Aircraft large-scale trajectory planning method based on feature space point matching
By using the feature space collocation method, the accuracy, continuity, and convergence of large-scale flight trajectory planning are improved, the computational complexity is reduced, and rapid planning is achieved.
Patent Information
- Application Number
- CN202511384725.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-26
- Publication Date
- 2025-12-05
- Estimated Expiration
- 2045-09-26
AI Technical Summary
In existing technologies, as the scale of trajectory planning problems increases, the computation time for matrix inversion and decomposition in spline interpolation systems increases, resulting in low accuracy, poor continuity, and difficulty in convergence of large-scale flight trajectory planning. Furthermore, the computational complexity is high, making it difficult to achieve rapid planning.
The method based on feature space collocation is adopted. By setting the flight trajectory planning space, multiple flight trajectory spline functions are established. The optimal boundary value condition vector is obtained through the feature representation module. The flight trajectory of the aircraft is obtained.
It improves the accuracy, continuity, and convergence of large-scale flight trajectory planning, while reducing computational complexity and enabling rapid planning.
Smart Images
Figure CN120871980B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of unmanned aerial vehicle control, and particularly relates to a large-scale aerial vehicle trajectory planning method based on feature space point matching. BACKGROUND
[0002] With the continuous improvement of the intelligence level of aerial vehicles, the complexity of their flight tasks is increasing day by day. In order to complete complex flight tasks, aerial vehicles need to pass through a large number of task path points during flight, and the aerial vehicle trajectory planning method is required to generate a flight trajectory that passes through all the task path points. In addition, the spatial optimality and the temporal optimality of the trajectory need to be considered simultaneously in the trajectory optimization process to meet the requirements of flight efficiency and trajectory feasibility. The computational complexity of large-scale space-time trajectory optimization problems is high, and therefore, a basis function trajectory representation method can be used to convert the high-dimensional space-time optimization space of trajectory planning into a low-dimensional parameter optimization space of trajectory basis functions, thereby reducing the computational complexity. The trajectory optimization method using basis functions can be divided into global point matching method and local point matching method. The global point matching method can usually only achieve optimization of the total time of the flight trajectory, while the local point matching method can more flexibly achieve spatial interpolation of the task path points and local time optimization, and is more widely used in complex flight task trajectory planning.
[0003] The local point matching method uses spline basis functions to interpolate and fit the flight trajectory, realizes spatial optimization of the trajectory by optimizing high-order boundary conditions of the trajectory task points, realizes time optimization by optimizing the spline interpolation system matrix, and realizes the continuity of the flight trajectory by increasing the sectional coordination constraints at the task path points. Since the spline interpolation system matrix is a sick matrix, the numerical stability of the flight trajectory planning method based on the local point matching method deteriorates with the increase of the trajectory scale, resulting in low accuracy, poor continuity and convergence difficulty of large-scale flight trajectory planning. Although the closed-loop optimization of the spline interpolation system or the decomposition of the spline interpolation system matrix can reduce the numerical error to some extent, it cannot change the sick characteristics of the spline interpolation system matrix, and has limited improvement on the numerical stability of large-scale trajectory planning. In addition, with the increase of the scale of the trajectory planning problem, the calculation time of the closed-loop inversion and decomposition of the spline interpolation system matrix increases synchronously, and it is difficult to realize the rapid planning of large-scale flight trajectories. SUMMARY
[0004] In order to solve the above technical problems, the present application mainly aims at the problem that, in the prior art, the calculation time of closed loop inversion and decomposition of spline interpolation system matrix increases synchronously with the increase of the scale of trajectory planning problem, and it is difficult to realize rapid planning of large-scale flight trajectory. The present application provides a large-scale aircraft trajectory planning method based on feature space point matching, which is based on local point matching method, has optimal numerical stability, and obviously improves the accuracy, continuity and convergence of large-scale trajectory planning; at the same time, it has smaller calculation complexity, and obviously improves the speed of large-scale flight trajectory planning.
[0005] The purpose of the present application is to provide a large-scale aircraft trajectory planning method based on feature space point matching, comprising:
[0006] Setting a flight trajectory planning space;
[0007] According to the flight trajectory planning space, a multi-order multi-segment flight trajectory spline function is established;
[0008] According to each flight trajectory spline function, a spline basis function interpolation system of aircraft trajectory is established;
[0009] According to each flight trajectory spline function, based on time normalization, the normalized flight trajectory spline function of each segment is obtained;
[0010] According to the normalized flight trajectory spline function of each segment, the time and space characteristics of flight trajectory are obtained, and the feature representation form of the spline basis function interpolation system of aircraft trajectory is established;
[0011] According to the flight task, a target function of flight trajectory planning is established;
[0012] According to the time and space characteristics of flight trajectory, the target function of flight trajectory planning is represented, and the feature representation form of aircraft trajectory planning problem is obtained;
[0013] The feature representation form of aircraft trajectory planning problem is solved, and combined with the feature representation form of the spline basis function interpolation system of aircraft trajectory, the optimal boundary value condition vector in the trajectory feature space is obtained;
[0014] According to the optimal boundary value condition vector in the trajectory feature space, the optimal boundary value condition vector in the flight trajectory planning space is obtained;
[0015] According to the optimal boundary value condition vector in the flight trajectory planning space and the spline basis function interpolation system of aircraft trajectory, the flight trajectory of the aircraft is obtained.
[0016] Preferably, the spline basis function interpolation system of aircraft trajectory is established according to the following steps:
[0017] An interpolation system of each segment flight trajectory spline function is obtained according to the segment flight trajectory spline function;
[0018] An interpolation system of each segment flight trajectory spline function is obtained according to the segment flight trajectory spline function;
[0019] The interpolation system of each segment flight trajectory spline function is obtained according to the segment flight trajectory spline function;
[0020]
[0021] In the formula, is an interpolation matrix;
[0022] is a boundary value condition vector in a trajectory feature space; is a real number set; is an order of a flight trajectory; is a number of mission path points; r is a highest optimization order of a flight trajectory; is a parameter vector of a spline base function interpolation system of a flight trajectory.
[0023] Preferably, the characteristic representation form of the spline base function interpolation system of the flight trajectory is established according to the following steps:
[0024] A spline base function interpolation system of each segment normalized flight trajectory is obtained according to the normalized segment flight trajectory spline function;
[0025] A spline function interpolation system of each segment normalized trajectory is obtained by combining the spline base function interpolation system of each segment normalized flight trajectory at the normalized boundary;
[0026] The spline function interpolation system of each segment normalized trajectory is combined to establish a characteristic representation form of the spline base function interpolation system of the flight trajectory.
[0027] Preferably, the spline function interpolation system of each segment normalized trajectory is:
[0028]
[0029] In the formula, , respectively represent the transposition of the interpolation matrix , or ; , is a joint boundary condition vector when t and are normalized; represents the joint boundary condition vector in ; and a normalized boundary vector; a normalized parameter vector of the flight trajectory.
[0030] Preferably, the characteristic representation of the spline basis function interpolation system of the aircraft trajectory is characterized by:
[0031]
[0032] wherein, is a normalized interpolation matrix; is a boundary condition vector in the normalized trajectory characteristic space; is a normalized parameter vector of the spline basis function interpolation system of the aircraft trajectory.
[0033] Preferably, the objective function of the flight trajectory planning is as follows:
[0034]
[0035] wherein, is a cost function; is a weight of a time term in the objective function, which is a user-defined parameter; is a vector composed of time assignments of all m flight trajectories, wherein, , i =1, …, m; is a boundary vector; is a flight trajectory constraint region, is a feasible region of the trajectory j derivative, which is a user-defined constraint; is a norm operator; is a set of m-order positive real numbers; J is a sign of the objective function.
[0036] Preferably, a nonlinear optimizer is used to solve the characteristic representation of the aircraft trajectory planning problem.
[0037] Preferably, in the process of obtaining the flight trajectory of the aircraft, the following steps are included:
[0038] obtaining an inverse matrix of a matrix in the spline basis function interpolation system of the aircraft trajectory;
[0039] obtaining a normalized parameter vector of the spline basis function interpolation system of the aircraft trajectory according to the optimal boundary condition vector in the flight trajectory planning space and the inverse matrix;
[0040] obtaining the flight trajectory of the aircraft according to the normalized parameter vector of the spline basis function interpolation system of the aircraft trajectory.
[0041] The application also provides a large-scale aircraft trajectory planning system based on feature space point matching, comprising:
[0042] A function establishing module is configured to set a flight trajectory planning space, establish a multi-order multi-segment flight trajectory spline function according to the flight trajectory planning space, and establish a spline basis function interpolation system of the aircraft trajectory according to each flight trajectory spline function;
[0043] A feature characterization module is configured to obtain normalized flight trajectory spline functions according to each flight trajectory spline function based on time normalization, obtain time and space features of the flight trajectory according to the normalized flight trajectory spline functions, establish a feature characterization form of the spline basis function interpolation system of the aircraft trajectory, establish an objective function of the flight trajectory planning according to the flight mission, characterize the objective function of the flight trajectory planning according to the time and space features of the flight trajectory, and obtain a feature characterization form of the aircraft trajectory planning problem;
[0044] A boundary defining module is configured to solve the feature characterization form of the aircraft trajectory planning problem, obtain an optimal boundary value condition vector in a trajectory feature space in combination with the feature characterization form of the spline basis function interpolation system of the aircraft trajectory, and obtain an optimal boundary value condition vector in the flight trajectory planning space according to the optimal boundary value condition vector in the trajectory feature space;
[0045] A trajectory obtaining module is configured to obtain the flight trajectory of the aircraft according to the optimal boundary value condition vector in the flight trajectory planning space and the spline basis function interpolation system of the aircraft trajectory.
[0046] The application has at least the following beneficial effects:
[0047] The application provides a large-scale aircraft trajectory planning method based on feature space point matching, which is based on a local point matching method, establishes a spline basis function interpolation system of the aircraft trajectory, and extracts time and space features of the flight trajectory by using spectral characteristics of a trajectory spline system matrix, so that the spectral characteristics of the flight trajectory spline basis function interpolation system matrix are not changed with optimization of a local time of the trajectory, and optimal numerical stability is maintained, and the precision, continuity and convergence of the large-scale trajectory planning are obviously improved.
[0048] The flight trajectory spline basis function interpolation system matrix established in the method has a block diagonal structure, and the diagonal matrix blocks are the same, so that the method has smaller calculation complexity, and the speed of the large-scale flight trajectory planning is obviously improved. BRIEF DESCRIPTION OF DRAWINGS
[0049] Figure 1A feature space point-based aircraft large-scale trajectory planning method flowchart is provided.
[0050] Figure 2 A 20-path point flight trajectory without using feature space points.
[0051] Figure 3 A 20-path point flight trajectory using feature space points.
[0052] Figure 4 A 100-path point flight trajectory without using feature space points.
[0053] Figure 5 A 100-path point flight trajectory using feature space points.
[0054] Figure 6 A flight trajectory planning convergence process without using feature space points.
[0055] Figure 7 A flight trajectory planning convergence process using feature space points.
[0056] Figure 8 A flight trajectory planning calculation time comparison using and not using feature space points. DETAILED DESCRIPTION
[0057] In order to illustrate the technical means and effects adopted by the present application to achieve the predetermined object of the application, the following will be described in detail in combination with embodiments.
[0058] The present application aims to provide a feature space point-based aircraft large-scale trajectory planning method, mainly having an aircraft large-scale trajectory planning method with optimal numerical stability and smaller calculation complexity. The present application extracts the time and space characteristics of the flight trajectory by using the spectral characteristics of the trajectory spline system matrix, and performs point matching in the feature space of the flight trajectory, thereby improving the accuracy, continuity, convergence and speed of large-scale flight trajectory planning.
[0059] In order to achieve the above-mentioned object, a feature space point-based aircraft large-scale trajectory planning method comprises:
[0060] S1, setting a flight trajectory planning space;
[0061] According to the flight trajectory planning space, a multi-order multi-segment flight trajectory spline function is established;
[0062] According to each flight trajectory spline function, a spline basis function interpolation system of the aircraft trajectory is established;
[0063] The spline basis function interpolation system of the aircraft trajectory is established according to the following steps:
[0064] obtaining an interpolation system of each flight trajectory spline function according to each flight trajectory spline function;
[0065] obtaining a spline base function interpolation system of the aircraft trajectory by combining the interpolation systems of all the flight trajectory spline functions.
[0066] The spline base function interpolation system of the aircraft trajectory is:
[0067]
[0068] In the formula, is a block diagonal matrix;
[0069] is a boundary value condition vector in the trajectory feature space; is a real set; n is the order of the flight trajectory, for example, if a 5th order polynomial trajectory is selected, then n = 5; m is the number of task path points, for example, if the flight trajectory needs to pass through 7 path points, then m = 7; r is the highest optimization order of the flight trajectory, for example, if the highest order motion variable in the objective function and the constraint condition of the flight trajectory optimization is acceleration, then r = 2; is a parameter vector of the spline base function interpolation system of the aircraft trajectory.
[0070] S2, obtaining a normalized flight trajectory spline function according to each flight trajectory spline function based on time normalization;
[0071] According to the normalized flight trajectory spline function, the time and space characteristics of the flight trajectory are obtained, and a characteristic representation form of the spline base function interpolation system of the aircraft trajectory is established;
[0072] The characteristic representation form of the spline base function interpolation system of the aircraft trajectory is established according to the following steps:
[0073] obtaining a normalized flight trajectory spline base function interpolation system of each flight trajectory according to the normalized flight trajectory spline function;
[0074] combining the normalized flight trajectory spline base function interpolation systems of each flight trajectory at the normalized boundary to obtain a spline function interpolation system of each normalized trajectory;
[0075] combining the spline function interpolation systems of all the normalized trajectories to establish a characteristic representation form of the spline base function interpolation system of the aircraft trajectory.
[0076] The spline function interpolation system of each normalized trajectory is:
[0077]
[0078] wherein, respectively represent the interpolation matrix the transpose of t = 1 or -1 in , is a monomial basis vector, is the derivative of
[0079] , ,
[0080] is when ; is the derivative of the normalized flight trajectory with respect to the normalized time variable;
[0081] is the parameter vector of the normalized flight trajectory.
[0082] The characteristic representation form of the spline basis function interpolation system of the aircraft trajectory is:
[0083]
[0084] wherein, is a normalized interpolation matrix, including i block diagonal matrices, each of which is ;
[0085] is a boundary value condition vector in the normalized trajectory characteristic space; is the parameter vector of the spline basis function interpolation system of the normalized aircraft trajectory.
[0086] S3, establishing a target function of flight trajectory planning according to a flight task;
[0087] characterizing the target function of flight trajectory planning according to the time and space characteristics of the flight trajectory, and obtaining a characteristic representation form of the aircraft trajectory planning problem;
[0088] The target function of the flight trajectory planning is as follows:
[0089]
[0090] wherein, is a cost function; is the weight of the time item in the target function, which is a user-defined parameter; is a vector composed of the time allocation of all m flight trajectories, wherein, , i =1,…,m; is a boundary vector; is a flight trajectory constraint region, is a feasible region of the m-th derivative of the trajectory, j is a user-defined constraint; is a norm operator; is a set of m-order positive real numbers; J is a target function symbol.
[0091] S4, solve the characteristic representation form of the aircraft trajectory planning problem, and combine the characteristic representation form of the spline basis function interpolation system of the aircraft trajectory to obtain the optimal boundary value condition vector in the trajectory characteristic space;
[0092] According to the optimal boundary value condition vector in the trajectory characteristic space, obtain the optimal boundary value condition vector in the flight trajectory planning space;
[0093] The characteristic representation form of the aircraft trajectory planning problem is solved by using a nonlinear optimizer.
[0094] S5, according to the optimal boundary value condition vector in the flight trajectory planning space, and the spline basis function interpolation system of the aircraft trajectory, obtain the flight trajectory of the aircraft.
[0095] In the process of obtaining the flight trajectory of the aircraft, comprising:
[0096] Obtain the inverse matrix of the matrix in the spline basis function interpolation system of the aircraft trajectory;
[0097] According to the optimal boundary value condition vector in the flight trajectory planning space, and the inverse matrix of the matrix, obtain the spline basis function interpolation system parameter vector of the aircraft trajectory;
[0098] According to the spline basis function interpolation system parameter vector of the aircraft trajectory, obtain the flight trajectory of the aircraft.
[0099] In order to further illustrate the aircraft large-scale trajectory planning method based on feature space matching points provided by the application, it is described in combination with the drawings.
[0100] Referring to Figure 1 The aircraft large-scale trajectory planning method based on feature space matching points, comprising:
[0101] Step S1: clearly define the flight trajectory planning space, define the boundary value condition of the flight trajectory planning according to the aircraft task, and establish the spline basis function interpolation system of the aircraft trajectory;Step S1 specifically comprises:
[0102] Step S101: Using the output space of the aircraft system as the trajectory planning space, for each output quantity in the output space, establish an n-order, m-segment flight trajectory spline function, where m is the number of mission path points. The i-th segment of the flight trajectory spline function is expressed as:
[0103] (1)
[0104] In the formula, Let be the arrival time of the i-th task path point; For the first i The segment trajectory, where t is the trajectory time; It is the set of nth-order polynomials; For the first i The time range of the segment trajectory, lower limit upper limit .
[0105] It should be noted that the spline function representation of the flight trajectory describes the changes of the aircraft's position, velocity, acceleration and other states in three-dimensional space with time (or other parameters) through piecewise polynomials (spline functions). Its core is to use the piecewise smoothness and local controllability of spline functions to satisfy the dynamic constraints of the aircraft's motion (such as avoiding sudden changes in velocity and acceleration).
[0106] Step S102: The first in equation (1) i The j-th derivative of the spline function of the flight trajectory segment can be expressed as:
[0107] (2)
[0108] In the formula, ; It is the parameter vector of the spline function of the i-th flight trajectory segment; the superscript j indicates the order of the derivative; It is the set of real numbers; Let i be the time range of the i-th trajectory segment, with the lower limit being... upper limit .
[0109] Step S103: The derivatives from order 0 to r in equation (2) of step S102 are combined and expressed in the following vector form:
[0110] (3)
[0111] In the formula, For the interpolation matrix, This is the boundary condition vector.
[0112] Step S104: ... for and The joint interpolation matrix at each time step, and For and The boundary condition vector is introduced into equation (3) at the moment;
[0113] wherein, , , , Further, equation (3) in step S103 is solved at and to obtain the interpolation system of the i-th flight trajectory spline function:
[0114] (4)
[0115] Step S105: According to equation (4), the interpolation system of the first to m-th flight trajectory spline function is solved to obtain the joint interpolation system of all m flight trajectories:
[0116] (5)
[0117] wherein, is the joint interpolation matrix of all m trajectories, which is a block diagonal matrix, and the i-th diagonal block matrix is in step S104;
[0118] , represents the joint boundary condition vector of all m trajectories; is the joint parameter vector of all m trajectories, which is calculated by step S504.
[0119] Step S2: For the spline basis function interpolation system of the aircraft trajectory established in step S1, the time and space characteristics of the flight trajectory are extracted to obtain the boundary value condition in the trajectory characteristic space, and a characteristic representation form of the spline basis function interpolation system of the aircraft trajectory is established;
[0120] Step S2 specifically includes:
[0121] Step S201: Define as the normalized time interval, as the normalized time variable. And define the bijective as the time normalization function, wherein, , , .
[0122] Step S202: Based on the bijective defined in step S201, the following mapping can be further defined to realize the i-th normalized flight trajectory spline function:
[0123] (6)
[0124] where, is given by step S201; is the normalized flight trajectory spline function of the ith segment, which preserves the geometric characteristics of the original flight trajectory.
[0125] Step S203: j-th order differentiation of equation (6) in step S202 is performed to obtain:
[0126] (7)
[0127] where, is the normalized flight trajectory spline function with respect to the normalized time variable ; and is the -th power of -j ; and
[0128] Combining the 0-th to r-th order derivatives in equation (7) can be expressed as:
[0129] (7.b)
[0130] where, is the normalized boundary condition vector; diag{} represents a diagonal matrix, the superscripts 0, 1,..., r represent the powers, and the subscripts represent the ith segment of the trajectory. is half of the time interval , see step S201; is the boundary condition vector, see step S103.
[0131] Step S204: can be expressed in a form similar to equation (2), by replacing the time variable in equation (2) with , to obtain:
[0132] (8.a)
[0133] where, is the parameter vector of the normalized flight trajectory, which is optimized by step S402.
[0134] Combining the 0-th to r-th order derivatives in equation (8.a) can be expressed in the following vector form:
[0135] (8)
[0136] where, the expression of the interpolation matrix is the same as that of in equation (3), only replacing t with the normalized time variable ; is the normalized boundary condition vector, see equation (7.b).
[0137] Step S205: The equation (8) in step S204 is solved simultaneously at to obtain the spline function interpolation system of the i-th segment of the normalized trajectory:
[0138] (9)
[0139] wherein, , respectively represent the transpose of the interpolation matrix in, or ; , wherein, , is the parameter vector of the normalized flight trajectory; T represents the vector transpose.
[0140] Step S206: The equation (9) in step S205 is solved to obtain the normalized joint interpolation system of all m segments of the flight trajectory:
[0141] (10)
[0142] wherein, is the normalized joint interpolation matrix of all m segments of the trajectory, which is a block diagonal matrix, and all m diagonal block matrices are ;
[0143] represents the normalized joint boundary condition vector of all m segments of the trajectory; is the joint parameter vector of all m segments of the trajectory.
[0144] Step S3: Establishing the objective function of the flight trajectory planning according to the flight mission, and characterizing the objective function of the flight trajectory planning according to the time and space characteristics of the flight trajectory extracted in step S2, to establish the characteristic representation form of the aircraft trajectory planning problem;
[0145] Step S3 specifically includes:
[0146] Step S301: The objective function of the flight trajectory planning is established as:
[0147] (11)
[0148] wherein, is the cost function; is the weight of the time term in the objective function, which is a user-defined parameter; is the time allocation vector of all m flight segments, where, , i =1, …, m; is the boundary vector; is the flight trajectory constraint region; is the trajectory's j derivative feasible region, which is user-defined constraints.
[0149] Step S302: Substitute equation (7.b) into equation (11), then the characteristic representation of the aircraft trajectory planning objective function is:
[0150] (12)
[0151] where, where, is the normalized feasible region in step S301, and the specific form is: ; is the time allocation vector, see step S301;
[0152] Step S4: Solve the characteristic representation of the aircraft trajectory planning problem established in step S3 to obtain the optimal flight trajectory in the trajectory characteristic space;
[0153] Step S4 specifically includes:
[0154] Step S401: Substitute equation (8) in step S204 into equation (12) in step S302 to obtain:
[0155] (13)
[0156] where, is the cost function; is the weight of the time term in the objective function, which is a user-defined parameter; is the parameter vector of the normalized flight trajectory; is the derivative of the normalized flight trajectory; is the m derivative of the normalized flight trajectory; is the interpolation matrix when t = γ; is the norm operator;
[0157] Step S402: Use the user-selected nonlinear optimizer to solve the aircraft trajectory planning problem equation (13) in step S401 to obtain the optimal parameter vector of the normalized trajectory and the optimal time characteristic vector . Further, the optimal normalized segmented trajectory .
[0158] Step S403: Establishing the optimal boundary value condition vector in the feature space according to the definition in step S205 and step S206 , , , , .
[0159] Step S5: Solving the inverse matrix of the spline basis function interpolation system matrix of the aircraft trajectory established in step S1, projecting the optimal flight trajectory in the trajectory feature space obtained in step S4 to the aircraft trajectory planning space defined in step S1 to obtain the flight trajectory planning result of the aircraft.
[0160] Step S5 specifically includes:
[0161] Step S501: Based on the optimal time feature vector obtained in step S402 , using the definition in step S203, calculate the block matrix:
[0162] , i = 1, …, m (14)
[0163] Step S502: Based on the optimal boundary value condition vector in the feature space obtained in step S403 and the obtained in step S501 , calculate the optimal boundary value condition vector in the aircraft trajectory planning space .
[0164] Step S503: Calculate the inverse matrix of the spline basis function interpolation system matrix of the aircraft trajectory established in step S105 , the element of the qth row and the cth column is:
[0165] (15)
[0166] In the formula, is a quadratic elementary symmetric function, , , is a permutation combination operator;
[0167] (16)
[0168] In the formula, 0, , 1, , and The first one defined in step S101 i The lower and upper limits of the time range of the segment trajectory; r is the maximum order value of the boundary condition vector of the flight trajectory.
[0169] Step S504: Use the optimal boundary value vector obtained in step S502. The inverse matrix of the spline basis function interpolation system matrix obtained in step S503 The spline basis function interpolation system parameter vector for calculating the aircraft trajectory is: Then, the flight trajectory of the aircraft is obtained according to equation (2) in step S102.
[0170] This embodiment uses the linear quadratic shortest time trajectory planning problem of unmanned aerial vehicles as an example to illustrate a large-scale trajectory planning method for aircraft based on feature space collocation provided by the present invention.
[0171] In this embodiment, the time weight in the objective function of flight trajectory planning is 100, and the weight of the quadratic term is 1. The stopping condition for trajectory planning is that the gradient of the objective function in the interior point method is less than 10. -7 Or the change in the objective function is less than 10. -3 .
[0172] See Figure 2 The image shows the flight trajectory of 20 random flight path points planned by the local collocation method without using feature space collocation. (See [link to relevant documentation]). Figure 3 The image shows a flight trajectory planned using the feature space collocation method disclosed in this invention. (Comparison) Figure 2 and Figure 3 It can be seen that using feature space point allocation significantly improves the accuracy and continuity of flight trajectory planning.
[0173] See Figure 4 The image shows the flight trajectory of 100 random flight path points planned using the local collocation method without using feature space collocation. (See [link to relevant documentation]). Figure 5 The image shows a flight trajectory planned using the feature space collocation method disclosed in this invention. (Comparison) Figure 4 and Figure 5 It can be seen that using feature space point collocation significantly improves the accuracy and continuity of large-scale flight trajectory planning. (Comparison) Figure 4 and Figure 2 ,as well as Figure 5 and Figure 3 It can be seen that using feature space collocation significantly improves the numerical stability of flight trajectory planning.
[0174] See Figure 6 The image shows the convergence process of the optimized flight trajectories of the seven flight path points planned by the local collocation method without using the feature space collocation method. See also...Figure 7 As shown in the figure, it is an optimization convergence process of a flight trajectory planned by using the feature space collocation method. Figure 6 And Figure 7 It can be seen that the convergence of the flight trajectory planning by using the feature space collocation method is obviously improved.
[0175] Referring to Figure 8 As shown in the figure, it is the planning calculation time of flight trajectories of different scales without using the feature space collocation method and using the feature space collocation method. It can be seen that the speed of the large-scale flight trajectory planning by using the feature space collocation method provided by the present application is improved by nearly ten times.
[0176] The present application provides a large-scale trajectory planning system for aircraft based on feature space collocation, comprising:
[0177] The function establishing module is used for setting a flight trajectory planning space; establishing a multi-order multi-segment flight trajectory spline function according to the flight trajectory planning space; and establishing a spline basis function interpolation system of the aircraft trajectory according to each flight trajectory spline function.
[0178] The feature representation module is used for obtaining each normalized flight trajectory spline function based on time normalization according to each flight trajectory spline function; obtaining the time and space features of the flight trajectory and establishing a feature representation form of the spline basis function interpolation system of the aircraft trajectory according to each normalized flight trajectory spline function; establishing an objective function of the flight trajectory planning according to the flight task; representing the objective function of the flight trajectory planning according to the time and space features of the flight trajectory, and obtaining a feature representation form of the aircraft trajectory planning problem;
[0179] The boundary defining module is used for solving the feature representation form of the aircraft trajectory planning problem, and obtaining an optimal boundary value condition vector in the trajectory feature space in combination with the feature representation form of the spline basis function interpolation system of the aircraft trajectory; and obtaining an optimal boundary value condition vector in the flight trajectory planning space according to the optimal boundary value condition vector in the trajectory feature space.
[0180] The trajectory obtaining module is used for obtaining the flight trajectory of the aircraft according to the optimal boundary value condition vector in the flight trajectory planning space and the spline basis function interpolation system of the aircraft trajectory.
[0181] The above only describes the preferred embodiments of the present application, and is not used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the principles of the present application shall be included in the protection scope of the present application.
Claims
1. A method for large-scale trajectory planning of an aircraft based on feature space matching, characterized in that, The method comprises the following steps: setting a flight trajectory planning space; establishing a multi-order multi-segment flight trajectory spline function according to the flight trajectory planning space; establishing a spline basis function interpolation system of the aircraft trajectory according to each segment of the flight trajectory spline function; obtaining a normalized flight trajectory spline function of each segment according to each segment of the flight trajectory spline function based on time normalization; obtaining time and space characteristics of the flight trajectory and establishing a characteristic representation form of the spline basis function interpolation system of the aircraft trajectory according to the normalized flight trajectory spline function of each segment; establishing a target function of the flight trajectory planning according to the flight task; characterizing the target function of the flight trajectory planning according to the time and space characteristics of the flight trajectory, and obtaining a characteristic representation form of the aircraft trajectory planning problem; solving the characteristic representation form of the aircraft trajectory planning problem, and combining the characteristic representation form of the spline basis function interpolation system of the aircraft trajectory to obtain an optimal boundary value condition vector in a trajectory characteristic space; obtaining an optimal boundary value condition vector in the flight trajectory planning space according to the optimal boundary value condition vector in the trajectory characteristic space; obtaining the flight trajectory of the aircraft according to the optimal boundary value condition vector in the flight trajectory planning space and the spline basis function interpolation system of the aircraft trajectory. The spline basis function interpolation system of the aircraft trajectory is established according to the following steps: obtaining an interpolation system of each segment of the flight trajectory spline function according to each segment of the flight trajectory spline function; combining the interpolation systems of all segments of the flight trajectory spline function to obtain the spline basis function interpolation system of the aircraft trajectory. The spline basis function interpolation system of the aircraft trajectory is as follows: wherein is an interpolation matrix; is a boundary value condition vector within the trajectory feature space; is a real number set; is an order of the flight trajectory; is a number of mission waypoints; r is a highest optimization order of the flight trajectory; is a parameter vector of a spline basis function interpolation system of the aircraft trajectory; The characteristic representation form of the spline basis function interpolation system of the aircraft trajectory is established according to the following steps: obtaining a normalized spline basis function interpolation system of each segment of the aircraft trajectory according to the normalized flight trajectory spline function of each segment; combining the normalized spline basis function interpolation systems of each segment of the aircraft trajectory at the normalized boundaries to obtain a spline function interpolation system of each normalized trajectory; combining the spline function interpolation systems of all segments of the normalized trajectory to establish the characteristic representation form of the spline basis function interpolation system of the aircraft trajectory.
2. The feature space based aircraft large scale trajectory planning method of claim 1, wherein, The spline function interpolation system of each normalized trajectory is as follows: wherein , denote the interpolation matrix , or its transpose; , is the normalized and momentary joint boundary condition vector; denotes the normalized boundary vector at time is the normalized parameter vector of the flight trajectory.
3. The feature space based aircraft large scale trajectory planning method of claim 2, wherein, The characteristic representation form of the spline basis function interpolation system of the aircraft trajectory is as follows: wherein is the normalized interpolation matrix; is the boundary value condition vector in the normalized trajectory feature space; is the spline basis function interpolation system parameter vector of the normalized aircraft trajectory.
4. The feature space based aircraft large scale trajectory planning method of claim 1, wherein, The target function of the flight trajectory planning is as follows: wherein, is a cost function; is a weight of the time term in the objective function, is a user-defined parameter; is a vector of time assignments of all m flight trajectories, wherein, , i = 1,..., m; is a boundary vector; is a flight trajectory constraint region, is a feasible region of the trajectory's j derivative, is a user-defined constraint; is a norm operator; is a set of m-order positive real numbers; J is a sign of the objective function.
5. The feature space based point matching method for large scale aircraft trajectory planning according to claim 1, wherein, The characteristic representation form of the aircraft trajectory planning problem is solved by using a nonlinear optimizer.
6. The feature space point matching based aircraft large scale trajectory planning method of claim 1, wherein, In the process of obtaining the flight trajectory of the aircraft, the following steps are included: obtaining an inverse matrix of a matrix in the spline basis function interpolation system of the aircraft trajectory; obtaining a spline basis function interpolation system parameter vector of the aircraft trajectory according to the optimal boundary value condition vector in the flight trajectory planning space and the inverse matrix; obtaining the flight trajectory of the aircraft according to the spline basis function interpolation system parameter vector of the aircraft trajectory.
7. An aircraft large-scale trajectory planning system based on feature space collocation, characterized in that, The method comprises the following steps: The function establishing module is configured to set a flight trajectory planning space, establish a multi-order multi-segment flight trajectory spline function according to the flight trajectory planning space, and establish a spline base function interpolation system of the aircraft trajectory according to each flight trajectory spline function; The characteristic representation module is configured to obtain normalized flight trajectory spline functions according to each flight trajectory spline function based on time normalization, obtain time and space characteristics of the flight trajectory according to the normalized flight trajectory spline functions, establish a characteristic representation form of the spline base function interpolation system of the aircraft trajectory, establish a flight trajectory planning objective function according to a flight task, represent the flight trajectory planning objective function according to the time and space characteristics of the flight trajectory, and obtain a characteristic representation form of the aircraft trajectory planning problem; The boundary defining module is configured to solve the characteristic representation form of the aircraft trajectory planning problem, obtain an optimal boundary value condition vector in a trajectory characteristic space in combination with the characteristic representation form of the spline base function interpolation system of the aircraft trajectory, and obtain an optimal boundary value condition vector in the flight trajectory planning space according to the optimal boundary value condition vector in the trajectory characteristic space; The trajectory obtaining module is configured to obtain the flight trajectory of the aircraft according to the optimal boundary value condition vector in the flight trajectory planning space and the spline base function interpolation system of the aircraft trajectory.
Citation Information
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