A method for trajectory planning for regulating the visible time and uncertainty of a spacecraft

Abstract

This invention discloses a trajectory planning method for adjusting the visibility time and uncertainty of a spacecraft, relating to the field of spacecraft technology. The method includes: establishing a spacecraft dynamics model considering perturbations and a geometric visibility constraint model for a situational awareness device; defining a vertex detection angle as an intermediate variable relating the spacecraft's visibility time and state uncertainty; solving for the vertex detection angle of the spacecraft relative to the situational awareness device based on latitudinal argument matching and Newton's iteration method; constructing an optimization problem with the spacecraft's pulse velocity increment as the optimization variable and maximizing or minimizing the square of the vertex detection angle as the optimization objective, and numerically solving it using a sequential quadratic programming algorithm to obtain the optimal pulse velocity increment; and performing spacecraft orbital maneuvers based on the optimal pulse velocity increment. This invention can establish the relationship between the orbital maneuver vector and the detected characteristic indicators, enabling rapid optimization of the spacecraft maneuver vector.

Description

Technical Field

[0001] This invention relates to the field of spacecraft technology, and in particular to a trajectory planning method for adjusting the visible time and uncertainty of spacecraft. Background Technology

[0002] Situational awareness systems are a core support for ensuring the safe operation of spacecraft and the successful execution of spacecraft missions. Generally, on-orbit operations and telemetry / remote control of spacecraft must be conducted within a space domain where effective situational awareness information is available. Situational awareness capabilities directly impact mission planning and orbit design. Furthermore, for spacecraft performing critical missions, avoiding continuous probing by non-cooperative situational awareness systems can effectively protect critical technologies and mission intentions from leakage.

[0003] Orbital maneuver design has always been a core issue in spacecraft mission planning. With the increasing number of low Earth orbit satellites and the growing demand for on-orbit maneuvering, how to proactively consider and control the "detected characteristics" (such as visibility time and state uncertainty) of spacecraft relative to the situational awareness system during mission planning and maneuver design has become a critical technical problem that urgently needs to be solved.

[0004] Currently, the existing technical solutions to this problem mainly fall into the following two categories: One approach treats visibility time and uncertainties as post-hoc statistics. This type of approach typically involves first extrapolating the spacecraft trajectory using high-precision numerical orbital integration, and then determining the visibility window by calculating the space-to-ground geometry at each step length. To find an orbital maneuver scheme that meets specific visibility time requirements, extensive iterative searches using optimization methods such as Monte Carlo simulations or particle swarm optimization are necessary. This type of approach lacks intermediate variables that directly correlate orbital geometry with the relative station position, making it difficult to establish the relationship between the orbital maneuver vector and the detected characteristics, resulting in low optimization efficiency.

[0005] Another approach is to use the trace of the spacecraft's covariance matrix relative to the station as the optimization objective to account for uncertainties. However, this approach requires uncertainty evolution calculations in every optimization step, and the mapping relationship between uncertainty and orbital maneuver vectors is complex, making it difficult to solve using efficient numerical optimization methods. The computation is time-consuming and cannot meet the requirements of onboard autonomous planning or rapid mission response. Summary of the Invention

[0006] To address some or all of the technical problems existing in the prior art, the present invention provides a trajectory planning method for adjusting the visible time and uncertainty of spacecraft.

[0007] The technical solution of the present invention is as follows: A trajectory planning method for adjusting the visible time and uncertainty of a spacecraft is provided, the method comprising: A spacecraft dynamics model considering perturbations is established, and a geometric visibility constraint model for situational awareness equipment is established, which includes field-of-view constraints and Earth occlusion constraints. The over-vertex detection angle is defined as the angle between the vector from the Earth's center to the situational awareness device and the vector from the Earth's center to the spacecraft's nadir point at the moment the spacecraft passes over the apex. The over-vertex detection angle is used as an intermediate variable that relates the spacecraft's visible time and state uncertainty. Based on latitude argument matching and Newton's iteration method, the over-vertex detection angle of the spacecraft relative to the situational awareness equipment is solved; Using the spacecraft's pulse velocity increment as the optimization variable and maximizing or minimizing the square of the over-the-vertex detection angle as the optimization objective, an optimization problem is constructed and numerically solved using a sequential quadratic programming algorithm to obtain the optimal pulse velocity increment. Specifically, when it is necessary to minimize the spacecraft's visibility time relative to the situational awareness equipment, the optimization objective is to maximize the square of the over-the-vertex detection angle; when it is necessary to maximize the spacecraft's visibility time relative to the situational awareness equipment, the optimization objective is to minimize the square of the over-the-vertex detection angle. Spacecraft orbital maneuvers are performed based on the optimal pulse velocity increment.

[0008] Furthermore, in some implementations, the over-the-vertex detection angle of the spacecraft relative to the situational awareness equipment is solved based on latitudinal argument matching and Newton's iteration method, including: Based on the orbital elements of the spacecraft and the relative magnitude of the orbital inclination of the spacecraft and the latitude of the situational awareness equipment, the target latitude argument is calculated using the latitude argument calculation formula when the latitude of the spacecraft's nadir point is equal to the latitude of the situational awareness equipment. Calculate the target mean apogee angle corresponding to the target latitude argument, and use the analytical solution of the flight time considering perturbation as the initial value of the flight time iteration of the spacecraft to the target mean apogee angle; Based on the initial value of the flight time iteration and the preset convergence condition, the Newton iteration method is used to solve the flight time of the spacecraft to the mean angle of approach to the target. Based on the flight time of the spacecraft to the target mean angle of approach, the longitude of the spacecraft's nadir point is calculated when the latitude of the spacecraft's nadir point is equal to the latitude of the situational awareness equipment, and the spacecraft's nadir point with a small difference from the longitude of the situational awareness equipment is selected as the nearest point. If the difference between the spacecraft's orbital inclination and the latitude of the situational awareness equipment is less than a preset angle threshold, the nearest point is used as the vertex and the vertex detection angle is calculated. Otherwise, based on the determined nearest point, the vertex detection angle is calculated using the spherical trigonometric sine theorem.

[0009] Furthermore, in some implementations, the formula for calculating the latitudinal argument is expressed as: ; in, Indicates the target latitude argument. Indicates the semi-major axis of the track. Indicates the latitude of the situational awareness device. Indicates the orbital inclination angle. Represents the unit step function. This represents the operation of the sine function.

[0010] Furthermore, in some implementations, the flight time for the spacecraft to reach the mean angle of approach to the target, calculated using Newton's iteration method, is expressed as: ; in, Indicates the first The flight time of the spacecraft to the target's mean angle of approach, obtained in the next iteration. Indicates the first The flight time of the spacecraft to the target's mean angle of approach, obtained in the next iteration. Indicates the target latitude argument. This indicates the spacecraft's flight from the initial moment to... The actual latitude argument corresponding to that moment. The symbol represents the partial derivative.

[0011] Furthermore, in some implementations, the longitude of the spacecraft's nadir point is calculated using the following formula when the latitude of the spacecraft's nadir point equals the latitude of the situational awareness equipment: ; in, This represents the longitude of the spacecraft's nadir point when its latitude equals that of the situational awareness equipment. Indicates the semi-major axis of the track. Indicates the orbital inclination angle. Indicates the target latitude argument. Indicates the right ascension of the ascending node. Represents the Earth's angular velocity of rotation. This indicates the flight time of the spacecraft to reach the mean angle of approach to the target. This represents the tangent function operation. This represents the operation of the cosine function. Represents a symbolic function.

[0012] Furthermore, in some implementations, the vertex detection angle is calculated using the sine theorem of spherical trigonometry based on determined nearest points, including: Construct a spherical triangle consisting of the location point of the situational awareness device, nearby points, and the vertex, wherein the trajectory direction of the sub-satellite point at the vertex is perpendicular to the arc segment from the location point of the situational awareness device to the vertex. Using the spacecraft orbital inclination, the latitude of the situational awareness equipment, and the longitude difference between the nearby point and the situational awareness equipment, the spherical angular distance from the position point of the situational awareness equipment to the arc segment corresponding to the vertex is calculated using the spherical trigonometric sine theorem and used as the vertex detection angle.

[0013] Furthermore, in some implementations, a sequential quadratic programming algorithm is used for numerical solution, including the following steps: Step 41, set the optimization variable as Set initial values ​​for optimization variables Initialize the iteration counter And order the first The optimization variable iteration value of the next iteration ;in, Indicates the pulse velocity increment of the spacecraft. Describing the L2 norm, The in-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. The out-of-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. This represents the initial value of the pulse velocity increment. This represents the initial value of the in-plane maneuver direction. The superscript indicates the initial value of the out-of-plane maneuvering direction angle. This represents the matrix transpose operation; Step 42, iterating based on the optimization variable values Given the initial spacecraft orbital elements, calculate the iterative values ​​of the optimization variables. The orbital elements of the spacecraft after the action are calculated, and the over-the-vertex detection angle of the spacecraft relative to the situational awareness equipment is solved based on the latitude argument matching and Newton's iteration method. Step 43: Calculate the iterative values ​​of the objective function in the optimization variables using numerical difference. The approximate matrix of the Jacobian matrix and the Hessian matrix at the given location; where, when the optimization objective is to maximize the square of the detection angle through the vertex, the objective function is defined as the square of the detection angle through the vertex; when the optimization objective is to minimize the square of the detection angle through the vertex, the objective function is defined as the negative value of the square of the detection angle through the vertex. Step 44: Construct and solve the corresponding quadratic programming subproblem using the approximation matrix to obtain the search direction. ; Step 45: Determine the optimal step size factor using the line search method. ; Step 46, let the first The optimization variable iteration value of the next iteration and set the iteration counter ; Step 47: Determine whether the preset iteration termination condition is met. If not, repeat steps 42-47. If yes, use the current iteration value of the optimization variable as the optimal pulse velocity increment.

[0014] Furthermore, in some implementations, the preset iteration termination condition includes: ; in, Represents the angle detected at the vertex. This represents the gradient vector of the objective function with respect to the optimization variables. This represents the maximum norm of the gradient vector of the objective function with respect to the optimization variables. This indicates a preset threshold.

[0015] Furthermore, in some embodiments, the method further includes: during spacecraft orbital maneuvers based on the optimal pulse velocity increment, calculating the spacecraft's visibility time and state uncertainty relative to the situational awareness equipment based on a geometric visibility constraint model.

[0016] Furthermore, in some implementations, information entropy is used to measure the state uncertainty of the spacecraft relative to the situational awareness equipment.

[0017] The main advantages of the technical solution of this invention are as follows: This invention provides a trajectory planning method for adjusting the visible time and uncertainty of a spacecraft. By defining the over-vertex detection angle as an intermediate variable relating the spacecraft's maneuver vector and the detected characteristics, it transforms the complex problem of optimizing the detected characteristics into a simple over-vertex geometric configuration adjustment problem. This solves the problems of existing technologies, such as the lack of intuitive and efficient optimization variables and the difficulty in establishing the relationship between the orbital maneuver vector and the detected characteristic indicators. Simultaneously, it employs a semi-analytical solution process based on latitude argument matching and Newton's iteration method to quickly obtain the over-vertex detection angle, and combines this with a sequential quadratic programming algorithm for incremental optimization of the spacecraft's pulse velocity. This avoids a large amount of numerical integration and uncertainty evolution calculations in each iteration, significantly improving the solution efficiency. It can complete the spacecraft maneuver vector optimization, which traditional methods would take hundreds of seconds, within seconds, balancing computational accuracy and speed. This method is suitable for scenarios with high timeliness requirements, such as on-board autonomous planning or rapid mission response. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and constitute a part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 A flowchart illustrating a trajectory planning method for adjusting the visible time and uncertainty of a spacecraft, provided as an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the relative positional relationship between a location point, a nearby point, and a vertex of a situational awareness device, provided in an embodiment of the present invention. Figure 3 A schematic diagram showing the visible time results when performing simulation experiments based on two methods, as provided in an embodiment of the present invention; Figure 4 A schematic diagram of the information entropy results corresponding to simulation experiments based on two methods provided in this embodiment of the invention; Figure 5 This is a schematic diagram illustrating the correlation between the vertex detection angle and the visible time, obtained from simulation experiment results, provided in an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the correlation between visible time and information entropy based on simulation experiment results, provided for an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0021] See Figure 1 This invention provides a trajectory planning method for adjusting the visible time and uncertainty of a spacecraft, the method comprising the following steps: Step 1: Establish a spacecraft dynamics model considering perturbations and a geometric visibility constraint model for situational awareness equipment. The geometric visibility constraint model includes field of view constraints and Earth occlusion constraints. Step 2: Define the vertex detection angle as the angle between the vector from the Earth's center to the situational awareness device and the vector from the Earth's center to the spacecraft's nadir point at the moment the spacecraft passes over the apex. Use the vertex detection angle as an intermediate variable that relates the spacecraft's visible time and state uncertainty. Step 3: Based on latitude argument matching and Newton's iteration method, solve for the over-the-vertex detection angle of the spacecraft relative to the situational awareness equipment; Step 4: Using the spacecraft's pulse velocity increment as the optimization variable and maximizing or minimizing the square of the over-the-vertex detection angle as the optimization objective, construct an optimization problem and use a sequential quadratic programming algorithm to numerically solve it to obtain the optimal pulse velocity increment; where, when it is necessary to minimize the spacecraft's visibility time relative to the situational awareness equipment, the optimization objective is to maximize the square of the over-the-vertex detection angle, and when it is necessary to maximize the spacecraft's visibility time relative to the situational awareness equipment, the optimization objective is to minimize the square of the over-the-vertex detection angle. Step 5: Perform spacecraft orbital maneuvers based on the optimal pulse velocity increment.

[0022] This invention provides a trajectory planning method for adjusting the visible time and uncertainty of a spacecraft. By defining the over-vertex detection angle as an intermediate variable relating the spacecraft's maneuver vector and the detected characteristics, it transforms the complex problem of optimizing the detected characteristics into a simple over-vertex geometric configuration adjustment problem. This solves the problems of existing technologies, such as the lack of intuitive and efficient optimization variables and the difficulty in establishing the relationship between the orbital maneuver vector and the detected characteristic indicators. Simultaneously, a semi-analytical solution process based on latitude argument matching and Newton's iteration method is used to quickly obtain the over-vertex detection angle. Combined with a sequential quadratic programming algorithm, the spacecraft's pulse velocity increment is optimized, avoiding a large amount of numerical integration and uncertainty evolution calculations in each iteration. This significantly improves the solution efficiency, enabling the optimization of the spacecraft's maneuver vector, which traditional methods require hundreds of seconds, to be completed in seconds. This method balances computational accuracy and speed, making it suitable for scenarios with high timeliness requirements, such as on-board autonomous planning or rapid mission response.

[0023] Furthermore, in this embodiment of the invention, based on the actual requirements of spacecraft orbital maneuvers, the J2 perturbation is considered. Therefore, a spacecraft dynamics model considering the J2 perturbation is established, as follows: ; in, Represents the spacecraft's position vector. Represents the Earth's gravitational constant. This represents the acceleration produced by the J2 term perturbation of non-spherical gravity. Indicates the thrust acceleration of a spacecraft engine. express The second derivative with respect to time, This represents the L2 norm.

[0024] During spacecraft orbital maneuvers, when the duration of the thrust applied during the maneuver is much shorter than the orbital period before and after the maneuver, it can be assumed that the thrust changes as a function of time as an impulse function, such that the impulse vector is the same as the impulse generated by the original thrust. Therefore, based on this impulse thrust assumption, the spacecraft engine thrust acceleration and the spacecraft's impulse velocity increment satisfy the following relationship: ; in, express The spacecraft engine thrust acceleration at any given moment, Represents the Dirac function, Represents a time variable. Indicates the total number of pulses applied. Indicates the first The moment when the pulse is applied, Indicates the initial moment of the spacecraft's orbital maneuver. Indicates the end time of the spacecraft's orbital maneuver. Indicates the first The pulse velocity increment of the spacecraft.

[0025] In this embodiment of the invention, when the spacecraft engine operates in impulse mode, the pulse velocity increment can be regarded as the product of thrust acceleration and time interval. The change in the spacecraft orbital elements under the action of the pulse velocity increment can be calculated using the following formula: ; in, This indicates the change in the semi-major axis of the orbit. Indicates the orbital angular velocity. Indicates the orbital eccentricity. Indicates the true nearest point angle. This represents the change in orbital eccentricity. Indicates the semi-major axis of the track. This represents the change in orbital inclination. Represents the spacecraft's position vector. Indicates the argument of latitude. This represents the change in right ascension at the ascending node. Indicates the orbital inclination angle. This represents the change in the perigee angle. This represents the change in the angle of approach. , , These represent the pulse velocity increments of the spacecraft. R-axis components, T-axis components, and N-axis components in the RTN coordinate system Describing the L2 norm, This represents the operation of the sine function. This represents the operation of the cosine function.

[0026] The orbital elements of a spacecraft include: semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and mean perigee.

[0027] In this embodiment of the invention, the formula for calculating the change in spacecraft orbital elements is used to solve for the spacecraft orbital elements after the optimization variable iteration value is applied during the subsequent numerical solution process using a sequential quadratic programming algorithm.

[0028] It should be noted that the trajectory planning method for adjusting the visible time and uncertainty of a spacecraft provided in this embodiment of the invention is based on the above-mentioned pulse thrust assumption.

[0029] Furthermore, in this embodiment of the invention, the geometric visibility constraint model of the situational awareness device includes a field of view constraint and an earth occlusion constraint. When the position vector of the spacecraft relative to the situational awareness device satisfies the geometric visibility constraint model, it means that the spacecraft can be detected by the situational awareness device.

[0030] In this embodiment of the invention, the field-of-view constraint indicates that the spacecraft is within the field of view of the situational awareness device. Specifically, the field-of-view constraint is expressed as follows: ; in, This represents the line-of-sight vector of the situational awareness device. This represents the position vector of the situational awareness equipment relative to the spacecraft. Indicates the field of view of the situational awareness device. Describing the L2 norm, This represents the operation of the inverse cosine function.

[0031] In this embodiment of the invention, the Earth occlusion constraint indicates that there is no Earth occlusion between the spacecraft and the situational awareness equipment, that is, the spacecraft is located above the horizontal plane where the situational awareness equipment is located. The Earth occlusion constraint is specifically expressed as follows: ; in, This indicates the pitch angle of the spacecraft relative to the situational awareness equipment.

[0032] In this embodiment of the invention, the geometric visibility constraint model of the situational awareness device is used to calculate and determine the visible time of the spacecraft relative to the situational awareness device during the spacecraft's orbital maneuver. The spacecraft is only visible to the situational awareness device when the relative positional relationship between the spacecraft and the situational awareness device satisfies the geometric visibility constraint model.

[0033] refer to Figure 2 Furthermore, in this embodiment of the invention, considering the complex evolution of spacecraft detection characteristics in situational awareness scenarios, it is difficult to directly solve the mapping relationship between spacecraft pulse velocity increment and spacecraft detection characteristics. Therefore, the vertex detection angle is defined as an intermediate variable that correlates the spacecraft maneuver vector and the spacecraft detection characteristics.

[0034] In this embodiment of the invention, the over-vertex detection angle of the spacecraft relative to the situational awareness device is calculated based on latitude argument matching and Newton's iteration method, further including the following steps: Step 31: Based on the orbital elements of the spacecraft and the relative magnitude of the orbital inclination of the spacecraft and the latitude of the situational awareness equipment, calculate the target latitude argument when the latitude of the spacecraft's nadir point is equal to the latitude of the situational awareness equipment using the latitude argument calculation formula. Step 32: Calculate the target mean apogee angle corresponding to the target latitude argument, and use the analytical solution of the flight time considering perturbation as the initial value of the flight time iteration for the spacecraft to fly to the target mean apogee angle; Step 33: Based on the initial value of the flight time iteration and the preset convergence condition, Newton's iteration method is used to solve the flight time of the spacecraft to the mean angle of approach to the target. Step 34: Based on the flight time of the spacecraft to the target mean angle of approach, calculate the longitude of the spacecraft's nadir point when the latitude of the spacecraft's nadir point is equal to the latitude of the situational awareness device, and select the spacecraft's nadir point with a small difference from the longitude of the situational awareness device as the nearest point; Step 35: If the difference between the spacecraft's orbital inclination and the latitude of the situational awareness device is less than a preset angle threshold, the nearest point is used as the vertex and the vertex detection angle is calculated; otherwise, based on the determined nearest point, the vertex detection angle is calculated using the spherical trigonometric sine theorem.

[0035] In this embodiment of the invention, based on the definition of the over-the-vertex detection angle, determining the over-the-vertex detection angle requires first determining the over-the-vertex point and the over-the-vertex time. Due to the influence of Earth's rotation and perturbations, directly solving for the over-the-vertex point and the over-the-vertex time is quite difficult. Therefore, in this embodiment of the invention, the over-the-vertex point and the over-the-vertex time are solved based on latitude argument matching and Newton's iteration method, thereby solving for the over-the-vertex detection angle of the spacecraft relative to the situational awareness equipment.

[0036] In this embodiment of the invention, based on the orbital elements of the spacecraft and the relative magnitudes of the spacecraft's orbital inclination and the latitude of the situational awareness device, the target latitude argument corresponding to the spacecraft's nadir point latitude being equal to the situational awareness device's latitude is calculated using the following latitude argument calculation formula: ; in, Indicates the target latitude argument. Indicates the semi-major axis of the track. Indicates the latitude of the situational awareness device. Indicates the orbital inclination angle. Represents the unit step function. This represents the operation of the sine function.

[0037] In this embodiment of the invention, when the spacecraft's orbital inclination is greater than the latitude of the situational awareness device, there are two target latitude argument solutions, namely... When the spacecraft's orbital inclination is equal to the latitude of the situational awareness equipment, there exists a common target latitude argument solution, i.e. When the spacecraft's orbital inclination is less than the latitude of the situational awareness equipment, the spacecraft is invisible to the situational awareness equipment during orbital maneuvers, and therefore there is no target latitude argument solution. Therefore, in this embodiment of the invention, only the case where the spacecraft's orbital inclination is greater than or equal to the latitude of the situational awareness equipment is considered.

[0038] In this embodiment of the invention, the target mean apogee angle corresponding to the target latitude argument is calculated using the following formula: ; ; in, Indicates the orbital eccentricity. Indicates the target is closer to the point angle. As an intermediate variable, Indicates the target latitude argument. Indicates the argument of perigee. Indicates the angle of the target's approximate point. This represents the tangent function operation. This represents the operation of the sine function.

[0039] In this embodiment of the invention, the analytical solution of the flight time considering the J2 term perturbation is used as the initial value of the flight time iteration for the spacecraft to fly to the target mean angle of approach.

[0040] Specifically, the initial value of the flight time iteration for the spacecraft to reach the target mean angle is expressed as: ; in, This represents the initial value for the flight time iteration. This represents the mean anomaly angle corresponding to the latitude argument at the initial moment. Represents the Earth's gravitational constant. Indicates the semi-major axis of the orbit at the initial moment. This represents the mean anterior angular velocity corresponding to the latitude argument at the initial moment. This represents the perigee angular velocity at the initial moment.

[0041] Setting: Number The flight time obtained in the next iteration for the spacecraft to reach the target's mean angle of approach is: ,exist to Performing a first-order Taylor expansion, we get: ; Based on the above formula, we can further obtain: ; in, Indicates the first The time step correction amount in the next iteration is used to correct the currently estimated flight time. This indicates the spacecraft's flight from the initial moment to... The actual latitude argument corresponding to that moment. The symbol represents the partial derivative.

[0042] Considering only the changes in the true anomaly angle and the argument of perigee, we can obtain: ; in, Indicates the true anterior angle of the target. Indicates the argument of the target's perigee.

[0043] Depend on and The partial derivative of the target latitude argument with respect to flight time can be obtained as follows: ; in, express The first derivative with respect to time Indicates the angle of approach. express The first derivative with respect to time express The true closest angle at any moment, express The orbital eccentricity at time t.

[0044] Based on the above analysis, in this embodiment of the invention, the flight time for the spacecraft to reach the mean angle of approach to the target using the Newton-Raphson iteration method is expressed as follows: ; in, Indicates the first The flight time of the spacecraft to the target's mean angle of approach, obtained in the next iteration. Indicates the first The flight time of the spacecraft to the target's mean angle of approach, obtained in the next iteration. Indicates the target latitude argument. This indicates the spacecraft's flight from the initial moment to... The actual latitude argument corresponding to the time.

[0045] In this embodiment of the invention, based on the flight time of the spacecraft to the target's mean angle of approach, the longitude of the spacecraft's nadir point when its latitude equals that of the situational awareness equipment is calculated using the following formula: ; in, This represents the longitude of the spacecraft's nadir point when its latitude equals that of the situational awareness equipment. Indicates the semi-major axis of the track. Indicates the orbital inclination angle. Indicates the target latitude argument. Indicates the right ascension of the ascending node. Represents the Earth's angular velocity of rotation. This indicates the flight time of the spacecraft to reach the mean angle of approach to the target. This represents the tangent function operation. This represents the operation of the cosine function. Represents a symbolic function.

[0046] In this embodiment of the invention, when the orbital inclination of the spacecraft is greater than the latitude of the situational awareness device, there are two target latitude argument solutions. At this time, when the latitude of the spacecraft's ground point is equal to the latitude of the situational awareness device, there are two corresponding spacecraft ground points. The spacecraft ground point with a smaller difference between its longitude and the longitude of the situational awareness device is selected as the nearest point.

[0047] In this embodiment of the invention, the preset angle threshold is 6°. If the difference between the spacecraft's orbital inclination angle and the latitude of the situational awareness device is less than 6°, the nearest point is taken as the vertex, the moment when the spacecraft flies to the nearest point is taken as the vertex crossing time, and the vertex crossing detection angle is calculated. Otherwise, based on the determined nearest point, the vertex crossing detection angle is calculated using the spherical trigonometric sine theorem.

[0048] In this embodiment of the invention, after determining the vertex and the vertex-crossing time, the vertex-crossing detection angle can be calculated using the following formula: ; in, Represents the angle detected at the vertex. This represents the position vector of the situational awareness device at the moment of overhead movement. This represents the angular momentum of the spacecraft at the moment of overhead. Describing the L2 norm, This represents the operation of the inverse cosine function.

[0049] In this embodiment of the invention, based on a determined nearest point, the detection angle through the vertex is calculated using the spherical trigonometric sine theorem, including: Construct a spherical triangle consisting of the location point of the situational awareness device, nearby points, and the vertex, wherein the trajectory direction of the sub-satellite point at the vertex is perpendicular to the arc segment from the location point of the situational awareness device to the vertex. Using the spacecraft orbital inclination, the latitude of the situational awareness equipment, and the longitude difference between the nearby point and the situational awareness equipment, the spherical angular distance from the position point of the situational awareness equipment to the arc segment corresponding to the vertex is calculated using the spherical trigonometric sine theorem and used as the vertex detection angle.

[0050] The spherical trigonometric sine theorem is common knowledge in this field, so it will not be elaborated here.

[0051] It should be noted that, in the appendix Figure 2 In the coordinate system, X, Y, and Z represent the three axes of the geocentric inertial coordinate system (ECI coordinate system).

[0052] Furthermore, in this embodiment of the invention, based on the definition of the vertex detection angle above, it can be seen that minimizing the vertex detection angle will maximize the visibility time of the spacecraft relative to the situational awareness device and minimize the state uncertainty of the spacecraft relative to the situational awareness device; while maximizing the vertex detection angle will minimize the visibility time of the spacecraft relative to the situational awareness device and maximize the state uncertainty of the spacecraft relative to the situational awareness device.

[0053] In this embodiment of the invention, when the pulse velocity increment of the spacecraft is used as the optimization variable and minimizing the square of the over-vertex detection angle is used as the optimization objective, the following optimization problem is constructed: ; When the spacecraft's pulse velocity increment is used as the optimization variable and the objective is to maximize the square of the detection angle at the vertex, the following optimization problem is constructed: ; in, Represents the angle detected at the vertex. Indicates the pulse velocity increment of the spacecraft. The in-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. The out-of-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. Indicates the initial orbital elements of the spacecraft. Indicates the longitude of the situational awareness device. Indicates the latitude of the situational awareness device. The mapping function representing the detected angle at the vertex. This indicates the maximum value of the spacecraft's pulse velocity increment. This represents the L2 norm.

[0054] In this embodiment of the invention, based on the constructed optimization problem, a sequential quadratic programming algorithm is used for numerical solution to obtain the optimal pulse velocity increment.

[0055] Specifically, in this embodiment of the invention, a sequential quadratic programming algorithm is used for numerical solution, including the following steps: Step 41, set the optimization variable as Set initial values ​​for optimization variables Initialize the iteration counter And order the first The optimization variable iteration value of the next iteration ;in, Indicates the pulse velocity increment of the spacecraft. Describing the L2 norm, The in-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. The out-of-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. This represents the initial value of the pulse velocity increment. This represents the initial value of the in-plane maneuver direction. The superscript indicates the initial value of the out-of-plane maneuvering direction angle. This represents the matrix transpose operation; Step 42, iterating based on the optimization variable values Given the initial spacecraft orbital elements, calculate the iterative values ​​of the optimization variables. The orbital elements of the spacecraft after the action are calculated, and the over-the-vertex detection angle of the spacecraft relative to the situational awareness equipment is solved based on the latitude argument matching and Newton's iteration method. Step 43: Calculate the iterative values ​​of the objective function in the optimization variables using numerical difference. The approximate matrix of the Jacobian matrix and the Hessian matrix at the given location; where, when the optimization objective is to maximize the square of the detection angle through the vertex, the objective function is defined as the square of the detection angle through the vertex; when the optimization objective is to minimize the square of the detection angle through the vertex, the objective function is defined as the negative value of the square of the detection angle through the vertex. Step 44: Construct and solve the corresponding quadratic programming subproblem using the approximate matrix to obtain the search direction. ; Step 45: Determine the optimal step size factor using the line search method. ; Step 46, let the first The optimization variable iteration value of the next iteration and set the iteration counter ; Step 47: Determine whether the preset iteration termination condition is met. If not, repeat steps 42-47. If yes, use the current iteration value of the optimization variable as the optimal pulse velocity increment.

[0056] In this embodiment of the invention, the initial values ​​of the optimization variables are set according to the actual situation, and the initial spacecraft orbital elements are determined according to the actual situation.

[0057] In this embodiment of the invention, the preset iteration termination condition is set according to actual needs.

[0058] In an optional embodiment of the present invention, the preset iteration termination condition includes: ;in, Represents the angle detected at the vertex. This represents the gradient vector of the objective function with respect to the optimization variables. This represents the maximum norm of the gradient vector of the objective function with respect to the optimization variables. Specifically, it can be expressed as: , This represents a preset threshold, for example, 10. -6 .

[0059] Furthermore, in this embodiment of the invention, when performing spacecraft orbital maneuvers based on the optimal pulse velocity increment, the acquired pulse velocity increment is converted to the RTN coordinate system.

[0060] Specifically, the following formula is used to... Transform to RTN coordinate system: ; in, , , These represent the pulse velocity increments of the spacecraft. R-axis components, T-axis components, and N-axis components in the RTN coordinate system.

[0061] Furthermore, in this embodiment of the invention, in step 5, during the spacecraft orbital maneuvering based on the optimal pulse velocity increment, the visible time and state uncertainty of the spacecraft relative to the situational awareness equipment are also calculated based on the geometric visibility constraint model.

[0062] In this embodiment of the invention, the visible time of a spacecraft relative to a situational awareness device can be calculated using the following formula: ; in, This indicates the visible time of the spacecraft relative to situational awareness equipment. Indicates the spacecraft's first The moment when it enters the detection range of the situational awareness equipment. Indicates the spacecraft's first The moment when the device leaves the detection range of the situational awareness equipment. This represents the total number of visible time windows.

[0063] Among them, based on the field of view constraints and Earth occlusion constraints established in step 1, it is determined whether the spacecraft is within the detection range of the situational awareness equipment at each moment.

[0064] In this embodiment of the invention, the state uncertainty of the spacecraft relative to the situational awareness equipment is measured using information entropy, and specifically calculated using the following formula: ; in, express The spacecraft's state relative to situational awareness equipment is uncertain at all times. Represents the natural constant. express The position covariance matrix of the spacecraft at any given time. This represents the dimension of the spacecraft's position covariance matrix. Represents the determinant of a matrix.

[0065] Specifically, when the spacecraft is outside the detection range of the situational awareness equipment, the generalized polynomial chaotic expansion method (GPC) is used to derive the spacecraft's position covariance matrix to maintain the nonlinearity of uncertainty propagation. When the spacecraft is within the detection range of the situational awareness equipment, i.e., when the geometric visibility constraint model of the situational awareness equipment is satisfied, the Kalman filter (KF) equation is used to update the spacecraft's position covariance matrix. Since the generalized polynomial chaotic expansion method and the Kalman filter equation are standard techniques in this field, they will not be elaborated upon here.

[0066] In this embodiment of the invention, an observation efficiency index is defined to measure the uncertainty of the spacecraft's state relative to the situational awareness equipment per unit time.

[0067] Specifically, the observation efficiency index is expressed as: ; in, Indicator of observation efficiency express The spacecraft's state relative to situational awareness equipment is uncertain at all times. This indicates the visible time of the spacecraft relative to situational awareness equipment. Indicates the initial moment of the spacecraft's orbital maneuver. Indicates the time at which the spacecraft's orbital maneuver ends.

[0068] To verify the effectiveness of the method provided in the embodiments of the present invention, simulation experiments were conducted based on the trajectory planning method (DAUA) for adjusting the visible time and uncertainty of spacecraft provided in the embodiments of the present invention and the traditional Monte Carlo (MC) optimization method.

[0069] In the simulation experiment of this invention embodiment, the spacecraft orbit is a circular orbit with an altitude of 1000km and an inclination of 36°. The longitude of the situational awareness device is 90°, and the latitude of the situational awareness device is 30°. The initial values ​​of the given optimization variables are... The simulation experiment of the Monte Carlo optimization method has 500 samples. The goal of the simulation experiment is to maximize the state uncertainty, which is measured by information entropy.

[0070] See Figure 3-4 , Figure 3 This is a schematic diagram showing the visible time results corresponding to simulation experiments based on two methods, provided in an embodiment of the present invention. Figure 4 This diagram illustrates the information entropy results obtained from simulation experiments using two different methods, as provided in this embodiment of the invention. It can be seen that the solution obtained by the trajectory planning method for adjusting spacecraft visibility time and uncertainty, provided in this embodiment of the invention, lies within the 2σ to 3σ confidence interval, and is superior to 99% of the solutions obtained by the Monte Carlo optimization method.

[0071] As can be seen from the table below, the trajectory planning method for adjusting the visible time and uncertainty of spacecraft provided by the embodiments of the present invention obtains a better solution while significantly reducing the calculation time from 937.23 seconds to 3.498 seconds, which is about 268 times faster.

[0072] Table 1 Simulation experimental results obtained using the two methods

[0073] See Figure 5 , Figure 5 This diagram illustrates the correlation between the over-the-vertex detection angle and visible time, obtained from simulation results, as provided in this embodiment of the invention. It shows a positive correlation between the over-the-vertex detection angle and visible time. In a static state without considering maneuvers, a smaller over-the-vertex detection angle means the situational awareness device's line of sight is closer to the spacecraft, resulting in a longer visible time. However, in a dynamic state considering maneuvers, applied pulse maneuvers significantly alter the orbital altitude, thus dominating the change in visible time. To reduce the over-the-vertex detection angle, applied pulse maneuvers often simultaneously and drastically reduce the orbital altitude. A lower orbital altitude causes the spacecraft's angular velocity to increase, leading to a shorter visible time per orbit. Therefore, in a dynamic state considering maneuvers, as the over-the-vertex detection angle decreases, the visible time shortens, and the observation efficiency index significantly improves.

[0074] See Figure 6 , Figure 6 This diagram illustrates the correlation between visible time and information entropy, obtained from simulation results, as provided in an embodiment of the present invention. It can be seen that visible time and information entropy generally exhibit a negative correlation. However, due to the influence of nonlinear time-varying dynamics, the same visible time may correspond to different state uncertainties, manifested as a "cluster" distribution in the diagram.

[0075] It should be noted that, in this document, relational terms such as “first” and “second” are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of trajectory planning for regulating the visible time and uncertainty of a spacecraft, characterized in that, The method includes: A spacecraft dynamics model considering perturbations is established, and a geometric visibility constraint model for situational awareness equipment is established, which includes field-of-view constraints and Earth occlusion constraints. The over-vertex detection angle is defined as the angle between the vector from the Earth's center to the situational awareness device and the vector from the Earth's center to the spacecraft's nadir point at the moment the spacecraft passes over the apex. The over-vertex detection angle is used as an intermediate variable that relates the spacecraft's visible time and state uncertainty. Based on latitude argument matching and Newton's iteration method, the over-vertex detection angle of the spacecraft relative to the situational awareness equipment is solved; Using the spacecraft's pulse velocity increment as the optimization variable and maximizing or minimizing the square of the over-the-vertex detection angle as the optimization objective, an optimization problem is constructed and numerically solved using a sequential quadratic programming algorithm to obtain the optimal pulse velocity increment. Specifically, when it is necessary to minimize the spacecraft's visibility time relative to the situational awareness equipment, the optimization objective is to maximize the square of the over-the-vertex detection angle; when it is necessary to maximize the spacecraft's visibility time relative to the situational awareness equipment, the optimization objective is to minimize the square of the over-the-vertex detection angle. Spacecraft orbital maneuvers are performed based on the optimal pulse velocity increment.

2. The method of claim 1, wherein, Based on latitudinal argument matching and Newton's iteration method, the over-vertex detection angle of the spacecraft relative to the situational awareness equipment is solved, including: Based on the orbital elements of the spacecraft and the relative magnitude of the orbital inclination of the spacecraft and the latitude of the situational awareness equipment, the target latitude argument is calculated using the latitude argument calculation formula when the latitude of the spacecraft's nadir point is equal to the latitude of the situational awareness equipment. Calculate the target mean apogee angle corresponding to the target latitude argument, and use the analytical solution of the flight time considering perturbation as the initial value of the flight time iteration of the spacecraft to the target mean apogee angle; Based on the initial value of the flight time iteration and the preset convergence condition, the Newton iteration method is used to solve the flight time of the spacecraft to the mean angle of approach to the target. Based on the flight time of the spacecraft to the target mean angle of approach, the longitude of the spacecraft's nadir point is calculated when the latitude of the spacecraft's nadir point is equal to the latitude of the situational awareness equipment, and the spacecraft's nadir point with a small difference from the longitude of the situational awareness equipment is selected as the nearest point. If the difference between the spacecraft's orbital inclination and the latitude of the situational awareness equipment is less than a preset angle threshold, the nearest point is used as the vertex and the vertex detection angle is calculated. Otherwise, based on the determined nearest point, the vertex detection angle is calculated using the spherical trigonometric sine theorem.

3. The method of claim 2, wherein, The formula for calculating the argument of latitude is expressed as: ； wherein, represents a target latitude angle, represents an orbital semi-major axis, represents a situational awareness device latitude, represents an orbital inclination, represents a unit step function, represents a sine function operation.

4. The method of claim 2, wherein, The flight time for the spacecraft to reach the mean angle of approach to the target, calculated using Newton's iterative method, is expressed as: ； in, Indicates the first The flight time of the spacecraft to the target's mean angle of approach, obtained in the next iteration. Indicates the first The flight time of the spacecraft to the target's mean angle of approach, obtained in the next iteration. Indicates the target latitude argument. This indicates the spacecraft's flight from the initial moment to... The actual latitude argument corresponding to that moment. The symbol represents the partial derivative.

5. The method of claim 2, wherein, The following formula can be used to calculate the longitude of the spacecraft's nadir point when its latitude equals that of the situational awareness equipment: ； in, This represents the longitude of the spacecraft's nadir point when its latitude equals that of the situational awareness equipment. Indicates the semi-major axis of the track. Indicates the orbital inclination angle. Indicates the target latitude argument. Indicates the right ascension of the ascending node. Represents the Earth's angular velocity of rotation. This indicates the flight time of the spacecraft to reach the mean angle of approach to the target. This represents the tangent function operation. This represents the operation of the cosine function. Represents a symbolic function.

6. The method of claim 2, wherein, Based on the determined nearest points, the detection angles of the vertices are calculated using the spherical trigonometric sine theorem, including: Construct a spherical triangle consisting of the location point of the situational awareness device, nearby points, and the vertex, wherein the trajectory direction of the sub-satellite point at the vertex is perpendicular to the arc segment from the location point of the situational awareness device to the vertex. Using the spacecraft orbital inclination, the latitude of the situational awareness equipment, and the longitude difference between the nearby point and the situational awareness equipment, the spherical angular distance from the position point of the situational awareness equipment to the arc segment corresponding to the vertex is calculated using the spherical trigonometric sine theorem and used as the vertex detection angle.

7. The method of claim 1, wherein, The numerical solution is obtained using a sequential quadratic programming algorithm, including the following steps: Step 41, set the optimization variable as Set initial values ​​for optimization variables Initialize the iteration counter And order the first The optimization variable iteration value of the next iteration ;in, Indicates the pulse velocity increment of the spacecraft. Describing the L2 norm, The in-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. The out-of-plane maneuvering direction angle representing the pulse velocity increment of the spacecraft. This represents the initial value of the pulse velocity increment. This represents the initial value of the in-plane maneuver direction. The superscript indicates the initial value of the out-of-plane maneuvering direction angle. This represents the matrix transpose operation; Step 42, compute optimization variable iteration value based on optimization variable iteration value and initial spacecraft orbit elements, compute optimization variable iteration value spacecraft orbit elements after action, and solve spacecraft relative over-the-horizon detection angle based on latitude argument matching and Newton iteration method; Step 43: Calculate the iterative values ​​of the objective function in the optimization variables using numerical difference. The approximate matrix of the Jacobian matrix and the Hessian matrix at the given location; where, when the optimization objective is to maximize the square of the detection angle through the vertex, the objective function is defined as the square of the detection angle through the vertex; when the optimization objective is to minimize the square of the detection angle through the vertex, the objective function is defined as the negative value of the square of the detection angle through the vertex. Step 44, construct a corresponding quadratic programming sub-problem using the approximation matrix and solve to obtain a search direction ; Step 45, the optimal step factor is determined by using line search method ; Step 46, let the first iteration of the optimization variable iteration value and let the iteration counter ; Step 47: Determine whether the preset iteration termination condition is met. If not, repeat steps 42-47. If yes, use the current iteration value of the optimization variable as the optimal pulse velocity increment.

8. The method of claim 7, wherein, The preset iteration termination condition comprises: ; in, Represents the angle detected at the vertex. This represents the gradient vector of the objective function with respect to the optimization variables. This represents the maximum norm of the gradient vector of the objective function with respect to the optimization variables. This indicates a preset threshold.

9. The method of claim 1, wherein, The method further includes: during the spacecraft orbital maneuvering based on the optimal pulse velocity increment, calculating the spacecraft's visibility time and state uncertainty relative to the situational awareness equipment based on a geometric visibility constraint model.

10. The method of claim 9, wherein, Information entropy is used to measure the state uncertainty of a spacecraft relative to situational awareness equipment.

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