A spacecraft concealed maneuvering trajectory planning method based on Bezier curve

Abstract

The present invention discloses a spacecraft concealed maneuvering trajectory planning method based on Bezier curves, which relates to the field of spacecraft technology, including: constructing a coordinate system for describing the relative motion of spacecraft, and establishing a spacecraft orbital dynamics model; constructing situational awareness constraints, control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft concealed maneuvering process based on the situational awareness capability of the monitoring satellite cluster; constructing a spacecraft concealed maneuvering trajectory planning model; using the Bezier curve, respectively converting the position parameters and control parameters of the spacecraft into algebraic equations; selecting the order and the number of points of the Bezier curve, constructing and solving a discrete form of the spacecraft concealed maneuvering trajectory planning model, and obtaining the state variables and control variables of the spacecraft between the starting position and the terminal position. The present invention can determine the concealed maneuvering trajectory that allows the spacecraft to avoid the monitoring of the monitoring satellite cluster, and can reduce the difficulty of solving, the amount of calculation and the time-consuming calculation.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft technology, and in particular to a spacecraft concealed maneuvering trajectory planning method based on Bezier curves. Background Art

[0002] At present, direct and indirect methods are usually used to obtain the corresponding numerical solutions when optimizing spacecraft trajectories. However, although the indirect method has a higher solution accuracy, it needs to construct and solve the relevant Hamiltonian function, has a small convergence domain, and takes a long time to calculate; although the direct method has a strong ability to handle nonlinear constraints, it is easy to fall into local optimal solutions and is sensitive to initial conditions. In particular, for problems with complex dynamics and strict constraints, the direct method may face convergence difficulties. In solving nonlinear programming problems with complex time-varying constraints such as spacecraft avoiding surveillance satellite clusters, both direct and indirect methods have great limitations. Summary of the invention

[0003] In order to solve some or all of the technical problems existing in the above-mentioned prior art, the present invention provides a spacecraft concealed maneuvering trajectory planning method based on Bezier curve.

[0004] The technical solution of the present invention is as follows:

[0005] A spacecraft concealed maneuver trajectory planning method based on Bezier curve is provided, including:

[0006] Construct a coordinate system to describe the relative motion of spacecraft and establish a spacecraft orbital dynamics model;

[0007] According to the situational awareness capability of the surveillance satellite cluster, the situational awareness constraints corresponding to the spacecraft's covert maneuvering process are constructed;

[0008] Construct control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft's concealed maneuvering process;

[0009] Based on the spacecraft orbital dynamics model, as well as the situational awareness constraints, control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft covert maneuvering process, a spacecraft covert maneuvering trajectory planning model is constructed;

[0010] Using Bezier curves, the position parameters, velocity parameters and control parameters of the spacecraft are converted into algebraic equations respectively;

[0011] The order and number of points of the Bezier curve are selected, and a discrete form of the spacecraft concealed maneuver trajectory planning model is constructed based on the spacecraft concealed maneuver trajectory planning model and algebraic equations.

[0012] Solve the discrete form of the spacecraft concealed maneuver trajectory planning model to obtain the state variables and control variables of the spacecraft between the starting position and the terminal position.

[0013] In some optional embodiments, a preset virtual reference point located on the orbit of the spacecraft is used as the origin, and a direction along the line connecting the preset virtual reference point and the center of the earth and pointing away from the center of the earth is used as the direction of the x Axis direction, so as to be in the orbital plane of the spacecraft and x The axis is perpendicular and points to the direction of the spacecraft's flight direction. y The axis direction is perpendicular to the orbital plane of the spacecraft and consistent with the direction of orbital angular momentum. z Axis direction, the LVLH coordinate system is constructed, and the LVLH coordinate system is used as the coordinate system for describing the relative motion of the spacecraft.

[0014] In some optional embodiments, the spacecraft orbital dynamics model is expressed as:

[0015] ;

[0016] in, , , Respectively , , The second derivative with respect to time is Respectively represent the spacecraft position in the LVLH coordinate system x axis, y Axis and z The weight below the axis, , Respectively , The first derivative with respect to time is is the angular velocity of the spacecraft, They represent the spacecraft control acceleration in the LVLH coordinate system. x axis, y Axis and z The weight below the axis.

[0017] In some optional embodiments, situational awareness constraints include surveillance satellite optical constraints and surveillance satellite radar constraints. The surveillance satellite optical constraints include: optical sensor field of view angle constraints; the surveillance satellite radar constraints include: radar detection pitch angle constraints, radar detection yaw angle constraints, and radar detection distance constraints.

[0018] In some optional implementations, the control capability constraint is expressed as:

[0019] ;

[0020] in, represents the control acceleration vector of the spacecraft in the LVLH coordinate system, , is the maximum control acceleration that the spacecraft engine can provide, Represents the 2-norm of a vector.

[0021] In some optional implementations, the boundary condition constraint is expressed as:

[0022] ;

[0023] in, Indicates the start time, , and They represent the starting time, starting position and starting speed of the given spacecraft concealed maneuver respectively. and They represent the spacecraft at the start time The position and velocity of represents the given spacecraft concealed maneuvering terminal position, Indicates that the spacecraft is at terminal time location, represents the given spacecraft concealed maneuvering terminal velocity, Indicates that the spacecraft is at terminal time speed.

[0024] In some optional embodiments, the performance indicator includes a minimum time or minimum speed increment;

[0025] The shortest performance index is expressed as:

[0026] ;

[0027] The minimum speed increment performance index is expressed as:

[0028] ;

[0029] in, , They represent the shortest time performance function and the minimum speed increment performance function respectively. Represents a time variable.

[0030] In some optional implementations, the spacecraft concealed maneuver trajectory planning model is expressed as:

[0031] ;

[0032] in, Indicates iThe optical sensor observation vector of the surveillance satellite, Represents the spacecraft relative to i The position vector of the monitoring satellite, Indicates i The maximum field of view of the optical sensor of a surveillance satellite, express The transpose of represents the 2-norm of a vector, Indicates the calculation of the arccosine function, Respectively represent i The monitoring satellite positions are in the LVLH coordinate system x axis, y Axis and z The weight below the axis, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system x The distance in the axial direction, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system y The distance in the axial direction, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system z The distance in the axial direction, Indicates i The elevation angle of the line between the surveillance satellite radar and the spacecraft, represents the calculation of the inverse tangent function, Indicates the monitoring satellite radar detection elevation angle search range, Indicates i The yaw angle of the line between the monitoring satellite radar and the spacecraft, Indicates the yaw angle search range of the surveillance satellite radar. Indicates i The distance between the monitoring satellite and the spacecraft, Indicates the maximum detection distance of the surveillance satellite radar. represents the situational awareness constraints of the surveillance satellite cluster, It said the surveillance satellite cluster could not detect the spacecraft. Indicates that the surveillance satellite cluster has detected the spacecraft, Indicates i surveillance satellite situational awareness constraints, Indicates i The surveillance satellites were unable to detect the spacecraft. Indicates i A surveillance satellite detected the spacecraft. Indicates the number of surveillance satellites in the surveillance satellite cluster, and Respectively represent i The surveillance satellite optical constraints and i surveillance satellite radar constraints, Indicates i When the optical sensors of a surveillance satellite cannot detect the spacecraft, the corresponding inequality holds true. , when the corresponding inequality does not hold, , Indicates i The surveillance satellite radar was unable to detect the spacecraft. Indicates i A surveillance satellite radar detection pitch angle constraint, when the corresponding inequality holds, , when the corresponding inequality does not hold, , Indicates i A surveillance satellite radar detects yaw angle constraints, and the corresponding inequality holds true. , when the corresponding inequality does not hold, , Indicates i surveillance satellite radar detection distance constraints, the corresponding inequality holds true, , when the corresponding inequality does not hold, .

[0033] In some optional implementations, the algebraic equation corresponding to the position parameter of the spacecraft is expressed as:

[0034] ;

[0035] The algebraic equation corresponding to the spacecraft velocity parameter is expressed as:

[0036] ;

[0037] The algebraic equations corresponding to the control parameters of the spacecraft are expressed as:

[0038] ;

[0039] in, is the normalized time scale, , represents the time variable, Indicates the terminal time, express The position vector of the spacecraft in the LVLH coordinate system at time, represents the order of the Bezier curve, Indicates the position of the Bezier curve control point. represents the state variable Bessel basis function, and Represents the position vector about The first and second derivatives of and They represent the state variable Bessel basis functions about The first and second derivatives of .

[0040] In some optional implementations, the discrete form of the spacecraft concealed maneuver trajectory planning model is expressed as:

[0041] ;

[0042] in, represents the number of selected matching points, represents the order of the Bezier curve, Indicates Points, suffix Indicates that the corresponding physical quantity is The value of the moment.

[0043] The main advantages of the technical solution of the present invention are as follows:

[0044] The spacecraft concealed maneuvering trajectory planning method based on Bezier curve of the present invention converts the state parameters and control parameters of the spacecraft into algebraic equations based on the Bezier curve, selects the order and the number of matching points of the Bezier curve, and combines the spacecraft orbital dynamics model, the surveillance satellite cluster situational awareness constraints, control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft concealed maneuvering process, to construct and solve a discrete form of spacecraft concealed maneuvering trajectory planning model. The concealed maneuvering trajectory of the spacecraft can be determined so that the spacecraft avoids the surveillance of the surveillance satellite cluster, and can reduce the difficulty of solving, reduce the amount of solution calculations and calculation time, reduce the solution requirements, and improve the solution accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings described herein are used to provide a further understanding of the embodiments of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0046] Figure 1 A flowchart of a spacecraft concealed maneuvering trajectory planning method based on Bezier curves provided in an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of the construction principle of the LVLH coordinate system provided by an embodiment of the present invention, wherein a spacecraft and a surveillance satellite are also shown;

[0048] Figure 3A schematic diagram of the principle of optical constraint of a surveillance satellite provided by an embodiment of the present invention;

[0049] Figure 4 A schematic diagram of the principles of surveillance satellite radar constraints provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0051] The technical solution provided by the embodiments of the present invention is described in detail below with reference to the accompanying drawings.

[0052] See also Figure 1 The embodiment of the present invention provides a spacecraft concealed maneuver trajectory planning method based on Bezier curve, the method comprising the following steps 1-7:

[0053] Step 1: Construct a coordinate system to describe the relative motion of the spacecraft and establish a spacecraft orbital dynamics model.

[0054] Specifically, since the spacecraft needs to satisfy the spacecraft orbital dynamics constraints during the orbital concealment maneuver, it is necessary to establish a corresponding spacecraft orbital dynamics model based on the spacecraft orbital dynamics constraints.

[0055] Furthermore, in an embodiment of the present invention, the purpose of spacecraft concealed maneuvering trajectory planning is to enable the spacecraft to avoid the surveillance detection of the surveillance satellite cluster, and the relative motion between the spacecraft and the surveillance satellite is involved in the spacecraft concealed maneuvering trajectory planning process. In order to facilitate the establishment of a spacecraft orbital dynamics model, surveillance satellite cluster situational awareness constraints, and to achieve rapid planning and solution of the spacecraft concealed maneuvering trajectory, in an embodiment of the present invention, a coordinate system for describing the relative motion of the spacecraft is constructed, and a spacecraft orbital dynamics model is established based on the constructed coordinate system.

[0056] refer to Figure 2 In the embodiment of the present invention, a preset virtual reference point located on the orbit of the spacecraft is taken as the origin O, and a direction along the line connecting the preset virtual reference point and the center of the earth and pointing away from the center of the earth is taken as x Axis direction, so as to be in the orbital plane of the spacecraft and x The axis is perpendicular and points to the direction of the spacecraft's flight direction. yThe axis direction is perpendicular to the orbital plane of the spacecraft and consistent with the direction of orbital angular momentum. z Axis direction, the LVLH coordinate system is constructed, and the LVLH coordinate system is used as the coordinate system for describing the relative motion of the spacecraft.

[0057] Among them, the virtual reference point is determined according to the actual situation.

[0058] Furthermore, in an embodiment of the present invention, based on the LVLH coordinate system constructed above, the established spacecraft orbital dynamics model is expressed as:

[0059] ;

[0060] in, , , Respectively , , The second derivative with respect to time is Respectively represent the spacecraft position in the LVLH coordinate system x axis, y Axis and z The weight below the axis, , Respectively , The first derivative with respect to time is is the angular velocity of the spacecraft, They represent the spacecraft control acceleration in the LVLH coordinate system. x axis, y Axis and z The weight below the axis.

[0061] Accordingly, in the embodiment of the present invention, the state variable of the spacecraft is expressed as , express The first derivative with respect to time is represents the position vector of the spacecraft in the LVLH coordinate system, , , the control variable is the control acceleration vector, expressed as , represents the control variable, represents the control acceleration vector of the spacecraft in the LVLH coordinate system.

[0062] Step 2: Based on the situational awareness capability of the surveillance satellite cluster, construct situational awareness constraints corresponding to the spacecraft's covert maneuvering process.

[0063] Surveillance satellites detect objects through the optical sensors and radars they carry. Therefore, when constructing situational awareness constraints corresponding to the spacecraft's covert maneuvers, it is necessary to comprehensively consider surveillance satellite optical constraints and radar constraints.

[0064] In the embodiment of the present invention, the monitoring satellite optical constraint includes: optical sensor field of view angle constraint; the monitoring satellite radar constraint includes: radar detection pitch angle constraint, radar detection yaw angle constraint, and radar detection distance constraint.

[0065] refer to Figure 3 Specifically, during the covert maneuvering of the spacecraft, the necessary condition for the surveillance satellite optical sensor to detect the spacecraft is that the spacecraft is within the field of view of the optical sensor, that is, the angle between the position vector of the spacecraft relative to the surveillance satellite and the observation vector of the optical sensor must be smaller than the maximum field of view angle of the optical sensor.

[0066] To this end, in the embodiment of the present invention, during the concealed maneuvering process of the spacecraft, the corresponding optical sensor field of view angle constraint is expressed as:

[0067] ;

[0068] in, Indicates i The optical sensor observation vector of the surveillance satellite, Represents the spacecraft relative to i The position vector of the monitoring satellite, Indicates i The maximum field of view of the optical sensor of a surveillance satellite, express The transpose of represents the 2-norm of a vector, represents the calculation of the arccosine function. When the above inequality holds, , indicating that the spacecraft is in i The optical sensor field of view of the surveillance satellite i The optical sensors of the surveillance satellites cannot detect the spacecraft. When the above inequality does not hold, , indicating that the spacecraft is in i Within the field of view of the optical sensor of the surveillance satellite, i A surveillance satellite's optical sensors can detect the spacecraft.

[0069] refer to Figure 4 The necessary conditions for the surveillance satellite radar to detect the spacecraft include that the spacecraft is located within the surveillance satellite radar detection pitch angle search range, that is, the pitch angle of the line connecting the surveillance satellite radar and the spacecraft must be within the surveillance satellite radar detection pitch angle search range.

[0070] To this end, in the embodiment of the present invention, during the concealed maneuvering process of the spacecraft, the corresponding radar detection pitch angle constraint is expressed as:

[0071] ;

[0072] in, and Respectively represent i The monitoring satellite positions are in the LVLH coordinate system x Axis and y The weight below the axis, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system x The distance in the axial direction, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system y The distance in the axial direction, Indicates i The elevation angle of the line between the surveillance satellite radar and the spacecraft, represents the calculation of the inverse tangent function, represents the monitoring satellite radar detection pitch angle search range. When the above inequality holds, , indicating that the spacecraft is not in the i Within the search range of the elevation angle detection of the surveillance satellite radar, i The surveillance satellite radar cannot detect the spacecraft. When the above inequality does not hold, , indicating that the spacecraft is in i Within the search range of the elevation angle detection of the surveillance satellite radar, i A surveillance satellite radar can detect the spacecraft.

[0073] refer to Figure 4 Furthermore, in an embodiment of the present invention, the necessary condition for the surveillance satellite radar to detect the spacecraft also includes that the spacecraft is located within the yaw angle search range detected by the surveillance satellite radar, that is, the yaw angle of the line connecting the surveillance satellite radar and the spacecraft must be within the yaw angle search range detected by the surveillance satellite radar.

[0074] To this end, in the embodiment of the present invention, during the concealed maneuvering process of the spacecraft, the corresponding radar detection yaw angle constraint is expressed as:

[0075] ;

[0076] in, Indicates i The monitoring satellite positions are in the LVLH coordinate system z The weight below the axis, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate systemz The distance in the axial direction, Indicates i The yaw angle of the line between the monitoring satellite radar and the spacecraft, represents the search range of the yaw angle detected by the surveillance satellite radar. When the above inequality holds, , indicating that the spacecraft is not in the i Within the yaw angle search range detected by the surveillance satellite radar, i The surveillance satellite radar cannot detect the spacecraft. When the above inequality does not hold, , indicating that the spacecraft is in i Within the yaw angle search range detected by the surveillance satellite radar, i A surveillance satellite radar can detect the spacecraft.

[0077] refer to Figure 4 Furthermore, in an embodiment of the present invention, the necessary condition for the surveillance satellite radar to detect the spacecraft also includes that the spacecraft is within the detection range of the surveillance satellite radar, that is, the distance between the surveillance satellite radar and the spacecraft must be within the detection range of the surveillance satellite radar.

[0078] To this end, in the embodiment of the present invention, during the concealed maneuvering process of the spacecraft, the corresponding radar detection distance constraint is expressed as:

[0079] ;

[0080] in, Indicates i The distance between the monitoring satellite and the spacecraft, represents the maximum detection distance of the surveillance satellite radar. When the above inequality holds, , indicating that the spacecraft is not in the i Within the detection range of surveillance satellite radars, i The surveillance satellite radar cannot detect the spacecraft. When the above inequality does not hold, , indicating that the spacecraft is in i Within the detection range of surveillance satellite radars, i A surveillance satellite radar can detect the spacecraft.

[0081] Furthermore, based on the analysis of the above surveillance satellite optical constraints and radar constraints, and according to the situational awareness capability of the surveillance satellite cluster, the situational awareness constraints corresponding to the spacecraft covert maneuvering process are expressed as follows:

[0082] ;

[0083] in, represents the situational awareness constraints of the surveillance satellite cluster, It said the surveillance satellite cluster could not detect the spacecraft. Indicates that the surveillance satellite cluster has detected the spacecraft, Indicates i surveillance satellite situational awareness constraints, Indicates i The surveillance satellites were unable to detect the spacecraft. Indicates i A surveillance satellite detected the spacecraft. Indicates the number of surveillance satellites in the surveillance satellite cluster. and Respectively represent i The surveillance satellite optical constraints and i surveillance satellite radar constraints, Indicates i The surveillance satellite's optical sensors were unable to detect the spacecraft. Indicates i The surveillance satellite radar was unable to detect the spacecraft. Indicates i A surveillance satellite radar detection pitch angle constraint, when the corresponding inequality holds, , when the corresponding inequality does not hold, , Indicates i A surveillance satellite radar detects yaw angle constraints, and the corresponding inequality holds true. , when the corresponding inequality does not hold, , Indicates i surveillance satellite radar detection distance constraints, the corresponding inequality holds true, , when the corresponding inequality does not hold, .

[0084] In an embodiment of the present invention, if at least one of the surveillance satellite optical sensor and the surveillance satellite radar can detect the spacecraft, it means that the spacecraft can be detected by the surveillance satellite; if at least one surveillance satellite in the surveillance satellite cluster can detect the spacecraft, it means that the spacecraft can be detected by the surveillance satellite cluster. If all the surveillance satellite optical sensors and surveillance satellite radars in the surveillance satellite cluster cannot detect the spacecraft, it means that the spacecraft cannot be detected by the surveillance satellite cluster. Among the above-mentioned surveillance satellite radar constraints, only at least one type of constraint needs to be satisfied, and then the surveillance satellite radar cannot detect the spacecraft.

[0085] Step 3: Construct the control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft's covert maneuvering process.

[0086] In the embodiment of the present invention, the control capability constraint corresponding to the spacecraft concealed maneuvering process is expressed as:

[0087] ;

[0088] in, Represents the maximum control acceleration that the spacecraft engine can provide.

[0089] Furthermore, in the embodiment of the present invention, during the spacecraft concealed maneuvering process, it is only necessary to control the spacecraft to reach a given terminal position and terminal speed, and the terminal time can be adjusted automatically according to the optimization target. To this end, in the embodiment of the present invention, the boundary condition constraints corresponding to the spacecraft concealed maneuvering process include: starting time constraint, starting position constraint, starting time speed constraint, terminal position constraint and terminal speed constraint.

[0090] Specifically, the boundary condition constraints corresponding to the spacecraft concealed maneuver process are expressed as:

[0091] ;

[0092] in, Indicates the start time, , and They represent the starting time, starting position and starting speed of the given spacecraft concealed maneuver respectively. and They represent the spacecraft at the start time The position and velocity of represents the given spacecraft concealed maneuvering terminal position, Indicates that the spacecraft is at terminal time location, represents the given spacecraft concealed maneuvering terminal velocity, Indicates that the spacecraft is at terminal time speed.

[0093] Among them, the starting time, starting position, starting speed, terminal position and terminal speed of the spacecraft's concealed maneuver are given according to actual conditions.

[0094] Furthermore, in an embodiment of the present invention, the performance indicator includes the shortest time or the minimum speed increment.

[0095] Specifically, the shortest time performance index is expressed as:

[0096] ;

[0097] The minimum speed increment performance index is expressed as:

[0098] ;

[0099] in, , They represent the shortest time performance function and the minimum speed increment performance function respectively. Represents a time variable.

[0100] In the actual spacecraft covert maneuvering process, the performance indicator can select the shortest time or minimum speed increment according to actual needs.

[0101] Step 4: Construct a spacecraft covert maneuver trajectory planning model based on the spacecraft orbital dynamics model and the situational awareness constraints, control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft covert maneuver process.

[0102] Specifically, in the embodiment of the present invention, based on the above-constructed spacecraft orbital dynamics model, and the above-set situational awareness constraints, control capability constraints, boundary condition constraints and performance indicators, the constructed spacecraft concealed maneuver trajectory planning model is expressed as:

[0103] .

[0104] Step 5: Use Bezier curves to convert the position parameters, velocity parameters, and control parameters of the spacecraft into algebraic equations.

[0105] The Bezier curve is a parametric mathematical curve defined by control points. The Bezier curve has the unique ability to generate continuous and smooth trajectories. Its derivatives of all orders exist, which means that the dynamic characteristics of the trajectory, such as velocity and acceleration, can be directly obtained by differentiation. This feature can greatly facilitate the real-time adjustment of the trajectory. A notable feature of the Bezier curve is that its shape is always within the convex hull formed by the control points, which makes it easier to handle obstacle constraints during path planning, ensuring that the generated trajectory will not collide with obstacles in the environment, and by adjusting the position of the control points, the shape of the Bezier curve can be flexibly changed to meet different trajectory optimization requirements.

[0106] In the embodiment of the present invention, the position parameter, velocity parameter and control parameter of the spacecraft are converted into algebraic equations respectively using Bezier curves.

[0107] Specifically, the algebraic equation corresponding to the position parameters of the spacecraft is expressed as:

[0108] ;

[0109] in, is the normalized time scale, , represents the time variable, Indicates the terminal time, express The position vector of the spacecraft in the LVLH coordinate system at time, represents the order of the Bezier curve, Indicates the position of the Bezier curve control point. represents the state variable Bessel basis functions.

[0110] Among them, the state variable Bessel basis function Defined as:

[0111] .

[0112] Furthermore, since the speed parameter and control parameter of the spacecraft can be expressed by the first-order derivative and the second-order derivative of the position parameter with respect to time, in the embodiment of the present invention, the algebraic equation corresponding to the speed parameter of the spacecraft is expressed as:

[0113] ;

[0114] The algebraic equations corresponding to the control parameters of the spacecraft are expressed as:

[0115] ;

[0116] in, and Represents the position vector about The first and second derivatives of and They represent the state variable Bessel basis functions about The first and second derivatives of .

[0117] Based on the above Definition, and They are defined as:

[0118] ;

[0119] .

[0120] Step 6, select the order and number of points of the Bezier curve, and construct a discrete form of the spacecraft concealed maneuvering trajectory planning model based on the spacecraft concealed maneuvering trajectory planning model and algebraic equations.

[0121] In an embodiment of the present invention, in order to solve the above-constructed spacecraft concealed maneuvering trajectory planning model, reduce the difficulty of solution, reduce the amount of solution calculations and calculation time, and improve the solution accuracy, based on the above-constructed spacecraft concealed maneuvering trajectory planning model and algebraic equations, the order and number of matching points of the Bezier curve are selected, and the Bezier curve principle is used to construct a discrete form of the spacecraft concealed maneuvering trajectory planning model.

[0122] Specifically, in the embodiment of the present invention, the discrete form of the spacecraft concealed maneuver trajectory planning model is expressed as:

[0123] ;

[0124] in, represents the number of selected matching points, represents the order of the Bezier curve, Indicates Points, suffix Indicates that the corresponding physical quantity is The value of the moment.

[0125] Step 7, solve the discrete form of the spacecraft concealed maneuver trajectory planning model to obtain the state variables and control variables of the spacecraft between the starting position and the terminal position.

[0126] In an embodiment of the present invention, an existing sequential quadratic programming algorithm is used to solve a discrete form of a spacecraft concealed maneuvering trajectory planning model, determine the terminal moment, the control point position of the Bezier curve and the concealed maneuvering trajectory of the spacecraft, and obtain the state variables and control variables of the spacecraft between the starting position and the terminal position.

[0127] Specifically, the sequential quadratic programming algorithm is used to solve the discrete form of the spacecraft concealed maneuver trajectory planning model, including the following steps:

[0128] Define the initial point: select an initial point as the starting point of the iteration;

[0129] Constructing augmented objective function: Using the objective function and constraints to construct augmented objective function, the constrained optimization problem is transformed into an unconstrained optimization problem;

[0130] Solve quadratic programming subproblems: In each iteration, a descent direction is determined by solving a quadratic programming subproblem;

[0131] Determine the search direction and step size: Determine the search direction and step size based on the descent direction obtained in the previous step;

[0132] Update iteration point: Update the current iteration point according to the search direction and step size;

[0133] Determine the termination condition: Check whether the termination condition is met. If so, stop the iteration; otherwise, return to the second step to continue the iteration. The termination condition may be, for example, reaching a preset number of iterations or the objective function value changing less than a preset threshold.

[0134] Output results: Output the final iteration results.

[0135] The Bezier curve-based spacecraft concealed maneuvering trajectory planning method provided in an embodiment of the present invention converts the state parameters and control parameters of the spacecraft into algebraic equations based on the Bezier curve, selects the order and number of matching points of the Bezier curve, and combines the spacecraft orbital dynamics model, the surveillance satellite cluster situational awareness constraints, control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft concealed maneuvering process, to construct and solve a discrete form of a spacecraft concealed maneuvering trajectory planning model. The concealed maneuvering trajectory of the spacecraft can be determined so that the spacecraft avoids the surveillance of the surveillance satellite cluster, and can reduce the difficulty of solving the problem, reduce the amount of solution calculations and the time consumption, reduce the solution requirements, and improve the solution accuracy.

[0136] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A spacecraft concealed maneuver trajectory planning method based on Bezier curve, characterized in that: include: Construct a coordinate system to describe the relative motion of spacecraft and establish a spacecraft orbital dynamics model; According to the situational awareness capability of the surveillance satellite cluster, the situational awareness constraints corresponding to the spacecraft's covert maneuvering process are constructed; Construct control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft's concealed maneuvering process; Based on the spacecraft orbital dynamics model, as well as the situational awareness constraints, control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft covert maneuvering process, a spacecraft covert maneuvering trajectory planning model is constructed; Using Bezier curves, the position parameters, velocity parameters and control parameters of the spacecraft are converted into algebraic equations respectively; The order and number of points of the Bezier curve are selected, and a discrete form of the spacecraft concealed maneuver trajectory planning model is constructed based on the spacecraft concealed maneuver trajectory planning model and algebraic equations. Solve the discrete form of the spacecraft concealed maneuver trajectory planning model to obtain the state variables and control variables of the spacecraft between the starting position and the terminal position.

2. The method for planning a spacecraft concealed maneuvering trajectory based on Bezier curve according to claim 1, characterized in that: The preset virtual reference point on the orbit of the spacecraft is taken as the origin, and the direction along the line connecting the preset virtual reference point and the center of the earth and pointing away from the center of the earth is taken as the x Axis direction, so as to be in the orbital plane of the spacecraft and x The axis is perpendicular and points to the direction of the spacecraft's flight direction as y The axis direction is perpendicular to the orbital plane of the spacecraft and consistent with the direction of orbital angular momentum. z Axis direction, the LVLH coordinate system is constructed, and the LVLH coordinate system is used as the coordinate system for describing the relative motion of the spacecraft.

3. The spacecraft concealed maneuvering trajectory planning method based on Bezier curve according to claim 2 is characterized in that: The spacecraft orbital dynamics model is expressed as: ； in, , , Respectively , , The second derivative with respect to time is Respectively represent the spacecraft position in the LVLH coordinate system x axis, y Axis and z The weight below the axis, , Respectively , The first derivative with respect to time is is the angular velocity of the spacecraft, They represent the spacecraft control acceleration in the LVLH coordinate system. x axis, y Axis and z The weight below the axis.

4. The method for planning a spacecraft concealed maneuvering trajectory based on Bezier curves according to claim 3, characterized in that: Situational awareness constraints include surveillance satellite optical constraints and surveillance satellite radar constraints. Surveillance satellite optical constraints include: optical sensor field of view angle constraints; surveillance satellite radar constraints include: radar detection pitch angle constraints, radar detection yaw angle constraints, and radar detection distance constraints.

5. The method for planning a spacecraft concealed maneuvering trajectory based on Bezier curves according to claim 4, characterized in that: The control capability constraint is expressed as: ； in, represents the control acceleration vector of the spacecraft in the LVLH coordinate system, , is the maximum control acceleration that the spacecraft engine can provide, Represents the 2-norm of a vector.

6. The method for planning a spacecraft concealed maneuvering trajectory based on Bezier curves according to claim 5, characterized in that: The boundary condition constraints are expressed as: ； in, Indicates the start time, , and They represent the starting time, starting position and starting speed of the given spacecraft concealed maneuver respectively. and They represent the spacecraft at the start time The position and velocity of represents the given spacecraft concealed maneuvering terminal position, Indicates that the spacecraft is at terminal time location, represents the given spacecraft concealed maneuvering terminal velocity, Indicates that the spacecraft is at terminal time speed.

7. The method for planning a spacecraft concealed maneuvering trajectory based on Bezier curves according to claim 6, characterized in that: Performance indicators include the shortest time or minimum velocity increment; The shortest performance index is expressed as: ； The minimum speed increment performance index is expressed as: ； in, , They represent the shortest time performance function and the minimum speed increment performance function respectively. Represents a time variable.

8. The method for planning a spacecraft concealed maneuvering trajectory based on Bezier curves according to claim 7, characterized in that: The spacecraft concealed maneuver trajectory planning model is expressed as: ； in, Indicates i The optical sensor observation vector of the surveillance satellite, Represents the spacecraft relative to i The position vector of the monitoring satellite, Indicates i The maximum field of view of the optical sensor of a surveillance satellite, express The transpose of represents the 2-norm of a vector, Represents the calculation of the arccosine function, Respectively represent i The surveillance satellite positions are in the LVLH coordinate system x axis, y Axis and z The weight below the axis, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system x The distance in the axial direction, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system y The distance in the axial direction, Indicates the spacecraft and i surveillance satellites in the LVLH coordinate system z The distance in the axial direction, Indicates i The elevation angle of the line between the surveillance satellite radar and the spacecraft, Indicates the calculation of the inverse tangent function, Indicates the monitoring satellite radar detection elevation angle search range, Indicates i The yaw angle of the line between the monitoring satellite radar and the spacecraft, Indicates the yaw angle search range of the surveillance satellite radar. Indicates i The distance between the monitoring satellite and the spacecraft, Indicates the maximum detection distance of the surveillance satellite radar. represents the situational awareness constraints of the surveillance satellite cluster, It said the surveillance satellite cluster could not detect the spacecraft. Indicates that the surveillance satellite cluster has detected the spacecraft. Indicates i surveillance satellite situational awareness constraints, Indicates i The surveillance satellites were unable to detect the spacecraft. Indicates i A surveillance satellite detected the spacecraft. Indicates the number of surveillance satellites in the surveillance satellite cluster. and Respectively represent i Optical constraints of surveillance satellites and i surveillance satellite radar constraints, Indicates i When the optical sensors of a surveillance satellite cannot detect the spacecraft, the corresponding inequality holds true. , when the corresponding inequality does not hold, , Indicates i The surveillance satellite radar was unable to detect the spacecraft. Indicates i A surveillance satellite radar detection pitch angle constraint, when the corresponding inequality holds, , when the corresponding inequality does not hold, , Indicates i A surveillance satellite radar detects yaw angle constraints, and the corresponding inequality holds true. , when the corresponding inequality does not hold, , Indicates i surveillance satellite radar detection distance constraints, the corresponding inequality holds true, , when the corresponding inequality does not hold, .

9. The spacecraft concealed maneuvering trajectory planning method based on Bezier curve according to claim 8, characterized in that: The algebraic equation corresponding to the position parameters of the spacecraft is expressed as: ； The algebraic equation corresponding to the spacecraft velocity parameter is expressed as: ； The algebraic equations corresponding to the control parameters of the spacecraft are expressed as: ； in, is the normalized time scale, , represents the time variable, Indicates the terminal time, express The position vector of the spacecraft in the LVLH coordinate system at time, represents the order of the Bezier curve, Indicates the position of the Bezier curve control point. represents the state variable Bessel basis function, and Represents the position vector about The first and second derivatives of and They represent the state variable Bessel basis functions about The first and second derivatives of .

10. The spacecraft concealed maneuvering trajectory planning method based on Bezier curve according to claim 9, characterized in that: The discrete form of the spacecraft concealed maneuver trajectory planning model is expressed as: ； in, represents the number of selected matching points, represents the order of the Bezier curve, Indicates Points, suffix Indicates that the corresponding physical quantity is The value of the moment.

Images