A control-distribution integrated full-distributed spacecraft cooperative attitude control method
By establishing a discrete linear model and model predictive control method, combined with the distributed optimization algorithm of the tracking alternating direction multiplier method, we have realized the spacecraft attitude cooperative control without a central controller. This solves the problems of dual-layer controllers relying on a central module and single-layer controllers not cooperating in the existing technology, and achieves overall performance optimization of the fully distributed system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2025-12-05
- Publication Date
- 2026-07-31
AI Technical Summary
In existing spacecraft attitude control methods, the two-layer controller structure relies on the central controller module and has allocation errors, while the single-layer controller structure requires information from all modules and is not in a cooperative state, resulting in poor overall system performance and high computational complexity.
A fully distributed spacecraft attitude cooperative control method integrating control and allocation is adopted. By establishing a discrete linear model, a model predictive control method is designed. Using the objective function and constraints under the model predictive control framework, a distributed optimization algorithm with alternating direction multipliers is adopted. Each module solves its own control strategy under the information conditions of adjacent modules, thus realizing fully distributed cooperative control.
Eliminating the need for a central controller simplifies control strategy calculations, enables a fully distributed system, adapts to module changes, improves overall system performance optimization, and reduces computational complexity and allocation errors.
Smart Images
Figure CN121657728B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of spacecraft attitude control technology, specifically relating to a fully distributed, control-allocation integrated spacecraft attitude cooperative control method. Background Technology
[0002] Takeover control utilizes the cellular satellite actuators attached to a spacecraft with failed actuators for attitude-assisted control, thereby extending the lifespan of the failed satellite and enabling the payload to achieve greater effectiveness. The combined spacecraft system consisting of the cellular satellite and the failed spacecraft is a highly redundant actuator system, as shown in the schematic diagram below. Figure 1 As shown, the number of actuator units is much greater than the motion degrees of freedom of the spacecraft. Therefore, in order to address the problems of the large number of cell stars, heterogeneous modules, and local communication in the takeover control system, a control allocation method is required.
[0003] Control allocation methods are currently divided into two categories:
[0004] The first type is the two-layer controller structure, where the control and distribution processes are separated, consisting of a control law calculation layer (upper layer) and a control distribution layer (lower layer). In the upper layer, the central controller designs the control law and calculates the total control torque. In the lower layer, the total control torque calculated by the upper layer is distributed to each actuator. This can be categorized into centralized and distributed methods. The centralized method involves both control and distribution being calculated by the central module, such as direct distribution, optimization, and pseudo-inverse methods. The distributed method involves each module in the distribution layer calculating its own control strategy based solely on the total control torque received from the upper layer module and the strategy information of adjacent modules.
[0005] The second type of method is a single-layer controller structure, which eliminates the need for a central controller to transmit and compute information back and forth. Each module can independently solve its own control strategy based on its own characteristics. Differential game theory strategies are generally used to solve this type of single-layer control allocation problem, allowing each module to make a final decision based on information from other modules, and the control strategy is obtained by solving for the Nash equilibrium.
[0006] The existing two types of technologies have the following shortcomings:
[0007] (1) The two-layer controller structure requires a central controller module.
[0008] This method requires the use of a central controller module to calculate the total control torque, representing a separation of control and distribution. Furthermore, the design of the upper-level control law needs to consider the capabilities of the cellular actuators, which makes the design process less simplified. Additionally, if some modules suddenly malfunction or reach saturation, the control requirements will not be met, leading to distribution errors or even loss of control.
[0009] (2) Most single-layer controller architectures require control information from all modules.
[0010] First, because the constraint of the differential game method used in single-layer modules is a differential equation that includes the inputs of all modules, most current methods require each module to know the information of all other modules, which is not a fully distributed approach. Second, in the few fully distributed game methods, each module needs to solve for a Nash equilibrium to obtain its own control strategy. In this case, the modules are in a non-cooperative state, and each module optimizes its own performance indicators while knowing the information of other modules, which cannot achieve the overall system optimization. In addition, the process of finding a Nash equilibrium for differential game strategies is complex and has low accuracy. Summary of the Invention
[0011] To address the aforementioned technical problems, this invention proposes a fully distributed, integrated control-allocation spacecraft attitude cooperative control method. This method eliminates the need for a central controller to design the overall control law, avoids allocation errors inherent in two-layer controller structures, simplifies the control strategy calculation process, and enables each module to solve its own control strategy based on the communication network diagram, receiving only information from adjacent modules. This achieves full distribution, and the various satellite modules cooperate to achieve overall optimal performance of the combined spacecraft system.
[0012] To achieve the above objectives, the present invention adopts the following technical solution:
[0013] A fully distributed, control-allocation integrated spacecraft attitude cooperative control method is implemented according to the following steps:
[0014] Step 1: Establish a discrete linear spacecraft attitude kinematics and dynamics model;
[0015] Step 2: Design a predictive control method for the combined spacecraft system model;
[0016] Step 3: Use a fully distributed attitude control allocation method to solve the overall optimization problem of the combined spacecraft system based on model predictive control in Step 2.
[0017] Furthermore, step 1 includes the following steps:
[0018] Step 1.1: Use attitude quaternions to represent the kinematic and dynamic system equations of the combined spacecraft's attitude tracking error;
[0019] Step 1.2: Introduce a pseudo-linear model with state correlation coefficients to linearize the nonlinear spacecraft attitude kinematics and dynamics system model, and discretize it using the Euler method to obtain the system discrete linearized model at the next sampling time.
[0020] Furthermore, step 2 includes the following steps:
[0021] Step 2.1: With the goal of maximizing the overall tracking speed of the system and minimizing energy consumption, design the objective function for each cell star at each sampling moment under the model prediction control framework;
[0022] Step 2.2: Set equality constraints for the model prediction equations and inequality constraints for the torques of each module and the dynamic performance of the system state during the optimization process;
[0023] Step 2.3: Combine the objective function obtained in Step 2.1 with the equality constraints and inequality constraints obtained in Step 2.2 to obtain the overall optimization problem of the combined spacecraft system.
[0024] Furthermore, step 3 includes the following steps:
[0025] Step 3.1: Analyze the differences between the overall optimization problem of the combined spacecraft system and the general form of the constrained coupling optimization problem;
[0026] Step 3.2: Transform the overall optimization problem of the combined spacecraft system into a general form of constrained coupled optimization problem;
[0027] Step 3.3: Use the distributed optimization algorithm of the alternating direction multiplier method to solve the constrained coupling optimization problem of the combined spacecraft system.
[0028] Furthermore, in step 2.1, the objective function for each cellular star at each sampling moment, designed with the goal of maximizing the overall system tracking speed and minimizing energy consumption, is as follows:
[0029] (3)
[0030] In the formula, Indicates the first The objective function of each cell star at each sampling time point Indicates the range of prediction and control; and They represent Time prediction System state at time and the first Control torque of each cell satellite module; for The first prediction range Control torque of each cell satellite module; for The state of a combined spacecraft system within a prediction range; weight matrix and weight matrix It is positive definite, among which The weight matrix represents the system state. This represents the weight matrix corresponding to the control torque; , , express The identity matrix, It is the Kronecker product.
[0031] Furthermore, in step 2.2, the specific process for setting the equality constraints of the model prediction equations and the inequality constraints of the torques of each module and the dynamic performance of the system state during the optimization process is as follows:
[0032] Step 2.2.1: Set the upper and lower limits of the torque that each module's actuator can control;
[0033] Step 2.2.2: Set time-varying dynamic constraints for attitude tracking error, design dynamic constraints for attitude error based on preset performance, and select boundary functions;
[0034] Step 2.2.3: Set the equation constraints for the prediction equation of error attitude dynamics.
[0035] Further, in step 2.2.3, the setting of the equation constraint for the prediction equation of the error attitude dynamics is specifically as follows:
[0036] (7)
[0037] In the formula, for The state of a combined spacecraft system within a predictable range, This represents the total number of cellular satellites in a combined spacecraft system. Let be the matrix to be calculated; ,in express The identity matrix; For cell satellite modules Installation matrix; for The first prediction range The control torque of each cell satellite module, among which... Represents the predicted cellular satellite module The The control torque at each sampling time; and
[0038] .
[0039] Further, in step 2.3, the objective function obtained in step 2.1 and the equality constraints and inequality constraints obtained in step 2.2 are combined to derive the overall optimization problem of the combined spacecraft system, specifically as follows:
[0040] Integrated spacecraft system During attitude control by the collaborative efforts of the individual satellite modules, the overall optimization problem of the combined spacecraft system needs to be solved as follows:
[0041] (8)
[0042] In the formula, This represents the total number of cellular satellites in a combined spacecraft system. Indicates the first Each sampling time, for The first prediction range Control torque of each cell satellite module; for The state of a combined spacecraft system within a predicted range, where Indicates the range of prediction and control; This represents the sum of the objective functions of each cell star at the k-th sampling time; Indicates the first Lower limit of control torque for individual cell satellite modules Indicates the first Upper limit of control torque for each cell satellite module; This represents the lower limit of the system's state performance. Indicates the upper limit of system state performance; It is a known coefficient matrix. Indicates the first The state at each sampling time; This represents the weight matrix corresponding to the control torque. The weight matrix represents the system state. ; ; It is the Kronecker product; Let be the matrix to be calculated. For another matrix to be calculated, specifically:
[0043] .
[0044] Further, in step 3.2, the transformation of the overall optimization problem of the combined spacecraft system into a general form of constrained coupled optimization problem specifically involves:
[0045] Introduce an additional optimization variable Its cost function is derived from Represent and set it as module 0; convert the dynamic equality constraints to , Given the known measured state, the overall optimization problem of the combined spacecraft system (8) is transformed into an optimization variable: The performance index function is: The constrained coupling optimization problem of a combined spacecraft system:
[0046] (10)
[0047] In the formula, This represents the cost function of module 0. ;when hour, For cell satellite modules The cost function; ,in express The identity matrix, For cell satellite modules Installation matrix; .
[0048] Furthermore, in step 3.3, the distributed optimization algorithm using the alternating direction multiplier method is employed to solve the constrained coupling optimization problem of the combined spacecraft system. The algorithm is as follows:
[0049] Step 1: Initialization , , , ,in, This indicates the exchange of parameters between adjacent modules;
[0050] Step 2: Module 0 Calculation Other modules calculate , ;
[0051] Step 3: Exchange parameters between each module and adjacent modules. and The information is then calculated by each module. ,
[0052] Step 4: Calculation of each module ,
[0053] Step 5: Solve the following optimization problem in module 0.
[0054]
[0055] The other modules solve the following optimization problems respectively. ,
[0056] Step 6: Module 0 Calculation ,
[0057] Other modules are calculated separately. ,
[0058] Step 7: Calculation of each module ,
[0059] Step 8: If as well as If the value is less than a certain order of magnitude, the iteration ends, and the optimized control strategy is... Conversely, return to step three and iterate repeatedly until convergence.
[0060] The algorithm involves iterative optimization of each module to obtain the sampling time. The control strategy, in which Indicates the first Individual cell satellite modules, Indicates the first Individual cell satellite modules, For the number of iterations, This represents the total number of cellular satellites in a combined spacecraft system. Indicates the first Each sampling time; in addition, Select the value corresponding to module 0. Cell satellite module The corresponding value is , Let be the matrix to be calculated. The matrix to be calculated is as follows:
[0061] ,
[0062] ,in express The identity matrix, For cell satellite modules Installation matrix; for Cell satellite module at sampling time The control strategy sequence, for The optimized state variable sequence at each sampling time. These are any suitable parameters that can be selected. and These are the variables to be exchanged that need to be calculated at the initial time. Represents cell satellite module The set of allowable control torque constraints; during the overall iteration process, the parameters passed between adjacent modules are... and as well as and ; and These are intermediate parameters used in the iterative optimization process, and are based on parameters passed between adjacent modules. and Calculated; This represents the cost function of module 0. ;when hour, For cell satellite modules The cost function; and For the variables to be optimized in step 5, and For the first The optimization variables obtained from the first iteration; and For the first The optimization variables obtained from the first iteration; the final optimized control strategy obtained after the eighth step is... ; The penalty coefficient is used; the iteration process ends when the error between the updated optimal solution and the previous optimal solution is less than a certain order of magnitude. The optimal solution obtained at this point is the solution obtained by each module at the sampling time. Control strategy.
[0063] Compared with the prior art, the present invention has the following beneficial technical effects:
[0064] 1) Compared with the methods available in the literature, the proposed control scheme solves the problem of separation of control and distribution. It does not require a central controller to perform centralized control law design and calculation, and is suitable for situations where each cell star module can only communicate with adjacent modules, thus realizing a fully distributed system.
[0065] 2) Unlike the two-layer control allocation method, which requires setting the upper limit of the total control torque in advance based on the number of cells and output capacity, the method proposed in this invention naturally considers the output torque constraint of each cell during the optimization process, replacing the upper limit of the total control torque. It can make full use of the torque output capacity of the actuator without knowing the overall information of the cell cluster.
[0066] 3) It remains applicable when adding or removing modules in the cell cluster, without needing to consider allocation errors or changes in the total control torque saturation limit, and has excellent fault tolerance and flexibility.
[0067] 4) Compared with the distributed Nash balancing method, the distributed method proposed in this invention is a cooperative state, which aims to achieve the optimal performance indicators of the whole system. Attached Figure Description
[0068] Figure 1A schematic diagram of a combined spacecraft system consisting of a cell star and a failed spacecraft.
[0069] Figure 2 This is a schematic diagram of the integrated control-allocation fully distributed spacecraft attitude cooperative control method adopted in this invention;
[0070] Figure 3 This is a control torque diagram for each satellite module in the embodiment;
[0071] Figure 4 This is a diagram showing the actual system attitude tracking error in the embodiment;
[0072] Figure 5 The difference in control torque between each cell satellite module obtained from centralized and distributed control in the embodiment;
[0073] Figure 6 The system states obtained from centralized and distributed control in the embodiments. The difference. Detailed Implementation
[0074] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0075] This invention provides a fully distributed, control-allocation integrated spacecraft attitude cooperative control method, see [link to relevant documentation]. Figure 2 It is done in the following steps:
[0076] Step 1: Establish a discrete linear spacecraft attitude kinematics and dynamics model;
[0077] Step 1.1: Use attitude quaternions to represent the kinematic and dynamic system equations of the combined spacecraft's attitude tracking error, specifically:
[0078] (1)
[0079] In the formula, Indicates the first Individual cell satellite modules, This represents the total number of cellular satellites in a combined spacecraft system; Let R be the attitude tracking error quaternion, where R represents the set of real numbers; The vector part of the attitude tracking error quaternion is represented. The scalar part of the attitude tracking error quaternion; Represents the cross product operator; The actual angular velocity of the combined spacecraft system, where Indicates along the coordinate axis , , Components in the three directions of the axis; for The cross product operator, To achieve the desired angular velocity of the combined spacecraft system, For attitude angular velocity tracking error, where This represents the direction transformation matrix, and ,satisfy . It is the inertial matrix of the combined spacecraft system; For cell satellite modules Installation matrix; Represents cell satellite module Control torque; for The identity matrix.
[0080] Step 1.2: Introduce a pseudo-linear model with state correlation coefficients to linearize the nonlinear spacecraft attitude kinematics and dynamics system model, and then discretize it using the Euler method to obtain the discrete linearized model of the system at the next sampling time, specifically:
[0081] (2)
[0082] In the formula, Indicates the first Each sampling time, Indicates the state of the system. , ,in, Indicates the sampling time. express The identity matrix; The matrix is divided into four blocks, and the calculation for each smaller block is as follows:
[0083]
[0084]
[0085]
[0086]
[0087]
[0088] Among them, matrix and They are represented as follows:
[0089]
[0090]
[0091] in, It is a parameter to be calculated in the matrix, in the attitude tracking error quaternion. .
[0092] Step 2: Design a predictive control method for the combined spacecraft system model, including the following steps:
[0093] Step 2.1: With the goal of maximizing the overall system tracking speed and minimizing energy consumption, design the objective function for each cellular star at each sampling time within the model prediction control framework. Specifically:
[0094] Select an appropriate forecasting and control range based on task requirements. ,definition and They are respectively Time prediction System state at time and the first Control torque of each cell satellite module.
[0095] To achieve fast attitude tracking while simultaneously reducing energy consumption, the objective function for each cellular star at each sampling time is set as follows:
[0096] (3)
[0097] In the formula, Indicates the first The objective function of each cell star at each sampling time point Indicates the range of prediction and control. for The first prediction range Control torque of each cell satellite module; for The state of a combined spacecraft system within a prediction range; weight matrix and weight matrix It is positive definite, among which The weight matrix represents the system state. The weight matrix representing the control torque needs to be set according to the actual engineering situation; , , express The identity matrix, It is the Kronecker product.
[0098] Step 2.2: Set the equality constraints for the model prediction equations and the inequality constraints for the torques of each module and the dynamic performance of the system state during the optimization process. The specific process is as follows:
[0099] Step 2.2.1: Set the constraints for the control torque of each module. , and These represent the upper and lower limits of the control torque that each module actuator can output.
[0100] Step 2.2.2: Set time-varying dynamic constraints for attitude tracking error. Design dynamic constraints for attitude error based on preset performance, and select boundary functions:
[0101] (4)
[0102] (5)
[0103] (6)
[0104] In the formula, This represents the vector part of the attitude tracking error quaternion; It is a single-column matrix with all elements equal to 1; , , In the first The values of the three corresponding boundary functions at each sampling time; , , To choose a reasonable positive real number, To track the rate of error convergence; To constrain the overshoot of the system response.
[0105] Step 2.2.3: Set the equation constraints for the prediction equation of error attitude dynamics.
[0106] The coupled equality constraints are obtained in the form of a predictive equation using formula (2), and the steps are as follows:
[0107]
[0108] From this, we can deduce that:
[0109] (7)
[0110] In the formula, for The state of a combined spacecraft system within a predictable range, This represents the total number of cellular satellites in a combined spacecraft system. Let be the matrix to be calculated. ,in express The identity matrix, For cell satellite modules Installation matrix, for The first prediction range The control torque of each cell satellite module, among which... Represents the predicted cellular satellite module The The control torque at each sampling time; and
[0111]
[0112] Step 2.3: Combine the objective function obtained in Step 2.1 with the equality constraints and inequality constraints obtained in Step 2.2 to derive the overall optimization problem of the combined spacecraft system, as follows:
[0113] Integrated spacecraft system During attitude control by the collaborative efforts of the individual satellite modules, the overall optimization problem of the combined spacecraft system needs to be solved as follows:
[0114] (8)
[0115] In the formula, This represents the total number of cellular satellites in a combined spacecraft system. for The first prediction range Control torque of individual cell satellite modules for The state of a combined spacecraft system within a predictable range, Let the sum of the objective functions of each cell star at the k-th sampling time be . Indicates the first Lower limit of control torque for individual cell satellite modules Indicates the first Upper limit of control torque for each cell satellite module This represents the lower limit of the system's state performance. This represents the upper limit of the system's state performance. It is a known coefficient matrix. Indicates the first The state at each sampling time. Among them... This represents the weight matrix corresponding to the control torque. The weight matrix represents the system state. ; ; It is the Kronecker product. Let be the matrix to be calculated. For another matrix to be calculated, specifically:
[0116]
[0117] Step 3: Solve the model predictive control-based optimization problem in Step 2 using a fully distributed attitude control allocation method, including the following steps:
[0118] Step 3.1: Analyze the differences between the overall optimization problem of the combined spacecraft system and the general form of the constrained coupling optimization problem;
[0119] The general form of the constrained coupled optimization problem is as follows:
[0120] (9)
[0121] In the formula: Represents cell satellite module The set of permissible control torque constraints; A represents the performance index function. i In question (9) Transformation matrix coefficients; b represents a known matrix.
[0122] It can be found that its performance index function and equality constraints contain... The optimization variables for each module, i.e. And it exists Performance index function The overall optimization problem of the combined spacecraft system (8) is as follows: One more optimization variable. Performance index function for indivual.
[0123] Step 3.2: Transform the overall optimization problem of the combined spacecraft system into a general form of constrained coupling optimization problem.
[0124] Introduce an additional optimization variable Its cost function is derived from This is indicated and set as module 0, which can be a module capable of providing torque. One of the modules, or a module that can communicate with other modules but does not need to provide torque. Converting dynamic equality constraints into... , Given the known measured state, the overall optimization problem (8) of the combined spacecraft system is transformed into an optimization variable: The performance index function is: The constrained coupling optimization problem of a combined spacecraft system:
[0125] (10)
[0126] In the formula, This represents the cost function of module 0. ;when hour, For cell satellite modules The cost function; , .
[0127] Step 3.3: The Tracking-ADMM distributed optimization algorithm is used to solve the constrained coupling optimization problem of the combined spacecraft system.
[0128] Traditional control allocation methods require a central processing unit to calculate and distribute control torques. However, when there are many satellites or limited satellite communication, this method increases the computational burden and affects control accuracy. Therefore, a distributed control method is needed, allowing each module to update its control strategy by knowing only the information of its neighbors and its own performance characteristics.
[0129] In a distributed model, communication constraints between adjacent modules can be addressed using undirected graph theory. To describe, the node set is Representation module, edge set This represents the communication link between modules. (Cell Satellite Module) Can be used with cell satellite modules For exchanging information Indicates. Cell satellite module Adjacent modules are denoted as and Define the consensus matrix. , its first Item for That is, the weights of the consensus matrix.
[0130] For consensus matrix In the absence of known circumstances, this invention proposes a per-cell satellite module Determine its adjacent modules The method. The total number of control modules is This includes module 0, which is used for optimization. However, a virtual module for actual control torque is not provided. Therefore, the consensus matrix in this paper... It is OK, A matrix of columns.
[0131] For cell satellite modules The weight of the adjacent module is set to For modules that are not adjacent to it, the weight is set to ;and It is then set to When a certain module When it fails, the modules connected to it Weights are set to Then the module Recalculate for .
[0132] (11)
[0133] Next, the Tracking-ADMM distributed optimization algorithm is used to solve the control strategy for each satellite module. The algorithm is as follows:
[0134] Step 1: Initialization , , , ,in, This indicates the exchange of parameters between adjacent modules;
[0135] Step 2: Module 0 Calculation Other modules calculate , ;
[0136] Step 3: Exchange parameters between each module and adjacent modules. and The information is then calculated by each module. ,
[0137] Step 4: Calculation of each module ,
[0138] Step 5: Solve the following optimization problem in module 0.
[0139]
[0140] The other modules solve the following optimization problems respectively. ,
[0141] Step 6: Module 0 Calculation ,
[0142] Other modules are calculated separately. ,
[0143] Step 7: Calculation of each module ,
[0144] Step 8: If as well as If the value is less than a certain order of magnitude (which can be set according to the actual engineering performance and accuracy requirements), then the iteration ends, and the optimized control strategy is the result. Conversely, if the result is not found, return to step three and iterate repeatedly until convergence.
[0145] The above algorithm iteratively optimizes each module to obtain the sampling time. The control strategy, in which Indicates the first Individual cell satellite modules, Indicates the first Each module For the number of iterations, This represents the total number of cellular satellites in a combined spacecraft system. Indicates the first Each sampling time. In addition, Here, the value corresponding to module 0 is selected. Cell satellite module The corresponding value is , Let be the matrix to be calculated. The matrix to be calculated is as follows:
[0146] ,
[0147] , for Cell satellite module at sampling time The control strategy sequence, for The optimized state variable sequence at each sampling time. For any arbitrarily chosen suitable parameters, at this point, only module 0 needs to monitor the state of the combined spacecraft system at each sampling time. Simply take the measurement. and These are the variables to be exchanged that need to be calculated at the initial time. Represents cell satellite module The set of allowable control torque constraints. During the overall iteration process, the parameters passed between adjacent modules are... and as well as and . and These are intermediate parameters used in the iterative optimization process, and are based on parameters passed between adjacent modules. and Calculated. This represents the cost function of module 0. ;when hour, For cell satellite modules The cost function. and For the variables to be optimized in step 5, and For the first The optimization variables obtained through iterative steps. and For the first The optimization variables obtained from the first iteration. The final optimized control strategy after the eighth step is... . The penalty coefficient can be selected according to actual needs. The iteration process ends when the error between the current solution and the previously updated optimal solution is less than a certain order of magnitude. The optimal solution obtained at this point is the solution obtained by each module at the sampling time. Control strategy.
[0148] Example
[0149] This invention is verified through numerical simulation. The numerical simulation problem, simulation design process, and simulation results are described below as an implementation method and technical evidence for this patent.
[0150] A fully distributed, control-distribution integrated spacecraft attitude cooperative control method is presented. The process steps of the method are described in the detailed implementation section. The following are the parameter settings and results of a simulation example.
[0151] 1. Numerical simulation parameter settings
[0152] The inertial matrix of a combined spacecraft system is defined as follows: .
[0153] Set the initial error attitude as follows: The initial angular velocity is The desired angular velocity is Choose the weight matrix. , Sampling time is The prediction time domain (i.e., the prediction and control range) is , , The preset performance parameters are designed as follows: , , , Total number of modules capable of providing control torque. In distributed algorithms .
[0154] The transformation matrix for each module is:
[0155]
[0156]
[0157]
[0158]
[0159] 2. Simulation results:
[0160] The simulation results of distributed attitude control for the combined spacecraft are as follows. Figure 3 and Figure 4 The figures represent the control torque of each cell star module and the actual spacecraft attitude tracking error, respectively. As shown in the figure, the system gradually stabilizes in about 55 seconds. In addition, all cell star modules meet the torque constraint conditions, and the attitude error fluctuates within the preset performance range, demonstrating excellent dynamic performance.
[0161] To verify the relationship between the centralized control allocation method used in optimization problem (8) and the distributed control allocation method used in the proposed optimization problem (9), i.e. the optimality and convergence of the proposed distributed algorithm, the centralized control was also simulated. Figure 5 This demonstrates the differences in control torque between various modules in centralized and distributed control. ,in, and These represent the control torques of each module in the centralized and the proposed distributed methods, respectively. Figure 6 The system states obtained by centralized and distributed control methods are shown. The difference, ,here Similarly, and These represent the system states in the centralized and proposed distributed methods, respectively. A comparison shows that the fully distributed control allocation result of this invention converges to the result of the centralized method.
[0162] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A fully distributed attitude cooperative control method integrating control and allocation, characterized in that: Follow these steps: Step 1: Establish a discrete linear spacecraft attitude kinematics and dynamics model; Step 2: Design a predictive control method for the combined spacecraft system model. Step 2.1: With the goal of maximizing the overall tracking speed of the system and minimizing energy consumption, design the objective function for each cell star at each sampling moment under the model prediction control framework; Step 2.2: Set equality constraints for the model prediction equations and inequality constraints for the torques of each module and the dynamic performance of the system state during the optimization process; Step 2.3: Combine the objective function obtained in Step 2.1 with the equality constraints and inequality constraints obtained in Step 2.2 to obtain the overall optimization problem of the combined spacecraft system; Step 3: Solve the overall optimization problem of the combined spacecraft system based on model predictive control in Step 2 using a fully distributed attitude control allocation method. Step 3.1: Analyze the differences between the overall optimization problem of the combined spacecraft system and the general form of the constrained coupling optimization problem; Step 3.2: Transform the overall optimization problem of the combined spacecraft system into a general constrained coupled optimization problem, specifically: Introduce an additional optimization variable Its cost function is derived from Indicate, and set it as a module Transform dynamic equality constraints into , Given the known measured states, the overall optimization problem of the combined spacecraft system is transformed into an optimization variable of... The performance index function is: The constrained coupling optimization problem of a combined spacecraft system: (10) In the formula, Representation module The cost function, ;when hour, For cell satellite modules The cost function; ,in express The identity matrix, For cell satellite modules Installation matrix; ; Step 3.3: Use the distributed optimization algorithm of the alternating direction multiplier method to solve the constrained coupling optimization problem of the combined spacecraft system.
2. The control-distribution integrated full-distributed posture cooperative control method according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: Use attitude quaternions to represent the kinematic and dynamic system equations of the combined spacecraft's attitude tracking error; Step 1.2: Introduce a pseudo-linear model with state correlation coefficients to linearize the nonlinear spacecraft attitude kinematics and dynamics system model, and discretize it using the Euler method to obtain the system discrete linearized model at the next sampling time.
3. The integrated control-distribution full-distributed posture cooperative control method according to claim 1, characterized in that, In step 2.1, with the goal of maximizing the overall tracking speed of the system and minimizing energy consumption, the objective function for each cellular star at each sampling moment is designed within the model prediction control framework, specifically as follows: (3) In the formula, Indicates the first The objective function of each cell star at each sampling time point Indicates the range of prediction and control; and They represent Time prediction System state at time and the first Control torque of each cell satellite module; for The first prediction range Control torque of each cell satellite module; for The state of a combined spacecraft system within a prediction range; weight matrix and weight matrix It is positive definite, among which The weight matrix represents the system state. This represents the weight matrix corresponding to the control torque; , , express The identity matrix, It is the Kronecker product.
4. The integrated control-distribution full-distributed posture cooperative control method according to claim 1, wherein, In step 2.2, the specific process of setting the equality constraints of the model prediction equations and the inequality constraints of the torques of each module and the dynamic performance of the system state during the optimization process is as follows: Step 2.2.1: Set the upper and lower limits of the torque that each module's actuator can control; Step 2.2.2: Set time-varying dynamic constraints for attitude tracking error, design dynamic constraints for attitude error based on preset performance, and select boundary functions; Step 2.2.3: Set the equation constraints for the prediction equation of error attitude dynamics.
5. The control-distribution integrated full-distributed posture cooperative control method according to claim 4, characterized in that, In step 2.2.3, the setting of the equation constraint for the prediction equation of the error attitude dynamics is specifically as follows: (7) In the formula, for The state of a combined spacecraft system within a predictable range, This represents the total number of cellular satellites in a combined spacecraft system. Let be the matrix to be calculated; ,in express The identity matrix; For cell satellite modules Installation matrix; for The first prediction range The control torque of each cell satellite module, among which... Represents the predicted cellular satellite module The The control torque at each sampling time; and 。 6. The control-distribution integrated full-distributed posture cooperative control method according to claim 1, wherein, In step 2.3, the objective function obtained in step 2.1 and the equality constraints and inequality constraints obtained in step 2.2 are combined to derive the overall optimization problem of the combined spacecraft system, specifically as follows: In a combined spacecraft system In the process of attitude control, the overall optimization problem of the combined spacecraft system needs to be solved as follows: (8) In the formula, The total number of cellular satellites in a combined spacecraft system. Indicates the first Each sampling time, for The first prediction range Control torque of each cell satellite module; for The state of a combined spacecraft system within a predicted range, where Indicates the range of prediction and control; Indicates the first The sum of the objective functions of each cell star at each sampling time; Indicates the first Lower limit of control torque for individual cell satellite modules Indicates the first Upper limit of control torque for each cell satellite module; This represents the lower limit of the system's state performance. Indicates the upper limit of system state performance; It is a known coefficient matrix. Indicates the first The state at each sampling time; This represents the weight matrix corresponding to the control torque. The weight matrix represents the system state. ; ; It is the Kronecker product; Let be the matrix to be calculated. For another matrix to be calculated, specifically: 。 7. The integrated control-distribution full-distributed posture cooperative control method according to claim 1, wherein, In step 3.3, the distributed optimization algorithm using the alternating direction multiplier method is employed to solve the constrained coupling optimization problem of the combined spacecraft system. The algorithm is as follows: First step: initialization , , , , wherein denotes the exchange of parameters between adjacent modules; Second step: module Computing , each of the other modules computes , ; Third step: each module exchanges parameters with adjacent modules and information, then each module calculates , Step 4: Each module calculates , Fifth step: module Solve the following optimization problem Other modules solve the following optimization problems, respectively Step 6: Module Computing , Other modules calculate Step 7: Each module calculates , Step 8: If and is less than a certain order of magnitude, then the iteration is ended and the obtained control strategy is the optimal one ; otherwise, return to step 3 and repeat the iteration until convergence. The algorithm involves iterative optimization of each module to obtain the sampling time. The control strategy, in which Indicates the first Individual cell satellite modules, Indicates the first Individual cell satellite modules, For the number of iterations, The total number of cellular satellites in a combined spacecraft system. Indicates the first Each sampling time; in addition, Select module The corresponding value is Cell satellite module The corresponding value is , Let be the matrix to be calculated. The matrix to be calculated is as follows: ， ,in express The identity matrix, For cell satellite modules Installation matrix; for Cell satellite module at sampling time The control strategy sequence, for The optimized state variable sequence at each sampling time. These are any suitable parameters that can be selected. and These are the variables to be exchanged that need to be calculated at the initial time. Represents cell satellite module The set of allowable control torque constraints; during the overall iteration process, the parameters passed between adjacent modules are... and as well as and ; and These are intermediate parameters used in the iterative optimization process, and are based on parameters passed between adjacent modules. and Calculated; Representation module The cost function, ;when hour, For cell satellite modules The cost function; and For the variables to be optimized in step 5, and For the first The optimization variables obtained from the first iteration; and For the first The optimization variables obtained from the first iteration; the final optimized control strategy obtained after the eighth step is... ; The penalty coefficient is used; the iteration process ends when the error between the updated optimal solution and the previous optimal solution is less than a certain order of magnitude. The optimal solution obtained at this point is the solution obtained by each module at the sampling time. Control strategy.