Real-time trajectory planning method for unmanned transport aircraft based on spatiotemporal bi-level planning algorithm
Patent Information
- Application Number
- CN202411300997.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-18
- Publication Date
- 2025-02-11
- Estimated Expiration
- 2044-09-18
Smart Images

Figure CN118816896B_ABST
Abstract
Description
Technical Field
[0001] The embodiments of the present invention relate to the field of control technology, and in particular to a real-time trajectory planning method for an unmanned transport aircraft based on a spatiotemporal double-layer planning algorithm. Background Art
[0002] At present, with the continuous development of modern information technology, drones have gradually spread from military applications to civilian fields. Now, civilian drones of various models and functions have been widely used in all walks of life, such as aerial photography, agricultural assistance, and inspection, making people's lives more enriched and convenient.
[0003] However, before unmanned transport aircraft are officially put on the market on a large scale, there are some problems that need to be solved urgently, especially the issue of flight safety. Compared with the civil aviation transportation industry, before the flight, all aircraft, including those in flight and waiting to fly, will be uniformly planned for the trajectory. During the flight, pilots will also use radar and ground commands to flexibly operate in response to various emergencies. While drones reduce a lot of manpower consumption, they also bring a lot of uncertainty. Since a complete air flight traffic system has not yet been formed, if it is not fully planned in advance, it is easy to cause safety hazards, especially the safety of ground personnel.
[0004] It can be seen that there is an urgent need for a real-time trajectory planning method for unmanned transport aircraft based on a spatiotemporal double-layer planning algorithm with high planning efficiency, adaptability and safety. Summary of the invention
[0005] In view of this, an embodiment of the present invention provides a real-time trajectory planning method for an unmanned transport aircraft based on a spatiotemporal dual-layer planning algorithm, which at least partially solves the problems of poor planning efficiency, adaptability and safety in the prior art.
[0006] The embodiment of the present invention provides a real-time trajectory planning method for an unmanned transport aircraft based on a spatiotemporal dual-layer planning algorithm, comprising:
[0007] Step 1, establishing a flight environment model for a large unmanned transport aircraft;
[0008] Step 2, establishing an optimal control model for trajectory optimization based on the flight dynamics constraints and process constraint model of the large unmanned transport aircraft;
[0009] Step 3, based on the flight environment model and optimal control model of the large unmanned transport aircraft, a spatiotemporal bi-level programming algorithm is used to solve the large unmanned transport aircraft trajectory planning problem in real time;
[0010] Step 4: To solve the track mutation problem within the target range neighborhood of the track node, the B-spline curve method is used to smooth the track within the target range.
[0011] According to a specific implementation of the embodiment of the present invention, step 1 specifically includes:
[0012] Step 1.1, use the grid method to divide the three-dimensional flight environment of the large unmanned transport aircraft so that each node can freely expand to the surrounding feasible area;
[0013] Step 1.2, according to the actual flight environment, use the function simulation method to create columnar obstacles, conical obstacles and cylindrical obstacles of different specifications, set the grid cost of the obstacle-free area to 1, and set the grid cost of the obstacle area to infinity.
[0014] According to a specific implementation of the embodiment of the present invention, step 2 specifically includes:
[0015] Step 2.1, establish the dynamics and kinematics equations of the large unmanned transport aircraft, and define its state matrix and input matrix as
[0016] ;
[0017] Among them, x, y and h represent the displacement of the UAV along the three axes of the inertial reference coordinate system, V represents the flight speed, and θ represents the track inclination angle. represents the track deviation angle, represents the flight angle of attack, σ represents the flight bank angle, and T represents the transpose of the matrix;
[0018] Step 2.2, establish the flight dynamics constraint and process constraint model of the large unmanned transport aircraft, wherein the expression of the flight dynamics constraint of the large unmanned transport aircraft is:
[0019] ;
[0020] in, , , , , as well as They represent the derivatives of each state quantity, L and D represent the aerodynamic lift and drag on the drone, P represents the engine thrust on the drone, m represents the mass of the drone, g represents the acceleration of gravity, and r represents the radius vector of the earth's center;
[0021] The process constraint model includes control quantity constraint and obstacle constraint, wherein the expression of the control quantity constraint is:
[0022] ;
[0023] in, and Represents the flight angle of attack The lower and upper limits of σ min and σ max Respectively represent the lower and upper limits of the roll angle σ;
[0024] The expression of the obstacle constraint is:
[0025] ;
[0026] Among them, (x cur , y cur , h cur ) and (x obs , y obs , h obs ) represent the current coordinates of the drone and the center coordinates of the obstacle in the current height plane, d represents the Euclidean distance between the current position of the drone and the center of the obstacle, R max Represents the maximum distance between the obstacle center and the boundary in all height planes, ε is a number greater than 1;
[0027] Step 2.3, based on the dynamics and kinematics equations and the process constraint model, establish the optimal control model for trajectory optimization of the large unmanned transport aircraft, where the expression of the optimal control model is:
[0028] ;
[0029] in, represents the endpoint cost function, g(x) represents the Lagrangian cost function, t represents time, t0 represents the initial time, t f represents the terminal time, x represents the state matrix, f represents the state equation, u represents the control matrix, represents the derivative of the state matrix, represents the end constraint equation, represents the constraint equation between obstacles and control quantities, and J is the objective function.
[0030] According to a specific implementation of the embodiment of the present invention, step 3 specifically includes:
[0031] Step 3.1, considering only obstacle constraints, select the distance function as The algorithm cost function, the outer layer is based on the space domain and flight environment model The algorithm quickly plans a shortest path, wherein the distance function is any one of the Euclidean distance, the Manhattan distance and the Minkowski distance;
[0032] Step 3.2, according to the optimal control model of trajectory planning and The track node information obtained by algorithm planning is used in the inner layer to parallelly calculate the optimal trajectory within each sub-interval composed of adjacent track nodes using the adaptive Radau pseudo-spectral method based on the time domain.
[0033] According to a specific implementation of the embodiment of the present invention, step 4 specifically includes:
[0034] Step 4.1, determine the order k and control point set u of the B-spline curve, and determine the form of the basis function;
[0035] Step 4.2, smoothing the flight track within a small neighborhood of the track node according to the B-spline curve equation;
[0036] Step 4.3, by adjusting the radius of the track node neighborhood, an iterative algorithm is used to obtain the optimal B-spline curve smoothing result.
[0037] The real-time trajectory planning scheme of an unmanned transport aircraft based on a spatiotemporal double-layer programming algorithm in an embodiment of the present invention includes: step 1, establishing a flight environment model of a large unmanned transport aircraft; step 2, establishing an optimal control model for trajectory optimization based on the flight dynamics constraints and process constraint models of the large unmanned transport aircraft; step 3, using a spatiotemporal double-layer programming algorithm to solve the trajectory planning problem of the large unmanned transport aircraft in real time based on the flight environment model and the optimal control model of the large unmanned transport aircraft; step 4, using a B-spline curve method to smooth the trajectory within the target range of the track node in order to solve the track mutation problem within the target range neighborhood.
[0038] The beneficial effects of the embodiments of the present invention are as follows: through the scheme of the present invention, a spatiotemporal double-layer programming algorithm is proposed to solve the real-time trajectory planning problem of large unmanned transport aircraft, wherein the outer layer is based on the spatial domain and adopts The algorithm quickly plans a shortest path and provides track node information. The inner layer uses the adaptive Radau pseudo-spectral method based on the time domain to plan the trajectory in parallel within each track node interval, so as to improve the track planning speed and enable the UAV to meet many process constraints during flight. The B-spline curve method is used to solve the problem of uneven track in a small neighborhood of the node. In order to solve the problem that the smoothed track may cross terrain obstacles, an iterative algorithm is used to optimize the neighborhood radius, thereby improving planning efficiency, adaptability and safety. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0040] Figure 1 A schematic flow chart of a method for real-time trajectory planning of an unmanned transport aircraft based on a spatiotemporal dual-layer planning algorithm provided by an embodiment of the present invention;
[0041] Figure 2 A B-spline curve optimization flow chart provided in an embodiment of the present invention;
[0042] Figure 3 A flow chart of a spatiotemporal dual-level programming algorithm provided by an embodiment of the present invention;
[0043] Figure 4 A schematic diagram of three-dimensional grid division provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0044] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.
[0045] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.
[0046] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present invention, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.
[0047] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention. The drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.
[0048] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.
[0049] An embodiment of the present invention provides a real-time trajectory planning method for an unmanned transport aircraft based on a spatiotemporal double-layer planning algorithm. The method can be applied to the trajectory planning process of scenarios such as unmanned aerial vehicle aerial photography, agricultural assistance, and inspection.
[0050] See also Figure 1 , is a flow chart of an aerial photography, agricultural assistance and inspection method provided by an embodiment of the present invention. Figure 1 As shown, the method mainly comprises the following steps:
[0051] Step 1, establishing a flight environment model for a large unmanned transport aircraft;
[0052] Furthermore, the step 1 specifically includes:
[0053] Step 1.1, use the grid method to divide the three-dimensional flight environment of the large unmanned transport aircraft so that each node can freely expand to the surrounding feasible area;
[0054] Step 1.2, according to the actual flight environment, use the function simulation method to create columnar obstacles, conical obstacles and cylindrical obstacles of different specifications, set the grid cost of the obstacle-free area to 1, and set the grid cost of the obstacle area to infinity.
[0055] In the specific implementation, first, the grid method can be used to divide the three-dimensional flight environment of the large unmanned transport aircraft. The three-dimensional grid division result is as follows: Figure 4 As shown, each node can be freely expanded to the surrounding feasible area. Secondly, according to the real flight environment, the function simulation method is used to create columnar obstacles, conical obstacles, and cylindrical obstacles of different sizes, and the grid cost of the obstacle-free area is set to 1, and the grid cost of the obstacle area is set to infinity.
[0056] Step 2, establishing an optimal control model for trajectory optimization based on the flight dynamics constraints and process constraint model of the large unmanned transport aircraft;
[0057] Based on the above embodiment, step 2 specifically includes:
[0058] Step 2.1, establish the dynamics and kinematics equations of the large unmanned transport aircraft, and define its state matrix and input matrix as
[0059] ;
[0060] Among them, x, y and h represent the displacement of the UAV along the three axes of the inertial reference coordinate system, V represents the flight speed, and θ represents the track inclination angle. represents the track deviation angle, represents the flight angle of attack, σ represents the flight bank angle, and T represents the transpose of the matrix;
[0061] Step 2.2, establish the flight dynamics constraint and process constraint model of the large unmanned transport aircraft, wherein the expression of the flight dynamics constraint of the large unmanned transport aircraft is:
[0062] ;
[0063] in, , , , , as well as They represent the derivatives of each state quantity, L and D represent the aerodynamic lift and drag on the drone, P represents the engine thrust on the drone, m represents the mass of the drone, g represents the acceleration of gravity, and r represents the radius vector of the earth's center;
[0064] The process constraint model includes control quantity constraint and obstacle constraint, wherein the expression of the control quantity constraint is:
[0065] ;
[0066] in, and Represents the flight angle of attack The lower and upper limits of σ min and σ max Respectively represent the lower and upper limits of the roll angle σ;
[0067] The expression of the obstacle constraint is:
[0068] ;
[0069] Among them, (x cur , y cur , h cur ) and (x obs , y obs , h obs ) represent the current coordinates of the drone and the center coordinates of the obstacle in the current height plane, d represents the Euclidean distance between the current position of the drone and the center of the obstacle, R max Represents the maximum distance between the obstacle center and the boundary in all height planes, ε is a number greater than 1;
[0070] Step 2.3, based on the dynamics and kinematics equations and the process constraint model, establish the optimal control model for trajectory optimization of large unmanned transport aircraft, where the expression of the optimal control model is:
[0071] ;
[0072] in, represents the endpoint cost function, g(x) represents the Lagrangian cost function, t represents time, t0 represents the initial time, t f represents the terminal time, x represents the state matrix, f represents the state equation, u represents the control matrix, represents the derivative of the state matrix, represents the end constraint equation, represents the constraint equation between obstacles and control quantities, and J is the objective function.
[0073] In the specific implementation, first, the dynamics and kinematics equations of the large unmanned transport aircraft can be established, and its state matrix and input matrix can be defined as follows:
[0074]
[0075] According to the dynamic analysis, the flight dynamics constraints of large unmanned transport aircraft are established as follows:
[0076] ;
[0077] in, , , , , as well as They represent the derivatives of each state quantity, L and D represent the aerodynamic lift and drag on the drone, P represents the engine thrust on the drone, m represents the mass of the drone, g represents the acceleration of gravity, and r represents the radius vector of the earth's center;
[0078] Secondly, a process constraint model of a large unmanned transport aircraft is established, which mainly includes control quantity constraints and obstacle constraints. The control quantity constraints are as follows:
[0079] ;
[0080] in, and Represents the flight angle of attack The lower and upper limits of σ min and σ max Represent the lower and upper limits of the roll angle σ respectively. The mathematical description of the obstacle constraint is as follows:
[0081] ;
[0082] Among them, (x cur , y cur , h cur ) and (x obs , y obs , h obs ) represent the current coordinates of the drone and the center coordinates of the obstacle in the current height plane, d represents the Euclidean distance between the current position of the drone and the center of the obstacle, R max Represents the maximum distance between the center of the obstacle and the boundary in all height planes, and ε is a number greater than 1.
[0083] Finally, according to the above constraints, the optimal control model for trajectory optimization of large unmanned transport aircraft is established as follows:
[0084] ;
[0085] Among them, x ini represents the initial state, x end Represents the terminal state, J is the objective function, and the essence of solving the optimal control problem is to find a set of control quantities that minimizes the objective function while satisfying the given constraints.
[0086] Step 3, based on the flight environment model and optimal control model of the large unmanned transport aircraft, a spatiotemporal bi-level programming algorithm is used to solve the large unmanned transport aircraft trajectory planning problem in real time;
[0087] Based on the above embodiment, step 3 specifically includes:
[0088] Step 3.1, considering only obstacle constraints, select the distance function as The algorithm cost function, the outer layer is based on the space domain and flight environment model The algorithm quickly plans a shortest path, wherein the distance function is any one of the Euclidean distance, the Manhattan distance and the Minkowski distance;
[0089] Step 3.2, according to the optimal control model of trajectory planning and The track node information obtained by algorithm planning is used in the inner layer to parallelly calculate the optimal trajectory within each sub-interval composed of adjacent track nodes using the adaptive Radau pseudo-spectral method based on the time domain.
[0090] In the specific implementation, firstly, only obstacle constraints are considered, and the outer layer is based on the space domain and flight environment model. The algorithm quickly plans a shortest flight path that provides track node information. To ensure the optimality of the planned path, it is crucial to design a reasonable cost function f(n). Since the planning goal is to find the shortest flight path, a distance function is selected as the cost function. Common distance functions include Euclidean distance:
[0091] ;
[0092] Manhattan distance:
[0093] ;
[0094] Minkowski distance:
[0095] ;
[0096] The Minkowski distance is a balance between the first two. When p=2, the Minkowski distance becomes the Euclidean distance, and when p=1, the Minkowski distance becomes the Manhattan distance.
[0097] Based on the flight environment modeling results of large unmanned transport aircraft, the present invention adopts the Euclidean distance function as The cost function of the algorithm is:
[0098] ;
[0099] Among them, (x cur , y cur , h cur ) and (x f , y f , h f ) represent the current coordinates and the end coordinates of the drone, respectively. g(n) is the minimum cost from the initial state to state n in the state space. The specific implementation steps of the algorithm are as follows:
[0100] Step 1: Initialize the flight starting point s and the end point f, create two lists, Open and Close, to store the points that can be expanded and the points that have been expanded respectively, and take the starting point s as the parent node;
[0101] Step 2: Add all the child nodes whose parent nodes are expandable and not stored in the Open and Close tables to the Open list, and check whether the end point f exists in the Open list. If so, output the final result. If not, proceed to the next step.
[0102] Step 3: Sort all nodes in the Open list according to the cost function;
[0103] Step 4: Take the best node in the Open list as the next parent node, move it to the Close list, and return to Step 2 for calculation;
[0104] At this point, the outer layer of large unmanned transport aircraft path planning based on the space domain is completed. However, during the flight of the large unmanned transport aircraft, many process constraints such as dynamic constraints and control quantity constraints must be met. The algorithm cannot handle these constraints well, and the path it plans has problems such as frequent turns and exceeding the maximum turning and climbing constraints of the drone itself. To solve this problem, the present invention uses the optimal control model and The track node information obtained by algorithm planning uses the adaptive Radau pseudo-spectral method in the time domain to parallelly calculate the optimal trajectory within each sub-interval composed of adjacent track nodes in the inner layer. By segmenting the time domain within these sub-intervals and using the Radau pseudo-spectral method in the segmented time segments, the state quantity and control quantity are discretely assigned points according to their corresponding point assignment rules, and Lagrange interpolation polynomials are constructed at discrete points to approximate the actual control quantity and state quantity. In order to meet the requirements of calculation accuracy, the two parameters h, the number of points in the segmented time segments and the order p of the selected Lagrange interpolation polynomial can be adaptively adjusted. The calculation steps are as follows:
[0105] Step 1: Set the number of initial points and the order of the initial polynomial;
[0106] Step 2: Use the Radau pseudo-spectral method to transform the optimal control problem within the interval composed of adjacent track nodes into a nonlinear programming problem and solve it;
[0107] Step 3: Calculate the error between the state quantity and the constraint. If the error is within the allowable range, output the calculation result.
[0108] Step 4: If the error exceeds the allowable range, increase the number of matching points or the order of the Lagrange interpolation polynomial and return to Step 2 for calculation.
[0109] The above optimal control problem based on time domain is solved in parallel within each interval formed by adjacent track nodes, which greatly improves the computational efficiency. max When , re-plan the outer path;
[0110] Step 4: To solve the track mutation problem within the target range neighborhood of the track node, the B-spline curve method is used to smooth the track within the target range.
[0111] Based on the above embodiment, step 4 specifically includes:
[0112] Step 4.1, determine the order k and control point set u of the B-spline curve, and determine the form of the basis function;
[0113] Step 4.2, smoothing the flight track within a small neighborhood of the track node according to the B-spline curve equation;
[0114] Step 4.3, by adjusting the neighborhood radius of the track node, an iterative algorithm is used to obtain the optimal B-spline curve smoothing result.
[0115] When implementing it, Figure 2 and Figure 3 As shown, first, determine the order k of the B-spline curve and the control point set u, and determine the basis function according to the following de Boor-Cox recursion formula:
[0116] ;
[0117] Among them, u represents the parameter value, indicating that the control point on the curve is to be calculated, and u i represents the parameter value of the ith control point, B i,k (u) represents the point on the B-spline curve at parameter value u, where i is the index of the control point and k is the degree of the curve, which affects the recursive depth of the B-spline basis function. Secondly, the B-spline curve in a small neighborhood of the track node is calculated according to the following formula to make the original track smoother.
[0118] ;
[0119] Among them, p(u) represents the point on the B-spline curve at the control point u, P i Represents the i-th control point. Finally, to ensure that the smoothed track can still avoid obstacles, the optimal B-spline curve smoothing result is obtained by adjusting the neighborhood radius of the track node and using an iterative algorithm.
[0120] The real-time trajectory planning method for unmanned transport aircraft based on a spatiotemporal double-layer planning algorithm provided in this embodiment solves the real-time trajectory planning problem of large unmanned transport aircraft by proposing a spatiotemporal double-layer planning algorithm, wherein the outer layer adopts an A* algorithm based on the spatial domain to quickly plan a shortest path and provide trajectory node information, and the inner layer adopts an adaptive Radau pseudo-spectral method based on the time domain to plan the trajectory in parallel within each trajectory node interval, thereby improving the trajectory planning speed and enabling the unmanned aircraft to meet many process constraints during flight; the B-spline curve method is used to solve the problem of uneven trajectory within a small neighborhood of the node, and in view of the problem that the smoothed trajectory may cross terrain obstacles, an iterative algorithm is used to optimize the neighborhood radius, thereby improving planning efficiency, adaptability and safety.
[0121] It should be understood that various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof.
[0122] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims
1. A real-time trajectory planning method for an unmanned transport aircraft based on a spatiotemporal dual-layer planning algorithm, characterized in that: include: Step 1, establishing a flight environment model for a large unmanned transport aircraft; Step 2, establishing an optimal control model for trajectory optimization based on the flight dynamics constraints and process constraint model of the large unmanned transport aircraft; Step 3, based on the flight environment model and optimal control model of the large unmanned transport aircraft, a spatiotemporal bi-level programming algorithm is used to solve the large unmanned transport aircraft trajectory planning problem in real time; The step 3 specifically includes: Step 3.1, considering only obstacle constraints, select the distance function as The algorithm cost function, the outer layer is based on the space domain and flight environment model The algorithm quickly plans a shortest path, wherein the distance function is any one of the Euclidean distance, the Manhattan distance and the Minkowski distance; Step 3.2, according to the optimal control model of trajectory planning and The track node information obtained by algorithm planning uses the adaptive Radau pseudo-spectral method based on the time domain to parallelly calculate the optimal trajectory within each sub-interval composed of adjacent track nodes; Step 4, in order to solve the track mutation problem within the target range neighborhood of the track node, the B-spline curve method is used to smooth the track within the target range; The step 4 specifically includes: Step 4.1, determine the order k and control point set u of the B-spline curve, and determine the form of the basis function; Step 4.2, smoothing the flight track within a small neighborhood of the track node according to the B-spline curve equation; Step 4.3, by adjusting the radius of the track node neighborhood, an iterative algorithm is used to obtain the optimal B-spline curve smoothing result.
2. The method according to claim 1, characterized in that , the step 1 specifically includes: Step 1.1, use the grid method to divide the three-dimensional flight environment of the large unmanned transport aircraft so that each node can freely expand to the surrounding feasible area; Step 1.2, according to the actual flight environment, use the function simulation method to create columnar obstacles, conical obstacles and cylindrical obstacles of different specifications, set the grid cost of the obstacle-free area to 1, and set the grid cost of the obstacle area to infinity.
3. The method according to claim 2, characterized in that , the step 2 specifically includes: Step 2.1, establish the dynamics and kinematics equations of the large unmanned transport aircraft, and define its state matrix and input matrix as ; Among them, x, y and h represent the displacement of the UAV along the three axes of the inertial reference coordinate system, V represents the flight speed, and θ represents the track inclination angle. represents the track deviation angle, represents the flight angle of attack, σ represents the flight bank angle, and T represents the transpose of the matrix; Step 2.2, establish the flight dynamics constraint and process constraint model of the large unmanned transport aircraft, wherein the expression of the flight dynamics constraint of the large unmanned transport aircraft is: ; in, , , , , as well as They represent the derivatives of each state quantity, L and D represent the aerodynamic lift and drag on the drone, P represents the engine thrust on the drone, m represents the mass of the drone, g represents the acceleration of gravity, and r represents the radius vector of the earth's center; The process constraint model includes control quantity constraint and obstacle constraint, wherein the expression of the control quantity constraint is: ; in, and Represents the flight angle of attack The lower and upper limits of σ min and σ max Respectively represent the lower and upper limits of the roll angle σ; The expression of the obstacle constraint is: ; Among them, (x cur , y cur , h cur ) and (x obs , y obs , h obs ) represent the current coordinates of the drone and the center coordinates of the obstacle in the current height plane, d represents the Euclidean distance between the current position of the drone and the center of the obstacle, R max Represents the maximum distance between the center of the obstacle and the boundary in all height planes, ε is a number greater than 1; Step 2.3, based on the dynamics and kinematics equations and the process constraint model, establish the optimal control model for trajectory optimization of the large unmanned transport aircraft, where the expression of the optimal control model is: ; in, represents the endpoint cost function, g(x) represents the Lagrangian cost function, t represents time, t0 represents the initial time, t f represents the terminal time, x represents the state matrix, f represents the state equation, u represents the control matrix, represents the derivative of the state matrix, represents the end constraint equation, represents the constraint equation between obstacles and control quantities, and J is the objective function.
Citation Information
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Hypersonic aircraft double-layer trajectory planning method based on pseudo-spectral method
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