes a time-varying elliptical restricted zone in the shape of an elliptical cone and a time-varying spherical restricted zone in the shape of a spherical cone. The time-varying elliptical restricted zone is: in represents the distance from the observer to the time-varying constraint forbidden zone, is the reference distance, is the eccentricity, is the angle, is the reference angle; The time-varying spherical restricted area is: in represents the distance from the observer to the time-varying constraint forbidden zone.

3. The time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to claim 2, characterized in that: In step S303, the sphere is converted into a spherical cone by the following method: Since the center of the spherical cone is known and the radius of the sphere is fixed, the cone trajectory point and the sphere can be determined; therefore, whether there is an intersection between the point of intersection of the motion trajectory point in the spherical cone and the sphere can be determined by judging whether the intersection of the vertex of the spherical cone and the sphere intersects; thus transforming the trajectory constraint problem into a vertex Whether the distance to the sphere is less than the radius of the sphere.

4. The time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to claim 3 is characterized in that: In step S303, the method for obtaining the intersection point is: At every moment , the equation of the circle at the base of the cone is: in, is the initial state, is the final state, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse; Determine whether the trajectory point satisfies the cone vertex constraint. If so, the trajectory point is inside the elliptical cone at this moment, 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 all points of the cone are inside the cone; if any point of the cone is not inside the cone, it means that there is at least one point that is not inside the cone; that is, the motion trajectory at this moment cannot intersect with the cone. Whether the trajectory point is inside the cone is expressed as a dual problem: in, in, 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; the trajectory points that meet the constraint condition are obtained by solving , and They represent the minimum spatial spacing that the motion trajectory needs to meet and the maximum displacement that the aircraft can achieve.

5. A time-optimal spacecraft attitude trajectory planning system under time-varying constraints, based on the time-optimal spacecraft attitude trajectory planning method under time-varying constraints according to any one of claims 1 to 4, characterized in that: include: The constraint restricted zone determination module is used to determine the time-varying constraint restricted zone before the mission begins; A judgment module, used to judge whether the time-varying constraint restricted areas can be avoided simultaneously; The first planning module is used to simultaneously avoid the time-varying constraint restricted areas that can be avoided at the same time, and to perform time-domain planning on the processed trajectory points and the trajectory points of the time-varying constraint restricted areas, so that the aircraft can complete the mission in the optimal time; The second planning module is used to perform different avoidance processing on the time-varying constraint restricted area problem that cannot be avoided simultaneously, and to perform time domain planning on the processed trajectory points and the trajectory points of the time-varying constraint restricted area, so that the aircraft can complete the mission under the optimal time.

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