Soft landing trajectory optimization method based on second-order cone preprocessing, medium and equipment

Abstract

The invention is suitable for the technical field of aircraft trajectory optimization, and relates to a soft landing trajectory optimization method, medium and equipment based on second-order cone preprocessing, and the method comprises the steps: constructing an SOCP problem based on a current soft landing trajectory planning problem, and obtaining an original constraint matrix of the SOCP problem; obtaining a plurality of dense sub-blocks according to the original constraint matrix, and identifying to obtain reversible sub-matrixes in the dense sub-blocks; eliminating a reversible submatrix in the original constraint matrix to obtain a pre-processed problem; and solving the pre-processed problem to obtain a pre-processed solution, and restoring the pre-processed solution to an original dimension to obtain a solution of the current soft landing trajectory planning problem. The problems of long solving time, high complexity, lack of a targeted optimization method and the like in a high-dimensional and complex constraint scene in the prior art are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aircraft trajectory optimization, in particular to a soft landing trajectory optimization method based on second-order cone preconditioning, a medium and equipment. BACKGROUND

[0002] With the increasing frequency of deep space exploration missions, soft landing trajectory planning has become one of the core technologies that determine whether a spacecraft can safely and accurately reach the target star surface. A typical soft landing process needs to generate an optimal landing trajectory in real time under the conditions of meeting multiple objectives such as complex dynamic constraints (such as thrust amplitude limit, attitude pointing constraint, glide angle constraint), safety constraints (such as obstacle avoidance, ground height maintenance), and fuel consumption minimization.

[0003] The prior art mainly models this problem as a nonlinear optimal control problem, and roughly divides it into two types of solution ideas: 1. Traditional numerical optimization method, the early scheme generally adopts a direct method (Direct Method) to parameterize the continuous time trajectory in the form of a polynomial or discrete points, and then converts it into a finite-dimensional nonlinear programming (NLP) problem, and then calls general numerical algorithms such as sequential quadratic programming (SQP), interior-point method (Interior-Point Method) or multiple shooting method (Multiple Shooting) for iterative solution; this method is theoretically mature, has high convergence accuracy, and has been successfully applied to the ground test verification of multiple lunar / mars landing missions. However, due to the strong nonlinearity of soft landing dynamics and the serious coupling of control variables, the calculation amount is huge, and the solving time is long, which makes it difficult to meet the real-time requirements.

[0004] 2. Method based on modern optimization solver, in recent years, researchers have found that the soft landing problem can be converted into a second-order cone programming (SOCP) problem, and then a special SOCP solver is called for solving. Compared with the traditional numerical optimization method, only a series of linear equations need to be solved, the computational complexity is significantly reduced, and the calculation efficiency is effectively improved; however, as the complexity of the task scene increases, the above optimization method still has the problems of long solving time, exponential growth of computational complexity when the problem size increases, lack of special acceleration techniques for soft landing characteristics, and general-purpose solver. In order to accommodate applications in various fields, a large amount of redundant interfaces and global fault tolerance strategies are retained, resulting in additional computational overhead.

[0005] Therefore, how to improve the existing technology to solve the problems of long solving time, high complexity, and lack of targeted optimization method in high-dimensional and complex constraint scenarios is a technical problem that needs to be solved in this field. SUMMARY

[0006] Based on this, the present application aims to provide a soft landing trajectory optimization method based on second-order cone preprocessing, a medium and equipment to solve at least one of the technical problems mentioned in the background art.

[0007] In the first aspect, the present application provides a soft landing trajectory optimization method based on second-order cone preprocessing, comprising: Based on the current soft landing trajectory planning problem, a SOCP problem is constructed, and the original constraint matrix of the SOCP problem is obtained; According to the original constraint matrix, a plurality of dense sub-blocks are obtained, and the reversible sub-matrix in the dense sub-block is identified; Eliminate the reversible sub-matrix in the original constraint matrix to obtain the preprocessed problem; Solve the preprocessed problem to obtain the preprocessed solution and restore it to the original dimension to obtain the solution of the current soft landing trajectory planning problem.

[0008] Further, based on the current soft landing trajectory planning problem, the step of constructing the SOCP problem comprises: According to the current soft landing trajectory planning problem, the actual flight time interval and the speed and thrust direction of each position on the continuous trajectory are obtained; Map the actual flight time interval to the standard calculation interval, and decompose the continuous trajectory into a plurality of discrete points, select and obtain the position, speed and thrust direction of a plurality of discrete points; According to the standard calculation interval and the differential matrix, the continuous differential equation is converted into an algebraic equation at the selected discrete points to obtain a nonlinear programming problem; Linearize the nonlinear programming problem by successive convexification, and construct the SOCP problem according to the position, speed and thrust direction constraints.

[0009] Further, according to the original constraint matrix, a plurality of dense sub-blocks are obtained, and the reversible sub-matrix in the dense sub-block is identified, comprising: Obtain the specific structure of the original constraint matrix, and identify the position information of each initial dense sub-block in the matrix; The position information includes the row and column where the initial dense sub-block is located; According to the position information, rearrange the rows and columns of the original constraint matrix structure, move each initial dense sub-block to the set position, and obtain a large dense block; Split the large dense block into a plurality of updated dense sub-blocks, and perform symbolic decomposition on each updated dense sub-block to obtain the number of non-zero elements filled after each updated dense sub-block is eliminated; Determine whether the number of fillings exceeds the set threshold, if not, identify the corresponding updated dense sub-block as a reversible sub-matrix.

[0010] Further steps, including obtaining the specific structure of the original constraint matrix and identifying the positional information of each initial dense sub-block in the matrix, include: Obtain the specific structure of the original constraint matrix to get the values ​​and positions of all elements in the matrix; Based on the value and position of the element, obtain the number of non-zero elements in each column of the matrix, and determine whether it is greater than a first set threshold. If so, it is a candidate column. Based on the value and position of the element, obtain the number of consecutive non-zero elements in the row containing the non-zero element in each candidate column, and determine whether it is greater than the first set threshold. If so, it is a dense column. Obtain adjacent dense columns as candidate dense sub-blocks, and determine whether the number of columns in each candidate dense sub-block is greater than the second set number threshold. If so, it is the initial dense sub-block, and the row and column of any element in the initial dense sub-block is used as its position information.

[0011] Furthermore, the step of rearranging the rows and columns of the original constraint matrix structure based on the position information and moving each initial dense sub-block to a set position includes: Based on the position information, determine whether there are dense sub-blocks in each row / column of the original constraint matrix structure. If so, it is a dense row / column; otherwise, it is a non-dense row / column. Move all dense rows / columns up / left sequentially until all dense rows / columns are above / to the left of non-dense rows / columns. Obtain the row index / column index of each dense row / column at this point, and construct a row arrangement / column arrangement mapping table based on the original row index / column index. The original constraint matrix structure is rearranged according to the row / column arrangement mapping table, and each initial dense sub-block is moved to the set position.

[0012] Furthermore, the step of splitting the large dense block into several updated dense sub-blocks includes: Split all the initial dense sub-blocks that make up the large dense block to update the dense sub-blocks; Alternatively, split the large dense block into two updated dense sub-blocks; Alternatively, extract large dense blocks to update dense sub-blocks.

[0013] Further steps to eliminate invertible submatrices from the original constraint matrix include: The original constraint matrix is ​​rearranged to obtain the permutation matrix; The permutation matrix is ​​decomposed into blocks to construct the first block equation and the second block equation; Construct an elimination function based on the first block of equations and substitute it into the second block of equations to eliminate the invertible submatrices in the original constraint matrix.

[0014] Furthermore, the steps of solving the preprocessed problem, obtaining the preprocessed solution, restoring it to the original dimensions, and obtaining the solution to the current soft landing trajectory planning problem include: Solve the preprocessed problem to obtain the preprocessed solution, including the preprocessed solution for the original variables and the preprocessed solution for the dual variables. Substitute the preprocessed solutions of the original variables and the dual variables into the restoration formula to restore their original dimensions, and obtain the rearranged solutions of the original variables and the rearranged solutions of the dual variables. The original and dual variable rearranged solutions are rearranged using the row / column arrangement mapping table to obtain the final original and dual variable solutions, which are the solutions to the current soft landing trajectory planning problem.

[0015] Secondly, this application also provides a computer storage medium storing executable program code; the executable program code is used to execute the soft landing trajectory optimization method based on second-order cone preprocessing as described in any one of the first aspects.

[0016] Thirdly, this application also provides a terminal device, including a memory and a processor; the memory stores program code executable by the processor; the program code is used to execute the soft landing trajectory optimization method based on second-order cone preprocessing as described in any one of the first aspects.

[0017] This invention provides a soft landing trajectory optimization method, medium, and device based on second-order cone preprocessing. It constructs a soft landing trajectory planning problem (SOCP) based on the current soft landing trajectory planning problem and obtains the original constraint matrix of the SOCP problem. By discretizing the continuous-time trajectory into finite-dimensional decision variables, a data foundation is provided for subsequent steps. Then, several dense sub-blocks are obtained based on the original constraint matrix, and invertible sub-matrices in the dense sub-blocks are identified to eliminate invertible sub-matrices in the original constraint matrix, resulting in a preprocessed problem. By eliminating invertible sub-matrices, the problem size can be significantly reduced, and the solution failure rate can be lowered. Finally, the preprocessed problem is solved to obtain the preprocessed solution, which is then restored to the original dimension to obtain the solution to the current soft landing trajectory planning problem. Restoring the solution of the preprocessed problem to the original dimension improves solution efficiency and numerical stability. This solves the problems of long solution time, high complexity, and lack of targeted optimization methods in existing technologies under high-dimensional and complex constraint scenarios. Attached Figure Description

[0018] Figure 1 This is a flowchart of a soft landing trajectory optimization method based on second-order cone preprocessing according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a method for dividing dense sub-blocks according to an embodiment of the present invention; Figure 3This is a schematic diagram of the original linear constraint matrix of the SOCP problem in an embodiment of the present invention; Figure 4 This is a schematic diagram of the original cone constraint matrix of the SOCP problem in an embodiment of the present invention; Figure 5 This is a schematic diagram of the linear constraint matrix of the preprocessed SOCP problem according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the cone constraint matrix of the preprocessed SOCP problem according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the original simulation results of the rising phase data BPSC1_new2 in an embodiment of the present invention; Figure 8 This is a schematic diagram of the simulation results after preprocessing of the rising phase data BPSC1_new2 in an embodiment of the present invention; Figure 9 This is a schematic diagram of the original simulation results of DPSC1_scale2 data during the descent phase in this embodiment of the invention. Figure 10 This is a schematic diagram of the simulation results after preprocessing the descent phase data DPSC1_scale2 according to an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] It should be noted that if the embodiments of the present invention involve directional indications, such as up, down, left, right, front, back, etc., these directional indications are only used to explain the relative positional relationships and movement of the components in a specific posture. If the specific posture changes, the directional indications will also change accordingly. Furthermore, if the embodiments of the present invention involve descriptions such as "first," "second," "S1," "S2," "step one," "step two," etc., these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance, or implicitly indicating the number of technical features indicated or the order of method execution. Those skilled in the art will understand that anything that does not violate the inventive concept and is within the scope of the present invention should be included in the protection scope of the present invention.

[0021] Currently, the optimization of soft landing trajectories for spacecraft typically employs methods based on modern optimization solvers. However, these solvers are time-consuming in solving soft landing problems, and their computational complexity increases exponentially with the problem size. Furthermore, to accommodate various applications, modern optimization solvers retain numerous redundant interfaces and global fault-tolerance strategies, resulting in additional computational overhead. They also lack specialized optimization techniques tailored to the characteristics of soft landing problems, failing to meet the urgent efficiency demands of the current aerospace industry. Therefore, [further optimization is needed]. Figure 1 As shown, this invention provides a soft landing trajectory optimization method based on second-order cone preprocessing. It achieves dimensionality reduction optimization of the SOCP problem through techniques such as dense block detection, matrix sorting, and matrix elimination, significantly improving the operational efficiency of the soft landing trajectory planning problem. Specifically, the method includes: S1: Based on the current soft landing trajectory planning problem, construct the SOCP problem and obtain the original constraint matrix of the SOCP problem; Specifically, soft landing trajectory planning is a key technology in the spacecraft landing process, requiring the solution of the optimal landing trajectory while satisfying dynamic constraints, safety constraints, and fuel consumption minimization. Optionally, based on the current soft landing trajectory planning problem, a second-order cone programming (SOCP) problem can be constructed, and the original constraint matrix of the SOCP problem can be obtained. The SOCP problem is a convex optimization problem with a linear objective function and constraints including linear constraints and second-order cone constraints.

[0022] Preferably, the steps for constructing the SOCP problem based on the current soft landing trajectory planning problem may include: S11: Based on the current soft landing trajectory planning problem, obtain the actual flight time interval and the velocity and thrust direction at each position on the continuous trajectory; S12: Map the actual flight time interval to the standard calculation interval, decompose the continuous trajectory into a finite number of discrete points, select and obtain the position, velocity and thrust direction of several discrete points; S13: Based on the standard computation interval and differential matrix, the continuous differential equation is transformed into an algebraic equation at selected discrete points, thus obtaining a nonlinear programming problem; S14: The nonlinear programming problem is linearized by successive convexity and the SOCP problem is constructed based on position, velocity and thrust direction constraints.

[0023] Specifically, based on the current soft landing trajectory planning problem, the actual flight time interval and the velocity and thrust direction at each position on the continuous trajectory are obtained. Then, the actual flight time interval is mapped to a standard calculation interval, and the continuous trajectory is decomposed into a finite number of discrete points. The position, velocity, and thrust direction of several discrete points are selected and obtained. Then, based on the standard calculation interval and the differential matrix, the continuous differential equation is transformed into algebraic equations on the selected discrete points. The algebraic equations include the position equation: the change in position equals the velocity; and the velocity equation: the change in velocity equals the applied force (gravity, thrust, drag, etc.). Boundary conditions are obtained, including initial conditions: the position and velocity of the launch point; terminal conditions: the position and velocity of the target orbit; and continuity conditions (multi-segment flight): the states between segments must be continuous. This results in a nonlinear programming problem. Since the discretized equations contain nonlinear terms (gravity and drag terms), the optimization problem becomes nonconvex, making it difficult to solve directly. Therefore, a successive convexification method can be used to linearize the nonlinear terms near the reference trajectory, transforming the problem into a convex optimization problem. Simultaneously, the thrust direction constraint is ||u|| ≤ 1. The problem itself involves second-order cone constraints. By combining the optimization problem with all constraints, the current soft landing trajectory planning problem is ultimately transformed into a SOCP problem. It is worth noting that the construction process and specific form of this SOCP problem can be arbitrarily set according to the flight trajectory, flight mode, flight strategy, flight phase, etc., and are not limited to the steps described above. Preferably, the flight phase includes the ascent phase (BPSC1_new2, DPSC1_new) and the descent phase (DPSC1_scale2), etc.

[0024] For example, the soft landing trajectory planning problem can be represented as follows: The parameters can be optionally defined as follows: For example, the SOCP problem during the ascent phase of flight, specifically when DPSC1_new is in the ascent phase, can be represented as follows: The decision variable x can be represented as follows: Preferably, each SOCP problem can be represented as shown in Equations 2-1, 2-2, and 2-3: 2-1 2-2 2-3 Where x is the decision variable, c is the objective function coefficient, T denotes the transpose operation, A is the linear constraint matrix, b is a vector, and K is the direct product of several "second-order cones". This is used to further obtain the original constraint matrices for each SOCP problem, including linear constraint matrices and cone constraint matrices. For example, the linear constraint matrix is ​​as follows: Figure 3 As shown, the cone constraint matrix is ​​as follows: Figure 4 As shown.

[0025] S2: Obtain several dense sub-blocks based on the original constraint matrix, and identify the invertible sub-matrices in the dense sub-blocks; Specifically, SOCP problems formed by the finite difference method typically contain multiple dense sub-blocks, where the upper left sub-block corresponds to free variables whose domain is from negative infinity to positive infinity. Dense sub-blocks can cause a surge in fill-in elements in sparse decomposition (such as Cholesky decomposition), increasing computational cost and memory consumption. If free variables (unbounded variables) are not specially handled, they can introduce ill-conditioned condition numbers, causing solver failure. Since SOCP problems formed by the finite difference method usually have a block structure, it is possible, but not limited to, to obtain several dense sub-blocks in the original constraint matrix of the SOCP problem and identify the invertible submatrices in the dense sub-blocks so that they can be eliminated in subsequent steps, thereby reducing the number of decision variables and cone dimension, and making the solver iterate faster.

[0026] Preferably, the step of obtaining several dense sub-blocks based on the original constraint matrix and identifying invertible sub-matrices within the dense sub-blocks may optionally include: S21: Obtain the specific structure of the original constraint matrix and identify the position information of each initial dense sub-block in the matrix; the position information includes the row and column where the initial dense sub-block is located; Specifically, but not limited to, obtaining the specific structure of the original constraint matrix, identifying the position information of each initial dense sub-block in the matrix; the position information includes the row and column of the initial dense sub-block, providing a data foundation for subsequent steps.

[0027] Preferably, the steps of obtaining the specific structure of the original constraint matrix and identifying the position information of each initial dense sub-block in the matrix may include: S211: Obtain the specific structure of the original constraint matrix to get the values ​​and positions of all elements in the matrix; S212: Based on the value and position of the element, obtain the number of non-zero elements in each column of the matrix, and determine whether it is greater than the first set threshold. If so, it is a candidate column. S213: Based on the value and position of the element, obtain the number of consecutive non-zero elements in the row where the non-zero element is located in each candidate column, and determine whether it is greater than the first set number threshold. If so, it is a dense column. S214: Obtain adjacent dense columns as candidate dense sub-blocks, and determine whether the number of columns in each candidate dense sub-block is greater than the second set quantity threshold. If so, it is the initial dense sub-block, and the row and column of any element in the initial dense sub-block is used as its position information.

[0028] Specifically, it is optional, but not limited to, setting a first and a second quantity threshold, and obtaining the specific structure of the original constraint matrix. Based on this structure, the values ​​and positions of all elements are obtained, providing a data foundation for subsequent steps. Then, based on the element values ​​and positions, the number of non-zero elements in each column of the matrix is ​​obtained, and it is determined whether this number exceeds the first set quantity threshold. If so, it indicates that the number of non-zero elements in that column meets the "dense" requirement and can therefore be used as a candidate column. Sparse columns are quickly eliminated by counting non-zero elements, improving data processing efficiency. Since the non-zero elements in dense blocks are continuous, further acquisition of each candidate column is required. The number of consecutive non-zero elements in the row containing a non-zero element in a column is counted, and it is determined whether this number exceeds a first set threshold. If so, it means that the number and arrangement of non-zero elements in the column meet the requirements and can be considered a dense column. Finally, adjacent dense columns are selected as candidate dense sub-blocks, and it is determined whether the number of columns in each candidate dense sub-block exceeds a second set threshold. If so, it is considered an initial dense sub-block, and the row and column of any element in the initial dense sub-block are used as its position information. By merging isolated dense columns into meaningful geometric sub-blocks, and then eliminating small dense blocks that do not meet the size requirements by counting the number of columns, the identification of each initial dense sub-block in the matrix is ​​completed.

[0029] S22: Rearrange the rows and columns of the original constraint matrix structure according to the position information, and move each initial dense sub-block to the set position to obtain a large dense block; Specifically, the original constraint matrix structure can be rearranged according to the row and column of the initial dense sub-block, moving each initial dense sub-block to a set position. Since all initial dense sub-blocks are now located in the same position within the constraint matrix, they can be considered as forming a large dense block, facilitating their elimination in subsequent steps, thereby reducing the problem size and improving computational efficiency. Preferably, the set position is the upper left corner of the matrix.

[0030] Preferably, the step of rearranging the rows and columns of the original constraint matrix structure according to the position information and moving each initial dense sub-block to a set position may include: S221: Based on the position information, determine whether there are dense sub-blocks in each row / column of the original constraint matrix structure. If so, it is a dense row / column; otherwise, it is a non-dense row / column. S222: Obtain the row index / column index of all dense rows / columns, and move them up / left in sequence until the row index / column index of all dense rows / columns is above / to the left of the row index / column index of non-dense rows / columns, in order to construct a row arrangement / column arrangement mapping table; S223: Rearrange the original constraint matrix structure according to the row / column arrangement mapping table, and move each initial dense sub-block to the set position.

[0031] Specifically, based on the position information of the dense sub-blocks, the rows and columns in the original matrix can be divided into dense rows / dense columns and non-dense rows / non-dense columns. The row index / column index of all dense rows / dense columns is obtained, and they are moved upwards / leftwards in sequence. Since each initial dense sub-block contains several dense rows and dense columns, the movement is performed on each dense sub-block as a whole until the row index / column index of all dense rows / dense columns is located above / to the left of the row index / column index of non-dense rows / non-dense columns. This constructs a row / column arrangement mapping table. The original constraint matrix structure is rearranged according to the row / column arrangement mapping table, and each initial dense sub-block is moved to a set position so that all dense sub-blocks are located on the diagonal of the upper left corner of the matrix, providing a data foundation for subsequent steps.

[0032] S23: Divide the large dense block into several updated dense sub-blocks, and perform symbol decomposition on each updated dense sub-block to obtain the number of non-zero elements that will be filled after each updated dense sub-block is eliminated; Specifically, in practical applications, the invertible submatrix in the constraint matrix structure is not necessarily better the larger it is. A larger invertible submatrix is ​​more likely to cause problems in the CU. -1 Since B introduces more non-zero elements, it is possible to split the large dense block into several updated dense sub-blocks and perform symbolic decomposition on each updated dense sub-block to obtain the number of non-zero elements that will be filled after each updated dense sub-block is eliminated. Then, the invertible submatrix can be identified based on the number of non-zero elements filled.

[0033] Preferably, since large dense blocks are composed of many small dense blocks, various splitting methods can be used during the splitting process, such as... Figure 2 As shown, there are three methods for partitioning dense sub-blocks. Therefore, the step of splitting a large dense block into several updated dense sub-blocks also includes: S231: Split all the initial dense sub-blocks that make up the large dense block, in order to update the dense sub-blocks; S232: Alternatively, split the large dense block into two updated dense sub-blocks; S233: Alternatively, extract large dense blocks to update dense sub-blocks.

[0034] Specifically, in practice, factors such as accuracy, time consumption of splitting operations, and time consumption of matrix operations need to be considered comprehensively. Therefore, those skilled in the art can choose one of the above three methods to further process the large dense block according to the on-site situation, so as to obtain several updated dense sub-blocks, so that subsequent processing (such as symbolic decomposition and numerical decomposition) can be carried out in a smaller local range, reducing computational complexity.

[0035] For example, one option is to split all the initial dense sub-blocks that make up the large dense block. To update the dense sub-blocks, the block is split k times, which means splitting the large dense block into the smallest possible size, obtaining k small dense sub-blocks in sequence, and eliminating them step by step through k matrix operations. Alternatively, the block can be split twice, with p = k / 2 (rounded down), which means splitting the large dense block into two blocks of size p and kp, and eliminating them through two matrix operations. Or, the block can be split once, which means treating the large dense block as a whole and eliminating it through one matrix operation.

[0036] S24: Determine whether the number of fills exceeds the set threshold. If not, identify the corresponding updated dense sub-block as an invertible sub-matrix.

[0037] Specifically, setting a threshold for the number of fill elements is optional, but not limited to it. Since one of the core objectives of symbolic decomposition is to minimize fill elements, if some reversible sub-blocks in dense sub-blocks introduce a large number of new non-zero elements during the elimination process, it will severely damage sparsity and lead to memory and computational explosion. Therefore, it is optional to perform symbolic decomposition on each dense sub-block to obtain the number of non-zero elements that will be introduced after the dense sub-block is eliminated, and to determine whether the number of fill elements exceeds the set threshold. If so, it is considered that the corresponding dense sub-block will introduce too many non-zero elements after elimination, affecting subsequent solution steps, so it needs to be retained. If not, it means that the corresponding dense sub-block will not introduce too many non-zero elements after elimination, and eliminating it will not affect subsequent solution steps. On the contrary, it can significantly reduce the scale of the problem and improve the solution efficiency. Therefore, the corresponding dense sub-block is identified as a reversible submatrix so that it can be removed in subsequent steps.

[0038] S3: Eliminate invertible submatrices from the original constraint matrix to obtain the preprocessed problem; Specifically, by concentrating dense blocks in the upper left corner, they can be easily eliminated through block elimination, avoiding the complex filling patterns caused by scattered dense blocks. Simultaneously, after sorting, the sparsity of the remaining matrix (non-dense parts) is maximized, reducing the number of filling elements during decomposition. Free variables (unbounded variables) must be eliminated first; otherwise, artificial boundaries (such as the Big M method) must be introduced, disrupting the problem structure. Therefore, invertible submatrices in the original constraint matrix can be eliminated, significantly reducing the problem size. This addresses the issues of numerous variables, large cones, and high dimensionality of the KKT system in the original problem, which required the solver to solve a large-scale linear system at each step, leading to poor real-time performance, large scale differences in some variables (such as the thrust direction unit vector and magnitude), high KKT matrix condition number, and slow solver convergence. Furthermore, due to the limited memory of the onboard computer, the original SOCP... The task may fail due to an excessive number of variables failing to load. Eliminating invertible submatrices from the original constraint matrix reduces the number of decision variables and the cone dimension, allowing for faster solver iteration. Block elimination removes ill-conditioned sub-blocks, improving numerical stability and reducing the failure rate. Furthermore, dimensionality reduction optimization decreases the size of the KKT system, reducing memory pressure on embedded platforms and making it suitable for onboard computing, thus improving solution efficiency and yielding a preprocessed problem. Preferably, the preprocessed problem can be obtained by eliminating invertible submatrices from the original constraint matrix.

[0039] More specifically, since many practical second-order cone programming (SOCP) models have structured characteristics, such as SOCP being used to solve discretized differential equations, matrix A in these problems often contains large multi-diagonal invertible submatrices. Selective elimination of these submatrices can significantly reduce the problem size. Therefore, it is possible to eliminate invertible submatrices in the updated constraint matrix to obtain a preprocessed problem, thereby reducing computational resource consumption in subsequent steps and improving computational efficiency. The constraint matrix of the preprocessed problem includes linear constraint matrices such as... Figure 5 As shown, the cone constraint matrix is ​​as follows: Figure 6 As shown, for the same SOCP problem, the number of variables and constraints after preprocessing is significantly reduced. Simultaneously, the number of dense sub-blocks decreases from 12 to 6, and the number of non-zero elements is reduced by approximately half. Since the most time-consuming part of the solver is assembling the matrix and solving the linear equation system, eliminating invertible sub-matrices in the updated constraint matrix to reduce the number of non-zero elements can greatly improve the solution efficiency.

[0040] Preferably, the step of eliminating invertible submatrices from the original constraint matrix to obtain the preprocessed problem may include: S31: Rearrange the original constraint matrix to obtain the permutation matrix; For example, the original constraint matrix structure can be rearranged to obtain the permutation matrix as shown in Equation 3-1: 3-1 Where x1 is a free variable, x2 is a second-order cone variable, U is an invertible submatrix, B, C, and D are submatrices, and b1 and b2 are subvectors.

[0041] S32: Perform block decomposition on the permutation matrix to construct the first block equation and the second block equation; For example, block decomposition can be performed based on the specific structure of the permutation matrix obtained in step S31, resulting in the first block equation and the second block equation as shown in equations 3-2 and 3-3, respectively: U x1 + B x2 = b1 3-2 C x1 + D x2 = b2 3-3 S33: Construct an elimination function based on the first block equation and substitute it into the second block equation to eliminate the invertible submatrices in the original constraint matrix.

[0042] For example, an elimination function can be optionally constructed based on the first block equation, as shown in Equation 3-4: x1= U⁻ 1 (b1- B x2) 3-4 Then, substituting into the second equation to eliminate the invertible submatrices in the original constraint matrix, we obtain equation 3-5: (D - CU -1 B)x2= b2- CU -1 b1 3-5 S4: Solve the preprocessed problem to obtain the preprocessed solution and restore it to the original dimension to obtain the solution to the current soft landing trajectory planning problem.

[0043] Specifically, since step S3 eliminates the invertible submatrices in the original constraint matrix to obtain the preprocessed problem, although the problem size is reduced and the solution speed is improved, the dimension of the preprocessed solution is less than that of the solution to the initial soft landing trajectory planning problem. Therefore, after solving the preprocessed problem and obtaining the preprocessed solution, it is necessary to restore the preprocessed solution to the original dimension to obtain the solution to the initial soft landing trajectory planning problem.

[0044] Preferably, the steps of solving the preprocessed problem to obtain the preprocessed solution and restoring it to the original dimension to obtain the solution to the current soft landing trajectory planning problem may include: S41: Solve the preprocessed problem to obtain the preprocessed solution, including the preprocessed solution of the original variables and the preprocessed solution of the dual variables; S42: Substitute the preprocessed solutions of the original variables and the dual variables into the restoration formula to restore their original dimensions and obtain the rearranged solutions of the original variables and the rearranged solutions of the dual variables. Specifically, solving the preprocessed problem yields a preprocessed solution, including the original variable preprocessed solution x2 and the dual variable preprocessed solution y2. The solutions obtained at this point are all dimensionality-reduced solutions, which need to be restored to their original dimensions to obtain the solution to the current soft landing trajectory planning problem.

[0045] For example, as shown in Equation 3-1, the solution to the original equation includes the original variables x1 and x2, and the dual variables y1 and y2. Since x1 and y1 are eliminated during the processing, while x2 and y2 are retained, Equation 3-1 needs to be transformed to obtain the restoration formulas 4-1 and 4-2: x1= U −1 (b1−B x2) 4-1 y1=U −T (−c1−C T y2) 4-2 Then, substituting x2 and y2 into equations 4-1 and 4-2 respectively, we can obtain the original dimension x solution as [x1, x2] and the original dimension y solution as [y1, y2].

[0046] S43: Rearrange the original variable rearrangement solution and the dual variable rearrangement solution according to the row / column arrangement mapping table to obtain the final original variable solution and dual variable solution, which are the solutions to the current soft landing trajectory planning problem.

[0047] Specifically, since the matrix is ​​rearranged in step S2, the solution obtained after restoring the dimensions is still in the order of the preprocessed rearrangement. Therefore, it is necessary to restore all rows and columns to their original order according to the row / column arrangement mapping table obtained in step S22 to obtain the final original variable solution and dual variable solution, which is the solution to the current soft landing trajectory planning problem.

[0048] This application provides a soft landing trajectory optimization method based on second-order cone preprocessing, which can significantly improve solution efficiency and computational performance. Simulation results for the ascent and descent phases are as follows: Figure 7 As shown in Tables 8, 9, and 10, it can be seen that after preprocessing the SOCP problem, the problem size is reduced, the solution efficiency is improved, and the simulation results remain unchanged. The simulation results before and after each stage of preprocessing are shown in Table 1. Table 1: Comparison of Preprocessing Results (Unit: seconds) It can be seen that preprocessing has the following advantages: 1. Significantly improved solution efficiency: - Compared to using the solver directly, preprocessing techniques further reduce solution time by 40%-50%. - BPSC1_new2 modeling method: After preprocessing, the solution time is reduced to 60.7% of the original problem. - DPSC1_new modeling method: After preprocessing, the solution time is reduced to 43.4% of the original problem. 2. Significant optimization effect on problem size: - The number of dense sub-blocks was reduced from 12 to 6, a reduction of 50%. - The number of non-zero elements has been reduced to about half. - The number of variables and constraints has been significantly reduced. 3. Preservation of solution accuracy: - Preprocessing does not affect solution accuracy - It can quickly restore the solution. - Ensure the practicality of the algorithm 4. Engineering application value: - Meets the real-time requirements of soft landing missions - Suitable for small to medium-sized trajectory planning problems - Provide efficient technical support for the soft landing of spacecraft In summary, the soft landing trajectory optimization method based on second-order cone preprocessing proposed in this application constructs a soft landing trajectory planning problem (SOCP) based on the current soft landing trajectory planning problem and obtains the original constraint matrix of the SOCP problem. By discretizing the continuous-time trajectory into finite-dimensional decision variables, a data foundation is provided for subsequent steps. Then, several dense sub-blocks are obtained based on the original constraint matrix, and invertible sub-matrices in the dense sub-blocks are identified to eliminate invertible sub-matrices in the original constraint matrix, resulting in a preprocessed problem. By eliminating invertible sub-matrices, the problem size can be significantly reduced, and the failure rate of the solution can be lowered. Finally, the preprocessed problem is solved to obtain the preprocessed solution, which is then restored to the original dimension to obtain the solution to the current soft landing trajectory planning problem. Restoring the solution of the preprocessed problem to the original dimension improves the solution efficiency and enhances numerical stability. This solves the problems of long solution time, high complexity, and lack of targeted optimization methods in existing technologies under high-dimensional and complex constraint scenarios.

[0049] On the other hand, the present invention also provides a computer storage medium storing executable program code; the executable program code is used to execute any of the above-mentioned soft landing trajectory optimization methods based on second-order cone preprocessing.

[0050] On the other hand, the present invention also provides a terminal device, including a memory and a processor; the memory stores program code that can be executed by the processor; the program code is used to execute any of the above-mentioned soft landing trajectory optimization methods based on second-order cone preprocessing.

[0051] For example, the program code can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the program code in the terminal device.

[0052] The terminal device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the terminal device may also include input / output devices, network access devices, buses, etc.

[0053] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0054] The memory can be an internal storage unit of the terminal device, such as a hard drive or RAM. The memory can also be an external storage device of the terminal device, such as a plug-in hard drive, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory can include both internal and external storage units of the terminal device. The memory is used to store the program code and other programs and data required by the terminal device. The memory can also be used to temporarily store data that has been output or will be output.

[0055] The aforementioned computer storage medium and terminal device are created based on the aforementioned soft landing trajectory optimization method based on second-order cone preprocessing. Their technical functions and beneficial effects will not be elaborated here. The technical features of the above embodiments can be combined arbitrarily. 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.

[0056] 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 soft landing trajectory optimization method based on second-order cone preprocessing, characterized in that, include: Based on the current soft landing trajectory planning problem, we construct the SOCP problem and obtain the original constraint matrix of the SOCP problem; Several dense sub-blocks are obtained based on the original constraint matrix, and invertible sub-matrices in the dense sub-blocks are identified; Eliminate the invertible submatrices in the original constraint matrix to obtain the preprocessed problem; Solve the preprocessed problem to obtain the preprocessed solution and restore it to the original dimension to obtain the solution to the current soft landing trajectory planning problem.

2. The method according to claim 1, characterized in that, Based on the current soft landing trajectory planning problem, the steps to construct the SOCP problem include: Based on the current soft landing trajectory planning problem, obtain the actual flight time interval and the velocity and thrust direction at each position on the continuous trajectory; The actual flight time interval is mapped to the standard calculation interval, and the continuous trajectory is decomposed into a finite number of discrete points. The positions, velocities and thrust directions of several discrete points are selected and obtained. Based on the standard computation interval and differential matrix, the continuous differential equation is transformed into an algebraic equation at selected discrete points, thus obtaining a nonlinear programming problem; The nonlinear programming problem is linearized by successive convexity transformation, and the SOCP problem is constructed based on position, velocity and thrust direction constraints.

3. The method according to claim 1, characterized in that, The steps of obtaining several dense sub-blocks based on the original constraint matrix and identifying invertible submatrices within the dense sub-blocks include: Obtain the specific structure of the original constraint matrix and identify the position information of each initial dense sub-block in the matrix; the position information includes the row and column where the initial dense sub-block is located; The original constraint matrix structure is rearranged based on the position information, and each initial dense sub-block is moved to a set position to obtain a large dense block. The large dense block is split into several updated dense sub-blocks, and symbol decomposition is performed on each updated dense sub-block to obtain the number of non-zero elements that will be filled after each updated dense sub-block is eliminated. Determine if the number of fills exceeds a set threshold. If not, identify the corresponding updated dense sub-block as an invertible submatrix.

4. The method according to claim 3, characterized in that, The steps for obtaining the specific structure of the original constraint matrix and identifying the position information of each initial dense sub-block in the matrix include: Obtain the specific structure of the original constraint matrix to get the values ​​and positions of all elements in the matrix; Based on the value and position of the element, obtain the number of non-zero elements in each column of the matrix, and determine whether it is greater than a first set threshold. If so, it is a candidate column. Based on the value and position of the element, obtain the number of consecutive non-zero elements in the row containing the non-zero element in each candidate column, and determine whether it is greater than the first set threshold. If so, it is a dense column. Obtain adjacent dense columns as candidate dense sub-blocks, and determine whether the number of columns in each candidate dense sub-block is greater than the second set number threshold. If so, it is the initial dense sub-block, and the row and column of any element in the initial dense sub-block is used as its position information.

5. The method according to claim 3, characterized in that, The steps of rearranging the rows and columns of the original constraint matrix structure based on the position information and moving each initial dense sub-block to a set position include: Based on the position information, determine whether there are dense sub-blocks in each row / column of the original constraint matrix structure. If so, it is a dense row / column; otherwise, it is a non-dense row / column. Move all dense rows / columns up / left sequentially until all dense rows / columns are above / to the left of non-dense rows / columns. Obtain the row index / column index of each dense row / column at this point, and construct a row arrangement / column arrangement mapping table based on the original row index / column index. The original constraint matrix structure is rearranged according to the row / column arrangement mapping table, and each initial dense sub-block is moved to the set position.

6. The method according to claim 3, characterized in that, The steps of splitting a large dense block into several updated dense sub-blocks include: Split all the initial dense sub-blocks that make up the large dense block to update the dense sub-blocks; Alternatively, split the large dense block into two updated dense sub-blocks; Alternatively, extract large dense blocks to update dense sub-blocks.

7. The method according to claim 1, characterized in that, The steps to eliminate invertible submatrices from the original constraint matrix include: The original constraint matrix is ​​rearranged to obtain the permutation matrix; The permutation matrix is ​​decomposed into blocks to construct the first block equation and the second block equation; Construct an elimination function based on the first block of equations and substitute it into the second block of equations to eliminate the invertible submatrices in the original constraint matrix.

8. The method according to claim 5, characterized in that, The steps for solving the preprocessed problem, obtaining the preprocessed solution, restoring it to the original dimensions, and obtaining the solution to the current soft landing trajectory planning problem include: Solve the preprocessed problem to obtain the preprocessed solution, including the preprocessed solution for the original variables and the preprocessed solution for the dual variables. Substitute the preprocessed solutions of the original variables and the dual variables into the restoration formula to restore their original dimensions, and obtain the rearranged solutions of the original variables and the rearranged solutions of the dual variables. The original and dual variable rearranged solutions are rearranged using the row / column arrangement mapping table to obtain the final original and dual variable solutions, which are the solutions to the current soft landing trajectory planning problem.

9. A computer storage medium, characterized in that, It stores executable program code; the executable program code is used to execute the soft landing trajectory optimization method based on second-order cone preprocessing as described in any one of claims 1 to 8.

10. A terminal device, characterized in that, It includes a memory and a processor; the memory stores program code that can be executed by the processor; the program code is used to execute the soft landing trajectory optimization method based on second-order cone preprocessing as described in any one of claims 1 to 8.

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