A method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage

Abstract

The present invention discloses a method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage, which relates to the field of spacecraft technology, including: constructing a spacecraft trajectory planning model based on a spacecraft orbital dynamics model, control capability constraints, boundary condition constraints and performance indicators corresponding to a spacecraft trajectory planning process; processing the spacecraft trajectory planning model using a pseudo-spectral method to obtain reference state variables and reference control variables of the spacecraft between a starting position and a terminal position; establishing a rapid spacecraft trajectory planning model based on reference variables using a motion camouflage algorithm; solving the rapid spacecraft trajectory planning model using a sequential quadratic programming algorithm and a model predictive control algorithm to obtain state variables and control variables of the spacecraft between a starting position and a terminal position. The present invention can reduce the amount of calculation in the spacecraft trajectory planning process, realize rapid spacecraft trajectory planning, and ensure the optimality of the obtained spacecraft trajectory planning results.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft technology, and in particular to a method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage. Background Art

[0002] In a complex space environment, spacecraft may face various unknown factors and potential risks, such as space debris, celestial gravitational disturbances, etc. During the orbital maneuvers of spacecraft, rapid planning and closed-loop control of spacecraft trajectories are of great significance for spacecraft to avoid space debris and achieve collision avoidance between spacecraft.

[0003] Spacecraft trajectory planning is essentially a complex nonlinear optimization problem with multiple constraints. Currently, direct and indirect methods are usually used to obtain numerical solutions. However, the theoretical derivation of the indirect method is complex, and it is difficult to handle complex constraints. In addition, the indirect method is sensitive to initial values, and the effect is poor when it is actually applied to solve spacecraft trajectory planning. The direct method usually uses a parameterization method to transform the optimal control problem in continuous space into a nonlinear programming problem. It can use the prior knowledge of the trajectory to set the initial guess, thereby widening the range of the convergence domain. However, the direct method generally obtains an approximate optimal solution rather than an exact optimal solution. In addition, the amount of calculation required to directly solve the spacecraft trajectory planning problem using the indirect method and the direct method is large, and the calculation takes a long time, making it difficult to use for rapid spacecraft trajectory planning. Summary of the invention

[0004] In order to solve some or all of the technical problems existing in the above-mentioned prior art, the present invention provides a method for rapid planning and closed-loop control of spacecraft trajectory based on pseudo-spectral motion camouflage.

[0005] The technical solution of the present invention is as follows:

[0006] A method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage is provided, including:

[0007] Build spacecraft orbital dynamics models;

[0008] Construct control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft trajectory planning process;

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

[0010] The general form of the spacecraft trajectory planning model is processed by using the pseudo-spectral method to obtain the discrete form of the spacecraft trajectory planning model, the discrete form of the spacecraft trajectory planning model is solved, and the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position are obtained;

[0011] Based on the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position, a fast spacecraft trajectory planning model is established using the motion camouflage algorithm.

[0012] The sequential quadratic programming algorithm and model predictive control algorithm are used to solve the spacecraft trajectory rapid 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, the spacecraft orbital dynamics model is expressed as:

[0014] ;

[0015] in, , and They represent the position vector, velocity vector and unit mass control acceleration vector of the spacecraft in the geocentric inertial system, respectively. , , , They represent the position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z Component below the axis, subscript Indicates the corresponding physical quantity in the geocentric inertial system x axis, y Axis and z The weight below the axis, represents the gravitational constant of the central celestial body around which the spacecraft orbits, , Respectively , First derivative with respect to time.

[0016] In some optional implementations, the control capability constraint is expressed as:

[0017] ;

[0018] in, is the maximum unit mass control acceleration that the spacecraft engine can provide, Represents the 2-norm of a vector.

[0019] In some optional implementations, the boundary condition constraint is expressed as:

[0020] ;

[0021] in, , and represent the starting time, starting position and starting speed of the given spacecraft maneuver respectively, and They represent the spacecraft at the start time The position and velocity of represents the given spacecraft maneuvering terminal position, Indicates that the spacecraft is at terminal time location, represents the given spacecraft maneuvering terminal velocity, Indicates that the spacecraft is at terminal time speed.

[0022] In some optional embodiments, the performance indicator includes the shortest time or the minimum speed increment;

[0023] The shortest performance index is expressed as:

[0024] ;

[0025] The minimum speed increment performance index is expressed as:

[0026] ;

[0027] in, , They represent the shortest time performance function and the minimum speed increment performance function respectively. Represents a time variable.

[0028] In some optional embodiments, the general form of the spacecraft trajectory planning model is expressed as:

[0029] .

[0030] In some optional implementations, the discrete form of the spacecraft trajectory planning model is expressed as:

[0031] ;

[0032] in, represents the performance indicator function, represents the terminal performance indicator in the performance indicator function, Indicates the start time The state variables, Indicates terminal time The state variables, represents the number of points in the divided time domain, Indicates A matching point, express The corresponding integral weight coefficient is, Indicates Matching points The state variables at Indicates Matching points The control variable at represents the Lagrange term integral part in the performance index function, Represents the state differential matrix No. k Line i Elements of the columns, state differential matrix is a The matrix of Indicates Matching points The state variables at represents the dynamic constraint, Indicates the first matching point The location of Indicates the first matching point The speed at Indicates Matching points The location of Indicates Matching points The speed at which the

[0033] In some optional embodiments, a sequential quadratic programming algorithm is used to solve the discrete form of the spacecraft trajectory planning model.

[0034] In some optional implementations, the spacecraft trajectory rapid planning model is expressed as:

[0035] ;

[0036] in, represents the position ratio, and Respectively The first and second derivatives with respect to time, They represent the optimized position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, represents the distance from the optimized position of the spacecraft to the center of the earth, , Respectively The second derivative with respect to time is They represent the reference position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, They represent the relative position between the preset reference point and the spacecraft reference position in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, Respectively The first derivative with respect to time is Respectively The second derivative with respect to time is Indicates the start time The position ratio, Indicates terminal time The position ratio, and Respectively and First derivative with respect to time.

[0037] In some optional implementations, the method of using a sequential quadratic programming algorithm and a model predictive control algorithm to solve a spacecraft trajectory rapid planning model and obtain state variables and control variables of the spacecraft between a starting position and a terminal position includes the following steps:

[0038] Step 601, determine the initial state of the spacecraft maneuver , Terminal state of spacecraft maneuver , the start time of the spacecraft maneuver , the maximum unit mass control acceleration of the spacecraft , set the step time step of rolling optimization , determine the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position;

[0039] Step 602, using a sequential quadratic programming algorithm to solve a spacecraft trajectory rapid planning model, and obtaining a spacecraft trajectory rapid planning result;

[0040] Step 603, using a model predictive control algorithm to track and control the spacecraft trajectory rapid planning result to obtain a tracking control result;

[0041] Step 604: Track the control result. The state variables of the spacecraft at time t are taken as the initial state of the spacecraft maneuver, and moment as the starting moment;

[0042] Step 605, looping through steps 602 to 604 until the spacecraft reaches a set terminal state, and obtaining the state variables and control variables of the spacecraft between the starting position and the terminal position.

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

[0044] The method for rapid planning and closed-loop control of spacecraft trajectories based on pseudo-spectral motion camouflage of the present invention solves the spacecraft trajectory planning model based on the pseudo-spectral method, uses the spacecraft trajectory obtained based on the pseudo-spectral method as a reference trajectory, establishes a rapid spacecraft trajectory planning model in combination with a motion camouflage algorithm, and uses a model predictive control algorithm to optimize the spacecraft trajectory and perform closed-loop control. This can reduce the amount of calculation in the spacecraft trajectory planning process, improve the calculation speed, realize rapid planning of the spacecraft trajectory, and ensure the optimality and accuracy of the obtained spacecraft trajectory planning results. 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 method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage provided by an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of the principle of a motion camouflage algorithm in a method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage provided in an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of the principles of a method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] 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.

[0050] The technical solution provided by the embodiments of the present invention is described in detail below with reference to the accompanying drawings.

[0051] See also Figure 1 The embodiment of the present invention provides a method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage, the method comprising the following steps 1-6:

[0052] Step 1: Establish a spacecraft orbital dynamics model.

[0053] Specifically, since the spacecraft needs to satisfy the spacecraft orbital dynamics constraints when performing trajectory planning, a corresponding spacecraft orbital dynamics model is established based on the spacecraft orbital dynamics constraints.

[0054] In the embodiment of the present invention, the established spacecraft orbital dynamics model is expressed as:

[0055] ;

[0056] in, , and They represent the position vector, velocity vector and unit mass control acceleration vector of the spacecraft in the geocentric inertial system, respectively. , , , They represent the position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z Component below the axis, subscript Indicates the corresponding physical quantity in the geocentric inertial system x axis, y Axis and z The weight below the axis, represents the gravitational constant of the central celestial body around which the spacecraft orbits, , Respectively , First derivative with respect to time.

[0057] Accordingly, in the embodiment of the present invention, the state variable of the spacecraft is expressed as , the control variable of the spacecraft is the unit mass control acceleration vector, expressed as , represents the control variable.

[0058] Step 2: Construct the control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft trajectory planning process.

[0059] In the embodiment of the present invention, the control capability constraint corresponding to the spacecraft trajectory planning process is expressed as:

[0060] ;

[0061] in, is the maximum unit mass control acceleration that the spacecraft engine can provide, Represents the 2-norm of a vector.

[0062] Furthermore, in the embodiment of the present invention, during the spacecraft trajectory planning process, it is only necessary to control the spacecraft to reach a given terminal position and terminal velocity, and the terminal time can be optimized and adjusted according to the optimization target. To this end, in the embodiment of the present invention, the boundary condition constraints corresponding to the spacecraft trajectory planning process include: starting time constraint, starting position constraint, starting time velocity constraint, terminal position constraint and terminal velocity constraint.

[0063] Specifically, the boundary condition constraints corresponding to the spacecraft trajectory planning process are expressed as:

[0064] ;

[0065] in, , and represent the starting time, starting position and starting speed of the given spacecraft maneuver respectively, and They represent the spacecraft at the start time The position and velocity of represents the given spacecraft maneuvering terminal position, Indicates that the spacecraft is at terminal time location, represents the given spacecraft maneuvering terminal velocity, Indicates that the spacecraft is at terminal time speed.

[0066] Among them, the starting time, starting position, starting speed, terminal position and terminal speed of the spacecraft maneuver are given according to actual conditions.

[0067] Furthermore, in an embodiment of the present invention, the performance indicator includes the shortest time or the minimum speed increment.

[0068] Specifically, the shortest time performance index is expressed as:

[0069] ;

[0070] The minimum speed increment performance index is expressed as:

[0071] ;

[0072] in, , They represent the shortest time performance function and the minimum speed increment performance function respectively. Represents a time variable.

[0073] In the actual spacecraft trajectory planning process, the performance indicator can select the shortest time or minimum velocity increment according to actual needs.

[0074] Step 3: construct a general form of spacecraft trajectory planning model based on the spacecraft orbital dynamics model, as well as the control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft trajectory planning process.

[0075] Specifically, in an embodiment of the present invention, based on the above-constructed spacecraft orbital dynamics model, and the control capability constraints, boundary condition constraints and performance indicators corresponding to the above-set spacecraft trajectory planning process, the general form of the constructed spacecraft trajectory planning model is expressed as:

[0076] .

[0077] Step 4: Use the pseudo-spectral method to process the general form of the spacecraft trajectory planning model, obtain the discrete form of the spacecraft trajectory planning model, solve the discrete form of the spacecraft trajectory planning model, and obtain the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position.

[0078] The pseudospectral method is an efficient numerical optimization method that discretizes continuous optimal control problems into nonlinear programming problems (NLP). It has been widely used in spacecraft trajectory planning. Therefore, the principle of the pseudospectral method will not be described in detail in the embodiments of the present invention.

[0079] In the embodiment of the present invention, when the general form of the spacecraft trajectory planning model is processed by the pseudo-spectral method, the following discrete form of the spacecraft trajectory planning model is established based on the general form of the spacecraft trajectory planning model constructed above:

[0080] ;

[0081] in, represents the performance indicator function, represents the terminal performance indicator in the performance indicator function, Indicates the start time The state variables, Indicates terminal time The state variables, represents the number of points in the divided time domain, Indicates A matching point, express The corresponding integral weight coefficient is, Indicates Matching points The state variables at Indicates Matching points The control variable at represents the Lagrange term integral part in the performance index function, Represents the state differential matrix No. k Line i Elements of the columns, state differential matrix is a The matrix of Indicates Matching points The state variables at represents the dynamic constraint, Indicates the first matching point The location of Indicates the first matching point The speed at Indicates Matching points The location of Indicates Matching points The speed at which the

[0082] It should be noted that since the pseudo-spectral method is a commonly used algorithm in the field of spacecraft trajectory planning, the principle and analysis process of the pseudo-spectral method will not be described in detail here.

[0083] Furthermore, in an embodiment of the present invention, after the general form of the spacecraft trajectory planning model is processed by the pseudo-spectral method to obtain the discrete form of the spacecraft trajectory planning model, the existing sequential quadratic programming algorithm is used to solve the discrete form of the spacecraft trajectory planning model, determine the reference trajectory of the spacecraft, and obtain the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position.

[0084] Step 5: Based on the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position, a motion camouflage algorithm is used to establish a spacecraft trajectory rapid planning model.

[0085] refer to Figure 2 In the embodiment of the present invention, for the rapid planning process of the spacecraft trajectory, the basic equation of motion camouflage can be expressed as:

[0086] ;

[0087] in, represents the optimized position of the spacecraft in the geocentric inertial system, , They represent the optimized position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, represents the reference position of the spacecraft in the Earth-centered inertial system, , They represent the reference position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, Indicates the relative position between the preset reference point and the spacecraft reference position. , Respectively represent the relative position in the Earth-centered inertial system x axis, y Axis and z The weight below the axis, Indicates the position of the preset reference point in the geocentric inertial system. , Respectively represent the preset reference point position in the Earth-centered inertial system x axis, y Axis and z The weight below the axis, Represents the position ratio.

[0088] In an embodiment of the present invention, the reference point and / or position ratio may be a preset parameter, which is pre-set according to actual conditions; the reference point and / or position ratio may also be an optimization variable, which is optimized and updated based on a preset initial value during subsequent optimization solution.

[0089] Furthermore, since the velocity and acceleration of the spacecraft can be represented by the first-order derivative and the second-order derivative of the position with respect to time, in the embodiment of the present invention, the motion camouflage equation for the velocity and acceleration of the spacecraft can be obtained according to the basic equation of motion camouflage set above.

[0090] Specifically, the motion camouflage equation for the velocity and acceleration of the spacecraft can be expressed as:

[0091] ;

[0092] in, and Respectively The first and second derivatives with respect to time, and Respectively The first and second derivatives with respect to time, and Respectively The first and second derivatives with respect to time, and Respectively First and second derivatives with respect to time.

[0093] Furthermore, we select the geocentric inertial system xUnit mass control acceleration in the axis direction As a control variable, according to the above spacecraft orbital dynamics model, we can get:

[0094] ;

[0095] in, express The second derivative with respect to time is , Represents the distance from the optimized position of the spacecraft to the center of the earth.

[0096] Combined with the motion camouflage equation for the acceleration of the spacecraft obtained above, the formula It can be further expressed as:

[0097] ;

[0098] By transforming the above formula, we can get:

[0099] ;

[0100] in, express The second derivative with respect to time is express The first derivative with respect to time is express Second derivative with respect to time.

[0101] Furthermore, we select the geocentric inertial system y Unit mass control acceleration in the axis direction and the Earth-centered inertial system z Unit mass control acceleration in the axis direction As a control variable, refer to the above analysis of the geocentric inertial system. x Unit mass control acceleration in the axis direction The analysis process can be obtained:

[0102] ;

[0103] ;

[0104] in, express The second derivative with respect to time is express The first derivative with respect to time is express The second derivative with respect to time is express The second derivative with respect to time is express The first derivative with respect to time is express Second derivative with respect to time.

[0105] Furthermore, in the embodiment of the present invention, since the start time, start position, start time velocity, terminal position and terminal velocity of the spacecraft maneuver are all pre-given specific values, the above values ​​are equal in the reference trajectory and the optimized trajectory obtained by solving. Therefore, the following conditions are satisfied at the start time and the terminal time:

[0106] , , , .

[0107] Furthermore, in an embodiment of the present invention, based on the above analysis, the following spacecraft trajectory rapid planning model is established:

[0108] ;

[0109] in, Indicates the start time The position ratio, Indicates terminal time The position ratio, and Respectively and First derivative with respect to time.

[0110] Step 6: Use the sequential quadratic programming algorithm and the model predictive control algorithm to solve the spacecraft trajectory rapid planning model and obtain the state variables and control variables of the spacecraft between the starting position and the terminal position.

[0111] refer to Figure 3 Specifically, in an embodiment of the present invention, a sequential quadratic programming algorithm and a model predictive control algorithm are used to solve a spacecraft trajectory rapid planning model, and the state variables and control variables of the spacecraft between the starting position and the terminal position are obtained, including the following steps:

[0112] Step 601, determine the initial state of the spacecraft maneuver , Terminal state of spacecraft maneuver , the start time of the spacecraft maneuver , the maximum unit mass control acceleration of the spacecraft , set the step time step of rolling optimization , determine the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position;

[0113] Step 602, using a sequential quadratic programming algorithm to solve a spacecraft trajectory rapid planning model, and obtaining a spacecraft trajectory rapid planning result;

[0114] Step 603, using a model predictive control algorithm to track and control the spacecraft trajectory rapid planning result to obtain a tracking control result;

[0115] Step 604: Track the control result. The state variables of the spacecraft at time t are taken as the initial state of the spacecraft maneuver, and moment as the starting moment;

[0116] Step 605, looping through steps 602 to 604 until the spacecraft reaches a set terminal state, and obtaining the state variables and control variables of the spacecraft between the starting position and the terminal position.

[0117] It should be noted that in step 601, the initial state of the spacecraft maneuver is determined. , Terminal state of spacecraft maneuver , the start time of the spacecraft maneuver , the maximum unit mass control acceleration of the spacecraft Set it according to the actual situation.

[0118] It should be noted that, in step 601 , the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position are the reference state variables and reference control variables obtained in step 4 .

[0119] Furthermore, in the embodiment of the present invention, in the above step 603, the model predictive control algorithm is used to track and control the spacecraft trajectory rapid planning result to obtain the tracking control result, which specifically includes the following steps:

[0120] Determine a prediction model, where the prediction model is the above-mentioned spacecraft trajectory rapid planning model;

[0121] In each control cycle, the current state and control information of the spacecraft are read. The state information of the spacecraft includes: position information and speed information, and the control information of the spacecraft includes: acceleration information;

[0122] Using the current spacecraft status and control information, predict the spacecraft status and control information in multiple future time steps;

[0123] Based on the state and control information of the spacecraft in multiple future time steps, the tracking error is calculated, the spacecraft trajectory rapid planning model is solved, the optimal control sequence within a specified period of time in the future is determined, and the first control information in the optimal control sequence is selected as the tracking control result.

[0124] Further, in the embodiment of the present invention, in the above step 4 and step 6, the process principles of using the sequential quadratic programming algorithm to solve the discrete form of the spacecraft trajectory planning model and using the sequential quadratic programming algorithm to solve the spacecraft trajectory fast planning model are the same, and specifically include the following steps:

[0125] Define the initial point: select an initial point as the starting point of the iteration;

[0126] 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;

[0127] Solve quadratic programming subproblems: In each iteration, a descent direction is determined by solving a quadratic programming subproblem;

[0128] Determine the search direction and step size: Determine the search direction and step size based on the descent direction obtained in the previous step;

[0129] Update iteration point: Update the current iteration point according to the search direction and step size;

[0130] 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.

[0131] Output results: Output the final iteration results.

[0132] The method for rapid planning and closed-loop control of spacecraft trajectories based on pseudo-spectral motion camouflage provided in an embodiment of the present invention solves the spacecraft trajectory planning model based on the pseudo-spectral method, uses the spacecraft trajectory obtained based on the pseudo-spectral method as a reference trajectory, establishes a rapid spacecraft trajectory planning model in combination with a motion camouflage algorithm, and uses a model predictive control algorithm to optimize the spacecraft trajectory and perform closed-loop control. This can reduce the amount of calculation in the spacecraft trajectory planning process, improve the calculation speed, realize rapid planning of the spacecraft trajectory, and ensure the optimality and accuracy of the obtained spacecraft trajectory planning results.

[0133] 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.

[0134] 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 method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage, characterized in that: include: Build spacecraft orbital dynamics models; Construct control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft trajectory planning process; Based on the spacecraft orbital dynamics model, as well as the control capability constraints, boundary condition constraints and performance indicators corresponding to the spacecraft trajectory planning process, a general form of spacecraft trajectory planning model is constructed; The general form of the spacecraft trajectory planning model is processed by using the pseudo-spectral method to obtain the discrete form of the spacecraft trajectory planning model, the discrete form of the spacecraft trajectory planning model is solved, and the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position are obtained; Based on the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position, a fast spacecraft trajectory planning model is established using the motion camouflage algorithm. The sequential quadratic programming algorithm and model predictive control algorithm are used to solve the spacecraft trajectory rapid 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 rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 1 is characterized in that: The spacecraft orbital dynamics model is expressed as: ； in, , and They represent the position vector, velocity vector and unit mass control acceleration vector of the spacecraft in the geocentric inertial system, respectively. , , , They represent the position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z Component below the axis, subscript Indicates the corresponding physical quantity in the geocentric inertial system x axis, y Axis and z The weight below the axis, represents the gravitational constant of the central celestial body around which the spacecraft orbits, , Respectively , First derivative with respect to time.

3. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 2 is characterized in that: The control capability constraint is expressed as: ； in, is the maximum unit mass control acceleration that the spacecraft engine can provide, Represents the 2-norm of a vector.

4. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 3 is characterized in that: The boundary condition constraints are expressed as: ； in, , and represent the starting time, starting position and starting speed of the given spacecraft maneuver respectively, and They represent the spacecraft at the start time The position and velocity of represents the given spacecraft maneuvering terminal position, Indicates that the spacecraft is at terminal time location, represents the given spacecraft maneuvering terminal velocity, Indicates that the spacecraft is at terminal time speed.

5. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 4 is characterized in that: The performance indicators include the shortest time or minimum speed 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.

6. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 5 is characterized in that: The general form of the spacecraft trajectory planning model is expressed as: 。 7. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 6 is characterized in that: The discrete form of the spacecraft trajectory planning model is expressed as: ； in, represents the performance indicator function, represents the terminal performance indicator in the performance indicator function, Indicates the start time The state variables, Indicates terminal time The state variables, represents the number of points in the divided time domain, Indicates A matching point, express The corresponding integral weight coefficient is, Indicates Matching points The state variables at Indicates Matching points The control variable at represents the Lagrange term integral part in the performance index function, Represents the state differential matrix No. k Line i Elements of the columns, state differential matrix is a The matrix of Indicates Matching points The state variables at represents the dynamic constraint, Indicates the first matching point The location of Indicates the first matching point The speed at Indicates Matching points The location of Indicates Matching points The speed at which the 8. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 7 is characterized in that: The discrete form of the spacecraft trajectory planning model is solved using a sequential quadratic programming algorithm.

9. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 8, characterized in that: The spacecraft trajectory rapid planning model is expressed as: ； in, represents the position ratio, and Respectively The first and second derivatives with respect to time, They represent the optimized position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, represents the distance from the optimized position of the spacecraft to the center of the earth, , Respectively The second derivative with respect to time is They represent the reference position of the spacecraft in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, They represent the relative position between the preset reference point and the spacecraft reference position in the Earth-centered inertial system. x axis, y Axis and z The weight below the axis, Respectively The first derivative with respect to time is Respectively The second derivative with respect to time is Indicates the start time The position ratio, Indicates terminal time The position ratio, and Respectively and First derivative with respect to time.

10. The method for rapid spacecraft trajectory planning and closed-loop control based on pseudo-spectral motion camouflage according to claim 9, characterized in that: The method of using a sequential quadratic programming algorithm and a model predictive control algorithm to solve a spacecraft trajectory rapid planning model and obtain state variables and control variables of the spacecraft between a starting position and a terminal position includes the following steps: Step 601, determine the initial state of the spacecraft maneuver , Terminal state of spacecraft maneuver , the start time of the spacecraft maneuver , the maximum unit mass control acceleration of the spacecraft , set the step time step of rolling optimization , determine the reference state variables and reference control variables of the spacecraft between the starting position and the terminal position; Step 602, using a sequential quadratic programming algorithm to solve a spacecraft trajectory rapid planning model, and obtaining a spacecraft trajectory rapid planning result; Step 603, using a model predictive control algorithm to track and control the spacecraft trajectory rapid planning result to obtain a tracking control result; Step 604: Track the control result. The state variables of the spacecraft at time t are taken as the initial state of the spacecraft maneuver, and moment as the starting moment; Step 605, looping through steps 602 to 604 until the spacecraft reaches a set terminal state, and obtaining the state variables and control variables of the spacecraft between the starting position and the terminal position.

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