Improved adaptive pseudospectral method-based attitude maneuver planning method for flexible remote sensing satellites

Abstract

The application relates to a flexible remote sensing satellite attitude maneuver planning method based on an improved adaptive pseudospectral method, relates to the technical field of flexible remote sensing satellite attitude control, and solves the problems that the existing method is prone to causing a large increase in the number of grid refinements, inevitably increasing the number of iterations, consuming more on-board computer resources, and further reducing the on-orbit application efficiency of a satellite, and the like, and comprises the following steps: firstly, combining satellite dynamics, kinematics and a vibration equation of a flexible accessory, a rigid-flexible coupling state space equation for an optimal control method is established; secondly, on the basis of establishing an optimal objective function containing algebra-differential constraints, control torque constraints, angular momentum constraints, path constraints and the shortest time, an improved hp adaptive pseudospectral method is used to convert an optimal control problem into a nonlinear programming problem for solving. The method can generate an optimal trajectory meeting various constraint requirements in the shortest time, and compared with a traditional hp adaptive pseudospectral method, the method is shorter in time consumption under the same precision and has higher solving efficiency.

Description

Technical Field

[0001] This invention relates to the field of attitude control technology for flexible remote sensing satellites, and more specifically to an attitude maneuver planning method for flexible remote sensing satellites based on an improved adaptive pseudospectral method. Background Technology

[0002] With the continuous development of space remote sensing technology, the control tasks and types of on-orbit satellites are becoming increasingly diversified. Utilizing high-resolution remote sensing satellites to acquire remote sensing images of ground targets in a short time has become an efficient means of information acquisition. High-speed, low-power, and high-precision optical remote sensing satellites have been widely used in many commercial fields such as national military security, natural disaster response, and remote communication. For example, in existing public literature, Zhang Liu, Zhang Xiaohan, Yue Qingxing, Liu Nian, Sun Kaipeng, Sun Jie, Fan Guowei. Attitude planning and rapid simulation method for staring imaging of optical remote sensing satellites [J]. Journal of Jilin University (Engineering Science), 2021, 51(1):340-348.

[0003] The technology of remote sensing satellites has evolved from initial nadir imaging to imaging during attitude adjustments. This new imaging mode places higher demands on satellite attitude maneuver control, and the various constraints during these maneuvers pose significant challenges to attitude planning and control. Remote sensing missions typically require satellites to possess large-angle, high-precision directional maneuver capabilities to improve observation efficiency. However, during maneuvers, constraints such as vibrations from flexible components like solar panels, actuator capabilities, and the influence of light sources on sensors and optical elements can lead to inappropriate attitudes and mission failure. Therefore, achieving multi-constraint attitude maneuvers for high-resolution remote sensing satellites under adverse conditions such as parameter uncertainties, external interference, flexible component vibrations, and actuator saturation has become an urgent problem to be solved.

[0004] The attitude dynamics and control problems of rigid-flexible coupled systems have attracted widespread attention from scholars both domestically and internationally. For the optimal control problem (OCP), based on Pontryagin's minimum (maximum) value principle, indirect methods have derived the necessary conditions for first-order optimality in OCP, constituting the Hamiltonian boundary value problem of OCP. For complex OCP problems, solving the two-point boundary value problem is very difficult, with a small convergence region. Non-physically meaningful costate variables require very rigorous initial value estimation to obtain convergent solutions. Therefore, indirect methods are greatly limited in practice. In recent years, the pseudospectral method in the direct collocation method has become an important method for handling optimal control problems. The idea of ​​the pseudospectral method is to approximate the state and control variables of a set of collocation points using orthogonal polynomials. Then, the optimal control problem is transformed into a discrete nonlinear programming problem. In recent years, the direct collocation method, represented by the pseudospectral method, has become an important method for solving complex optimal control problems, and the HP adaptive method originated from the finite element method.

[0005] Existing papers, such as: Zhou Wenya, Yang Di, Liang Xingang. Solving the optimal aerodynamic-assisted orbit transfer using the Gaussian pseudospectral method [J]. Journal of Jilin University (Engineering Science), 2010, 40(05): 1454-1459, apply the Gaussian pseudospectral method to the study of aerodynamic-assisted orbit transfer of coplanar high-orbit to low-orbit spacecraft. Wu Xiaowen et al. used the global pseudospectral method combined with intelligent algorithms (Wu Xiaowen. Research on Agile Satellite Attitude Maneuver Planning Method [D]. Harbin Engineering University, 2016.) to design agile satellite attitude maneuver trajectories with the premise of minimum energy. However, it is difficult to capture the discontinuity and non-smoothness of the solution for discontinuous or non-smooth optimization problems, resulting in reduced accuracy. At the same time, the influence of flexible components on the satellite is not considered. For example, existing papers include Wang Liying, Zhang Youan, Huang Jie, Constrained Terminal Guidance Law and Pseudospectral Trajectory Optimization [M]. Beijing: National Defense Industry Press, 2015; Liu Ruifan et al. proposed an improved hp adaptive pseudospectral method (Liu Ruifan, Yu Yunfeng, Yan Binbin. Hypersonic Vehicle Ascent Trajectory Planning Based on Improved hp Adaptive Pseudospectral Method [J]. Journal of Northwestern Polytechnical University, 2016, 34(05): 790-797.) and applied the algorithm to the minimum fuel-efficient climb problem of hypersonic vehicles, which can obtain a high-accuracy solution with less time cost.

[0006] Existing papers, such as: Yan Chuxiong, Tong Yinan, Song Jiahong, Lu Baogang, Zhao Liangbo. Trajectory optimization with terminal constraints based on multi-interval Radau pseudospectral method [J]. Tactical Missile Technology, 2021(02):94-100.DOI:10.16358 / j.issn.1009-1300.2021.9.093. The multi-interval Radau pseudospectral method is used to design a missile terminal trajectory optimization with multiple constraints. The designed trajectory curve is smooth and easy to implement. Hong Bei et al. applied the HP adaptive pseudospectral method to the rapid optimization problem of gliding trajectory and the reentry trajectory optimization problem (Hong Bei, Xin Wanqing. Application of HP adaptive pseudospectral method in rapid optimization of gliding trajectory [J]. Computer Measurement & Control, 2012, 20(05): 1283-1286. DOI: 10.16526 / j.cnki.11-4762 / tp.2012.05.018.). Su Zhijuan et al. proposed an improved adaptive pseudospectral method based on density function (Su Zhijuan. Energy-saving driving of medium and low speed maglev train based on improved adaptive pseudospectral method [D]. Beijing Jiaotong University, 2021. DOI: 10.26944 / d.cnki.gbfju.2021.001740.), and obtained the optimal energy-saving driving curve of medium and low speed maglev train, but the influence of control force factor was not considered, and the control force curve pulse phenomenon appeared.

[0007] Despite significant progress in existing research on the HP adaptive method, further exploration is needed to reduce computational complexity in pursuit of high-precision solutions. This is especially true when applying the traditional HP adaptive pseudospectral method to the optimal attitude planning problem for multi-constrained remote sensing satellites. As accuracy continues to improve, the number of mesh refinements increases dramatically, inevitably increasing the number of iterations, consuming more onboard computer resources, and reducing the effectiveness of satellite on-orbit applications.

[0008] The improved HP adaptive method proposed in this invention can significantly improve solution efficiency by reducing the computational load of the algorithm through improvements in sampling points and iteration criteria, while meeting accuracy requirements. Simulation results show that, compared with the existing HP adaptive pseudospectral method, the improved HP adaptive pseudospectral method can significantly reduce the number of mesh iterations and obtain a higher-accuracy solution with less time cost, verifying the superiority of the improved algorithm. Summary of the Invention

[0009] To address the problems of existing HP adaptive methods in handling optimal attitude planning for multi-constraint remote sensing satellites, which easily lead to a significant increase in the number of mesh refinements, inevitably increasing the number of iterations, consuming more onboard computer resources, and thus reducing the on-orbit application efficiency of the satellite, this invention provides a flexible remote sensing satellite attitude maneuver planning method based on an improved adaptive pseudospectral method.

[0010] A flexible remote sensing satellite attitude maneuver planning method based on an improved adaptive pseudospectral method is implemented through the following steps:

[0011] Step 1: Establish a continuous optimal control problem model, transform various constraints into an optimal control problem, and minimize the optimization performance index while satisfying multiple constraints.

[0012] Step 2: Discretize the optimal control problem and transform it into a nonlinear programming problem for solution. Use the improved HP adaptive Radau pseudospectral method for point collocation; the specific point collocation process is as follows:

[0013] Step Two: 1. Use error evaluation criteria to make a judgment:

[0014] Sampling points are selected using a Gaussian distribution, and the error criterion ε is determined. k Does the error exceed the error threshold ε of the differential-algebraic equation? If so, refine the network again using the improved HP adaptive pseudospectral method and execute step two; and set the error judgment criterion as the residual ε of the sampling point in the dynamic constraint equation. k Otherwise, proceed to step two five;

[0015] Step 22: Use the grid classification refinement criteria for judgment:

[0016] Standard for judging the curvature ρ kIs it greater than the scaling factor ρ? max If yes, refine the interval to improve accuracy and proceed to steps two and three; if no, increase the number of points to improve accuracy and proceed to steps two and three.

[0017] Steps two and three: Obtain new grid points and matching points;

[0018] Step 24: Substitute the new grid points and collocation points obtained in Step 2 into Step 2 to perform a new solution;

[0019] Step 25: Complete the iteration of the solution and use the current numerical solution as the final output.

[0020] The beneficial effects of this invention are as follows: First, the method of this invention combines satellite dynamics, kinematics, and vibration equations of flexible attachments to establish a rigid-flexible coupled state-space equation oriented towards optimal control. Second, based on the establishment of algebraic-differential constraints, control torque constraints, angular momentum constraints, path constraints, and with the shortest time as the optimization objective function, the improved hp adaptive Radau pseudospectral method is used to transform the optimal control problem into a general nonlinear programming problem for solution.

[0021] This invention addresses the multi-constraint attitude optimal maneuver planning problem for high-resolution flexible remote sensing satellites. To improve the efficiency of solving the optimal problem, an improved hp adaptive Radau pseudospectral method is proposed. This method allocates more sampling points to regions prone to abrupt changes during mesh refinement and modifies the curvature iteration criterion to ensure that more mesh points are allocated at abrupt changes. This significantly reduces the number of mesh iterations and shortens the computation time.

[0022] Based on the requirements of flexible satellite attitude maneuvering missions, this invention establishes a rigid-flexible coupling model. Under the premise of ensuring the normal operation of onboard equipment and not exceeding the capabilities of satellite actuators, it designs an optimal flexible remote sensing satellite attitude maneuvering planning method with a certain actual mission performance as the optimization index. Compared with the traditional HP adaptive pseudospectral method, this method generates the optimal trajectory that meets the set requirements in less simulation time and is more efficient at high precision.

[0023] Simulation results show that the method of the present invention can plan the optimal attitude maneuver trajectory while meeting the requirements of satellite maneuvering missions, and can achieve rapid and high-precision maneuvers. The method of the present invention provides a certain reference for high-resolution remote sensing satellites to perform complex space missions. Attached Figure Description

[0024] Figure 1 This is a flowchart of the flexible remote sensing satellite attitude maneuver planning method based on the improved HP adaptive pseudospectral method described in this invention.

[0025] Figure 2The following are simulation results of the flexible remote sensing satellite attitude maneuver planning method based on the improved hp adaptive pseudospectral method described in this invention: (a) shows the effect of three-axis Euler angle variation; (b) shows the effect of three-axis angular velocity variation; (c) shows the effect of three-axis flywheel control torque variation; (d) shows the effect of flexible attachment vibration displacement variation; and (e) shows the effect of flexible attachment vibration velocity variation.

[0026] Figure 3 To improve the comparison of the satellite's three-axis attitude angles before and after;

[0027] Figure 4 To improve the comparison diagram of the satellite's three-axis angular velocity before and after;

[0028] Figure 5 To improve the comparison diagram of the satellite's three-axis torque before and after;

[0029] Figure 6 (a) and (b) are comparison diagrams of the sampling point distribution before and after the improvement, respectively. Detailed Implementation

[0030] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a flexible remote sensing satellite attitude maneuver planning method based on an improved adaptive pseudospectral method. This method is implemented through the following steps:

[0031] Step 1: Establish a continuous optimal control problem model, transform various constraints into an optimal control problem, and minimize the optimization performance index while satisfying multiple constraints.

[0032] In this embodiment, the optimal control problem model is specifically: flexible satellite attitude dynamics and kinematics modeling;

[0033] According to the momentum and angular momentum theorems, and taking the inertial coordinate system as the reference coordinate system, the rigid-flexural coupling motion equations of the system consisting of the satellite body and its flexible components are as follows:

[0034]

[0035] In the formula, Here is the satellite's rotational inertia matrix; This is the angular velocity of the satellite relative to the inertial frame of reference. η is the coupling coefficient between the flexible attachment and the satellite; η is the displacement of the flexible attachment in the modal coordinate system. The angular momentum of the actuator; This represents the space disturbance torque experienced by the satellite. The symbol is defined as:

[0036]

[0037] For the spatial disturbance torque T present in the modeld Compensation can be achieved through attitude control algorithms, without initially considering the effects of space disturbances when designing the satellite's attitude and trajectory. A satellite kinematic model described by Euler angles is defined as θ. x ,θ y ,θ z These represent the roll angle, pitch angle, and yaw angle under the 3-2-1 turn sequence. Considering the satellite's inertial orientation and the small initial angle, the satellite's angular velocity can be approximated as...

[0038] The vibration equation of the flexible attachment can be expressed in modal coordinates as:

[0039]

[0040] In the formula, The damping ratio matrix represents the mode of the flexible attachment. This is the vibration frequency matrix of the flexible attachment modes.

[0041] Define state variable x = [θ η ω ω] η ] T θ is the satellite angle, ω η Let the velocity of the flexible attachment be in the modal coordinate system. Combining the satellite attitude dynamics and kinematic equations (1) and the vibration equations of the flexible attachment (2), the state-space equations are obtained as follows:

[0042]

[0043] In the formula:

[0044]

[0045] In the formula, I is the identity matrix. This equation describes the attitude changes of the satellite's rigid body and its flexible components, and demonstrates the strong nonlinear coupling relationship between the two.

[0046] In this embodiment, the trajectory optimization problem constrained by differential-algebraic constraints, path constraints, actuator torque constraints, and angular velocity measurement capability constraints is transformed into an optimal control problem within a finite time interval, i.e., within the time interval t∈[t0,t... f Given the initial value of the state variable x(t0), by setting the control torque T(t), the satellite attitude is maneuvered to the target attitude x(t0). Under the premise of satisfying the constraints, the maneuvering time of the satellite attitude is optimized, that is, the time interval (t) is optimal. f -t0) is the minimum. t0 represents the start time of the maneuver; t f Indicates the moment the maneuver is completed.

[0047] During attitude maneuvers, the constraints that need to be considered for a satellite are mainly the dynamic constraints from the satellite itself and the geometric constraints from the external environment.

[0048] The dynamic constraint is the on-board control torque T = [T x T y T z ] T Bounded sum ω=[ω x ω y ω z ] T Bounded.

[0049] Because satellites need to avoid dangerous orientations during maneuvers, these dangerous orientations are called attitude exclusion zones. Simultaneously, during ground communication, satellites need to keep their antennas pointed at ground stations; these areas are called mandatory zones. Abstracting these into geometric constraints, they mainly include two types: "forbidden zone constraints" and "mandatory zone constraints." Taking the "forbidden zone" where the field of view of satellite photosensitive devices must not approach bright celestial objects as an example:

[0050] Suppose the satellite is maneuvering to attitude [a] at this time. i β i γ i ] T The vector pointing from the satellite to the bright celestial body is [x] in the geocentric equatorial coordinate system. i y i z i ] T If the field of view is λ, then the satellite must satisfy the following constraints during maneuvering:

[0051]

[0052] Similarly, if it is a "mandatory region", then the following conditions should be met during the maneuver:

[0053]

[0054] Therefore, the optimal control problem of the Bolza type can be defined as follows:

[0055]

[0056] In the formula: Φ represents the current state value; G represents the boundary performance value; and λ1 and λ2 represent the field of view angles of the forbidden and forced regions, respectively.

[0057] The constraints are:

[0058]

[0059] Among them, f, C and These are differential-algebraic constraints, path constraints, and boundary constraints, respectively.

[0060] Step 2: Discretize the optimal control problem and transform it into a nonlinear programming problem for solution. Then, use the improved adaptive Radau pseudospectral method to collocate the points.

[0061] In this embodiment, the pseudospectral method is commonly used for spacecraft trajectory optimization problems. The adaptive Radau pseudospectral method is employed to solve the optimal trajectory planning problem. Legendre-Gauss-Radau (LGR) points are used for point collocation. By dividing the entire time interval into multiple sub-intervals, and using LGR point collocation within each sub-interval, the continuous optimal control problem is discretized. Numerical solutions for the state and control variables are obtained. The nonlinear optimal control problem is transformed into a nonlinear programming problem, which is finally solved using a nonlinear programming solver, such as the Snopt toolkit.

[0062] In this embodiment, an improved hp adaptive multi-interval point allocation method is used. For optimal control problems with simple and smooth constraints, the adaptive p method can obtain high-precision solutions with less computational cost. However, for optimal control problems with discontinuous or non-smooth dimensions, the adaptive h method can obtain higher-precision solutions. For problems that are smooth in some segments and non-smooth in others, the combination of the two methods can obtain the best approximate solution. This embodiment presents an improved hp adaptive pseudospectral method based on the Radau pseudospectral method, combining the adaptive h method with refined intervals and the adaptive p method with increased interpolation polynomial digits for optimized sampling point selection and iteration criterion selection. This method possesses the computational sparsity of the adaptive h method and the fast convergence of the adaptive p method, and can better find the positions of discontinuous points and singularities, achieving a balance between solution accuracy and computational cost. The specific point allocation process is as follows:

[0063] 1. Radau pseudospectral method first divides the overall time interval of the problem Divide into K sub-intervals, each sub-interval S k =[t k-1 ,t k ], k=1,2,3,...K are mapped to the interval τ∈[-1,1] through transformation, t k-1 and t k Let S be the initial and final times of the k-th interval; within the sub-interval S k =[t k-1 ,t k Select initial grid points [U0, U1, ..., U] within the range. k ] and point allocation

[0064] 2. Using the grid points and collocation points from step 2.1, the continuous optimal control problem is discretized using an NLP solver to obtain numerical solutions for the state and control variables.

[0065] 3. Judgment is made using error evaluation criteria: The residual ε of the dynamic constraint equation is obtained using sampling points from a Gaussian distribution. k If ε k If ≤ε, proceed to step 7; otherwise, proceed to step 4. Define ε as the set error threshold for the differential algebraic equation.

[0066] 4. Use the grid classification refinement criterion for judgment: if ρ k ≤ρ max If the accuracy is high, the accuracy can be improved by increasing the number of points; otherwise, the accuracy can be improved by refining the interval.

[0067] 5. Obtain new grid points and collocation points.

[0068] 6. Substitute the refined grid points and collocation points from step 2 into step 2 for a new round of solving.

[0069] 7. Complete the iteration of the solution and use the current numerical solution as the final output.

[0070] In this embodiment, the hp adaptive pseudospectral method first transforms the multi-interval continuous optimal control problem into a nonlinear programming problem. Referring to the error judgment criterion of the global pseudospectral method solution, it uses the segment [t] as the basis for the calculation. k-1 ,t k For example, let N k Let be the number of LGR points in the k-th segment, k∈[1,…,K]. In the traditional hp adaptive method, when performing error evaluation, the center point of adjacent LGR points is selected as the sampling point. However, the endpoints of each segment are where the points are most distributed. This results in fewer sampling points in some segments where abrupt changes are likely to occur. In order to achieve the preset accuracy, the grid needs to be further refined, increasing the number of grid iterations and greatly reducing the computational efficiency.

[0071] In this embodiment, the sampling points selected according to a Gaussian distribution are more reasonable for LGR point allocation compared to traditional sampling points, effectively compensating for the decrease in solution efficiency caused by insufficient sampling values ​​in the middle section of intervals prone to abrupt changes. 500 points are selected using a Gaussian distribution within the k-th interval. This sampling point is chosen because the probability of abrupt change occurring in the middle of a segment is much higher than at the ends. A comparison of sampling points before and after the improvement is provided. Figure 6 As shown.

[0072] In step 3 of this embodiment, the error judgment criterion ε k The residuals of the sampling points in the dynamic constraint equation can be expressed as:

[0073]

[0074] in, For the s-th sampling point The first-order differential residual of the v-th state variable at point v; For the s-th sampling point The residual of the w-th path constraint at point w.

[0075]

[0076]

[0077] In the formula, Let be the first-order differential residual of the s-th sampling point. For the path constraint residual of the s-th sampling point, Let [t] be the derivative of the state variable at the sampling point s. k-1 ,t k [ ] represents the time interval of the sampling points, f represents the differential constraint of the state equation, and C represents the path constraint. Let be the state variable value at the s-th sampling point. Let be the value of the control variable at the s-th sampling point.

[0078] In step 4 of this embodiment, a mesh classification refinement criterion based on state curvature is adopted:

[0079] definition For the maximum residual The column vector formed by the state variables, i.e.

[0080]

[0081] Meanwhile, the curvature of the l-th state variable at the p-th sampling point can be expressed as:

[0082]

[0083] right Sort:

[0084]

[0085] To further improve the efficiency of mesh refinement, the standard for classification refinement is set to one-quarter of the ratio of the maximum curvature to the standard deviation at each sampling point, taking curvature into account.

[0086]

[0087] In the formula, N represents the maximum curvature of each sampling point in the k-th interval. k-1 represents the number of sampling points. Let be the curvature of the l-th state at the i-th sampling point. This represents the average curvature at each sampling point.

[0088] The traditional HP adaptive method uses the ratio of the maximum value to the average value at each sampling point as the classification refinement standard, which mainly reflects the degree of deviation of discrete data from the average value. This paper chooses the standard deviation instead of the average value, which can better reflect the degree of deviation of discrete points. According to the improved sampling point diagram, the interval of the sampling points is reduced to 1 / 4 of the original interval, and the refinement standard at the sampling points is also reduced to 1 / 4 of the original interval.

[0089] In this embodiment, ρ is defined. max The scaling factor, which determines whether to refine the partitioning or increase the dimension of the interpolation polynomial, is a given constant.

[0090] 1) When ρ k All elements are greater than ρ max When the time interval is short, the trajectory can be considered relatively smooth, and the solution accuracy can be improved by increasing the number of points within the interval.

[0091] set up and This refers to the number of points within each subinterval before and after the update. It can be obtained from the following formula:

[0092]

[0093] Where C1 is an arbitrary integer constant that controls the increment of the number of points within each segment, and ceil is the round-up function.

[0094] 2) When ρ k There is a ratio ρ max For large elements, the trajectory can be considered non-smooth, and the solution accuracy can be improved by refining the intervals. The number of segments, seg, can be obtained by the following formula.

[0095]

[0096] Where C2 is an arbitrary integer constant that controls the number of sub-intervals. Each segment must consist of at least two segments, therefore seg cannot be less than 2. The position of the newly added segment point is ρ. k The sampling point corresponding to the local maximum value of the element.

[0097] In the improved adaptive pseudospectral method, the dimensions of the newly added partitions and interpolation polynomials are variable, which can greatly improve computational efficiency.

[0098] Specific Implementation Method Two: Combination Figures 2 to 6This embodiment describes a simulation using the flexible remote sensing satellite attitude maneuver planning method based on the improved hp adaptive pseudospectral method described in Specific Embodiment 1.

[0099] Taking a scenario where a certain type of optical remote sensing satellite with a flexible solar panel undergoes attitude maneuvers with non-zero terminal angle and angular velocity as an example, the effectiveness of the planning method in this implementation and its performance improvement in terms of computation time are illustrated. Specifically, the satellite's moment of inertia is considered as follows:

[0100]

[0101] The boundary constraints are:

[0102]

[0103] Path constraints: The vector of the prohibited region is [15.7°, -9.7°, 14.6°] in the geocentric equatorial coordinate system, and the field of view λ1 is 10°; the vector of the forced region is [17.8°, 0.55°, 19.26°] in the geocentric equatorial coordinate system, and the field of view λ2 is 30°.

[0104] To verify the effectiveness of this method in rapid maneuvering missions of remote sensing satellites, the objective function of the optimization problem is time optimization.

[0105] minJ = t f

[0106] The first-order frequency of the flexible solar panel is 2.23 Hz, the damping is 0.032, and the rigid-flexible coupling coefficient matrix is ​​[0.01, 0.0383, 0.01]. The maximum angular velocity of the flywheel is 5 rad / s, and the three-axis control torque range is [-0.25 Nm to 0.25 Nm].

[0107] An improved hp adaptive pseudospectral method is used to solve this optimal control problem, transforming the original problem into a nonlinear programming problem. The solution is performed using the MATLAB external package GPOPS2, with the NLP solver Snopt.

[0108] The software environment used in the optimization calculation was: Windows 10 Professional 64-bit operating system and MATLAB R2020b; the hardware environment was: Intel(R) Core(TM) i5-8400 processor and 12G memory.

[0109] Under the same error threshold ε, an improved HP adaptive Radau pseudospectral method is used to solve this problem, and compared with the traditional HP adaptive method. The maximum error is the maximum error reached within the error threshold, which can measure the accuracy of the results to a certain extent. Simulation parameter settings: Error threshold ε = 10 -5, proportionality factor ρ max =2, initial grid points are selected in the range [-1,1], and the initial LGR collocation number is 3. Simulations of all state and control variables are performed using the improved hp adaptive pseudospectral method, and the results are as follows. Figure 2 As shown.

[0110] In 10 -5 Simulation results of the improved accuracy method show that, within a simulation time of 2.28275 s, the flexible remote sensing satellite achieved a 27° maneuver within 25 s, with a non-zero terminal angular velocity, avoiding attitude restrictions. Furthermore, the vibration displacement of the flexible component in modal coordinates was less than 6*10. -3 m, angular velocity less than 8*10 -3 The proposed method can effectively solve the optimal control problem of the rigid-flexible coupled system with complex constraints, achieving a performance of m / s.

[0111] Under the same error threshold ε, the improved hp-adaptive Radau pseudospectral method proposed in this paper is used to solve this problem, and the results are compared with the traditional hp-adaptive method. The results are as follows: Figure 3 , 4 As shown in Figure 5.

[0112] Table 1 shows the optimization results of the hp adaptive pseudospectral method and the improved hp adaptive pseudospectral method under different solution accuracies. Table 1 is a comparison of the optimization results of the pseudospectral method under different accuracies.

[0113] Table 1

[0114]

[0115] The simulation results show that the method of this invention can solve the problem of rapid maneuvering of flexible remote sensing satellites more efficiently. Compared with the traditional HP adaptive pseudospectral method, as... Figures 3-5 As shown, the solution results of the two methods are basically the same. However, the method of this invention has obvious advantages in terms of mesh refinement, with fewer mesh iterations, smaller maximum error, and higher solution efficiency. As the accuracy increases, these advantages also increase, which can, to some extent, mitigate the impact of the long solution time when using the traditional pseudospectral method to solve high-precision attitude planning problems.

[0116] The method described in this embodiment addresses the multi-constraint attitude optimal maneuver planning problem for high-resolution flexible remote sensing satellites performing Earth observation missions, proposing an improved hp adaptive Radau pseudospectral method. This paper proposes an improved method employing a two-layer optimization iterative strategy. Optimization is performed using the residuals at Gaussian-distributed sampling points with differential-algebraic constraints as the error evaluation criterion. A secondary optimization is performed using one-quarter of the ratio of the maximum curvature to the standard deviation at each sampling point as the refinement criterion. These two aspects together improve the solution efficiency of the method.

[0117] This method can generate the optimal trajectory that meets all constraints in the shortest time, and it is faster than the traditional HP adaptive pseudospectral method at the same accuracy, thus exhibiting higher solution efficiency. This method provides a design basis for high-resolution remote sensing satellites to perform complex space missions and has engineering significance.

[0118] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0119] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A flexible remote sensing satellite attitude maneuver planning method based on an improved adaptive pseudospectral method, characterized by: This method is implemented by the following steps: Step 1: Establish a continuous optimal control problem model, transform various constraints into an optimal control problem, and minimize the optimization performance index while satisfying multiple constraints. The optimal control problem model specifically involves: attitude dynamics and kinematic modeling of flexible satellites; According to the momentum and angular momentum theorems, and taking the inertial coordinate system as the reference coordinate system, the rigid-flexural coupling dynamic equations of the system consisting of the satellite body and its flexible components are as follows: ； In the formula, Here is the satellite's rotational inertia matrix; This is the angular velocity of the satellite relative to the inertial frame of reference. The coupling coefficient between the flexible attachment and the satellite; This represents the displacement of the flexible attachment in the modal coordinate system. The angular momentum of the actuator; The space disturbance torque experienced by the satellite; The vibration equation of the flexible attachment is expressed in modal coordinates as follows: ； In the formula, The damping ratio matrix represents the mode of the flexible attachment. This represents the vibration frequency matrix of the flexible attachment modes. Step 2: Discretize the optimal control problem, transforming it into a nonlinear programming problem for solution, and use the improved adaptive Radau pseudospectral method for point collocation; the specific point collocation process is as follows: Step Two:

1. Use error evaluation criteria to make a judgment: Sampling points are selected using a Gaussian distribution, and the error criterion is used to determine whether it exceeds the error threshold of the differential-algebraic equation. If so, refine the network again using the improved HP adaptive pseudospectral method and execute step two; and set the error judgment criterion as the residual of the sampling point in the dynamic constraint equation. Otherwise, proceed to step two five; Step 22: Use the grid classification refinement criteria for judgment: Criteria for judging state curvature Is it greater than the scaling factor? ; If yes, refine the interval to improve accuracy, and proceed to steps two and three; if no, increase the number of points to improve accuracy, and proceed to steps two and three. Set the state curvature standard It is one-quarter of the ratio of the maximum curvature to the standard deviation at each sampling point; expressed by the following formula: ； In the formula, The maximum curvature value of each sampling point in the k-th interval. The number of sampling points. Let be the curvature of the l-th state at the i-th sampling point. This represents the average curvature at each sampling point; Increasing the number of matching points improves the solution accuracy, as expressed by the following formula: set up and To update the number of points within each subinterval before and after the update. It can be obtained from the following formula: ； In the formula, `ceil()` is an arbitrary integer constant that controls the increment of the number of dots in each segment. `ceil()` is the function that rounds up. The maximum residual; Refining the intervals improves accuracy; increasing the number of segments. It can be expressed as follows: ； In the formula, `<quotient>` is an arbitrary integer constant used to control the number of segments in the subinterval; the location of the newly added segment point is... The sampling point corresponding to the local maximum value of the element in the middle; Steps two and three: Obtain new grid points and matching points; Step 24: Substitute the new grid points and collocation points obtained in Step 2 into Step 2 to perform a new solution; Step 25: Complete the iteration of the solution and use the current numerical solution as the final output.

2. The attitude maneuver planning method for flexible remote sensing satellites based on the improved adaptive pseudospectral method according to claim 1, characterized in that: In step two, the adaptive Radau pseudospectral method is used to solve the optimal control problem. Specifically, the state and control variables are discretized using the pseudospectral method to obtain numerical solutions for the state and control variables. The nonlinear optimal control problem is then transformed into a nonlinear programming problem, which is solved using a nonlinear programming solver.

Images