Paragliding system trajectory planning method, device and equipment based on interval spline wavelet
By transforming the trajectory planning of the paraglider system into a nonlinear programming problem, and utilizing interval spline wavelet basis functions and wavelet coefficients, the problems of low computational efficiency and difficulty in satisfying constraints in traditional methods are solved, thus achieving efficient and accurate trajectory planning.
Patent Information
- Application Number
- CN202511260044.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-04
- Publication Date
- 2025-12-23
- Estimated Expiration
- 2045-09-04
AI Technical Summary
Traditional trajectory optimization methods are computationally inefficient in aircraft trajectory planning, struggle to meet endpoint constraints, and are poorly adaptable to trajectory changes. They are particularly difficult to achieve real-time planning and high accuracy in the high-dynamic scenarios of paraglider systems.
The trajectory planning process of the paraglider system is transformed from an optimal control problem into a nonlinear programming problem. By establishing interval spline wavelet basis functions and constructing wavelet coefficient forms, the trajectory planning results are solved using a nonlinear programming algorithm.
It significantly reduces computational dimensionality, strictly satisfies endpoint constraints, and adaptively captures trajectory mutations, thereby improving the speed, accuracy, and robustness of paraglider trajectory planning.
Smart Images
Figure CN120740614B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of aircraft trajectory optimization, and particularly relates to a wing-sail system trajectory planning method, device and equipment based on interval spline wavelet. BACKGROUND
[0002] Traditional trajectory optimization methods (such as pseudospectral method) take the values of state / control variables at discrete time points as optimization parameters, which results in: 1. high variable dimension and low computational efficiency; 2. difficulty in accurately satisfying trajectory endpoint constraints (such as specified landing pose); 3. poor adaptability to trajectory mutation. These defects seriously restrict real-time planning capability and end accuracy in the field of aircraft trajectory optimization, especially in high dynamic scenarios such as wing-sail system, existing methods are difficult to optimize computational efficiency and constraint satisfaction simultaneously. SUMMARY
[0003] In view of the above deficiencies in the prior art, the present application provides a wing-sail system trajectory planning method, device and equipment based on interval spline wavelet, which converts the trajectory planning process of the wing-sail system from an original optimal control problem to a nonlinear programming problem based on interval spline wavelet, thereby effectively realizing a coordinated breakthrough in speed, accuracy and robustness of wing-sail trajectory planning.
[0004] To achieve the above object, the present application provides a wing-sail system trajectory planning method based on interval spline wavelet, comprising the following steps:
[0005] Step 1, establishing a wing-sail dynamics model and constructing an interval spline wavelet basis function;
[0006] Step 2, defining the trajectory planning process of the wing-sail system as an optimal control problem, i.e. finding control variables and state variables , fixed initial time , free end time , minimizing performance index and determining constraint conditions, wherein, is a performance index function, is the state of the wing-sail system at the initial time, is the state of the wing-sail system at the end time;
[0007] Step 3, discretizing the time interval into multiple layers of collocation points, and expanding the state variables and control variables based on the interval spline wavelet basis function at the collocation points, and converting the constraint conditions into wavelet coefficient form, and converting the optimal control problem into a nonlinear programming problem;
[0008] Step 4, solving the nonlinear programming problem by using a nonlinear programming optimization algorithm to obtain the trajectory planning result of the wing-sail system.
[0009] In one embodiment, the parafoil dynamics model comprises nine degrees of freedom dynamics equations of the parafoil / load system, and kinematic equations of the hinge point between the parafoil and the load during homing ;
[0010] The nine degrees of freedom dynamics equations of the parafoil / load system are:
[0011] ;
[0012] wherein, is a generalized mass matrix, is a generalized force matrix, is a velocity of the hinge point between the parafoil and the load in the parafoil body coordinate system, is a rotational angular velocity of the load, is a rotational angular velocity of the parafoil;
[0013] The kinematic equations of the hinge point between the parafoil and the load during homing are:
[0014] ;
[0015] wherein, is a transformation matrix from the geodetic coordinate system to the parafoil body coordinate system.
[0016] In one embodiment, the interval spline wavelet basis function comprises an internal interval wavelet function and a boundary wavelet function , specifically:
[0017] ;
[0018] ;
[0019] wherein, is an internal scaling function, is a boundary scaling function, and is expressed as:
[0020] ;
[0021] ;
[0022] wherein, x is a normalized time coordinate, is a truncated power function.
[0023] In one embodiment, in step 3, all collocation points are defined as wherein, N j is the number of collocation points.
[0024] The state variables, expanded based on the interval spline wavelet basis function for collocation, are as follows:
[0025] ;
[0026] in, The state vector of the th A vector, State variables The Wavelet coefficients, For interval spline wavelet basis functions, The number of dimensions of the state variables;
[0027] The control variables, based on the interval spline wavelet basis function expansion for collocation, are as follows:
[0028] ;
[0029] in, For the control vector One portion, For control variables The Wavelet coefficients, For interval spline wavelet basis functions, To control the number of dimensions of the variable.
[0030] In one embodiment, the optimal control problem is transformed into a nonlinear programming problem as follows:
[0031] use matrix , The wavelet coefficients and discrete values of the state variables are stored separately, using... matrix , Store the wavelet coefficients and discrete values of the control variables separately;
[0032] The optimal control problem is transformed into a wavelet transform. and This is a nonlinear programming problem for optimizing parameters.
[0033] In one embodiment, the constraints include:
[0034] Differential constraints: ,in, The time derivative of the state variable. The nonlinear dynamic equations for the parachute system;
[0035] Path constraints: wherein, is a path constraint lower bound, is a path constraint function, is a path constraint upper bound;
[0036] Boundary constraint condition: wherein, is a boundary constraint lower bound, is a boundary constraint function, is a boundary constraint upper bound;
[0037] The process of converting the constraint condition into a wavelet coefficient form is:
[0038] Discretize the differential constraint condition into an equality equation matrix represented by a wavelet coefficient, that is: wherein, is a differential constraint residual error vector, is a coordinate conversion matrix of the wing parachute Euler angle time derivative to its body angular velocity;
[0039] Convert the path constraint condition into an expression of a wavelet coefficient, that is:
[0040] Discretize the boundary constraint condition into an expression of a wavelet coefficient, that is:
[0041] To achieve the above object, the application further provides a wing parachute system trajectory planning device based on an interval spline wavelet, which adopts the above method to plan a trajectory, and the device comprises:
[0042] A model construction unit is configured to establish a wing parachute dynamics model and construct an interval spline wavelet base function.
[0043] A planning definition unit is configured to define a trajectory planning process of a wing parachute system as an optimal control problem, that is, to find control variables and state variables , a fixed initial time , a free end time , to make a performance index minimum, and to determine constraint conditions, wherein, is a performance index function, is a state of the wing parachute system at the initial time, is a state of the wing parachute system at the end time.
[0044] A problem conversion unit is configured to discretize a time interval into multiple layers of collocation points, to expand state variables and control variables based on the interval spline wavelet base function at the collocation points, to convert the constraint conditions into a wavelet coefficient form, and to convert the optimal control problem into a nonlinear programming problem.
[0045] a trajectory planning unit configured to solve the nonlinear programming problem by using an optimization algorithm of nonlinear programming to obtain a trajectory planning result of the parafoil system.
[0046] To achieve the above object, the application further provides a terminal device, wherein the terminal device is provided with:
[0047] a memory configured to store a program;
[0048] a processor configured to execute the program stored in the memory, and when the program is executed, the processor is configured to execute the method as described above.
[0049] Compared with the prior art, the application has the following beneficial technical effects:
[0050] By constructing the interval spline wavelet basis function, the trajectory planning process of the parafoil system is converted from the original optimal control problem to the nonlinear programming problem, so that the trajectory planning result of the parafoil system can be solved by using the optimization algorithm of nonlinear programming, the calculation dimension is significantly reduced, the end point constraint can be strictly met, the trajectory mutation can be adaptively captured, and the coordinated breakthroughs in speed, accuracy and robustness of the parafoil trajectory planning are effectively realized. BRIEF DESCRIPTION OF DRAWINGS
[0051] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only show some embodiments of the application, and for those skilled in the art, other drawings can also be obtained according to the structures shown in the drawings without creative labor.
[0052] Figure 1 a flow chart of the parafoil system trajectory planning method based on the interval spline wavelet in the embodiments of the application;
[0053] Figure 2 a two-body model schematic diagram of the parafoil-load system in the embodiments of the application;
[0054] Figure 3 a collocation point schematic diagram in the embodiments of the application;
[0055] Figure 4 a plane case schematic diagram of the simulation example in the embodiments of the application;
[0056] Figure 5 a three-dimensional trajectory schematic diagram of the parafoil system at a wind speed of 4m / s in the simulation example in the embodiments of the application.
[0057] The objectives, functional characteristics and advantages of the present application will be further described with reference to the embodiments in combination with the accompanying drawings. DETAILED DESCRIPTION
[0058] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative effort fall within the protection scope of the present application.
[0059] In addition, the technical solutions among various embodiments of the present application can be combined with each other, but it must be based on the fact that a person of ordinary skill in the art can realize the combination. When the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist and is not within the protection scope of the present application.
[0060] As Figure 1 shown is a wing parachute system trajectory planning method based on interval spline wavelet according to the embodiment, which mainly includes the following steps.
[0061] Step 1, establishing a wing parachute dynamics model and constructing an interval spline wavelet basis function.
[0062] Step 2, defining the trajectory planning process of the wing parachute system as an optimal control problem, i.e., finding control variables and state variables , a fixed initial time , a free end time , making a performance index minimum, and determining a constraint condition, wherein, is a performance index function, is the state of the wing parachute system at the initial time, is the state of the wing parachute system at the end time.
[0063] Step 3, discretizing the time interval into multiple layers of collocation points, expanding the state variables and control variables based on the interval spline wavelet basis function on the collocation points, and converting the constraint condition into a wavelet coefficient form, converting the optimal control problem into a nonlinear programming problem.
[0064] Step 4, solving the nonlinear programming problem by using an optimization algorithm of nonlinear programming to obtain the trajectory planning result of the wing parachute system.
[0065] In the embodiment, the wing parachute dynamics model includes nine-degree-of-freedom dynamics equations of the wing parachute / load system, and a kinematics equation of displacement of the hinge point between the wing parachute and the load during the homing process.
[0066] Reference Figure 2 In the process of establishing the wing parachute dynamics model, the following three coordinate systems are mainly used:
[0067] Earth-fixed coordinate system : The origin is selected at the ground projection point of the wing parachute-load system after the wing parachute is fully deployed, the axis is vertically downward along the direction of gravity, the axis is perpendicular to the longitudinal symmetry plane of the wing parachute system, the axis is perpendicular to the longitudinal symmetry plane of the wing parachute system, the axis is perpendicular to the longitudinal symmetry plane of the wing parachute system, the axis and the axis form a right-handed orthogonal system;
[0068] Parachute body-fixed coordinate system established at the hinge point between the wing parachute and the load : the axis is downward along the symmetry axis of the parachute canopy, and the other axes conform to the right-hand rule;
[0069] Load-fixed coordinate system established at the hinge point between the wing parachute and the load : the axis is downward along the symmetry axis of the load, and the other axes conform to the right-hand rule.
[0070] The vector from the hinge point to the center of mass of the load is denoted as , and the vector from the hinge point to the center of mass of the wing parachute is denoted as . The velocity of the hinge point between the wing parachute and the load in the parachute body coordinate system is denoted as , the angular velocity of the wing parachute and the load is respectively denoted as , , the Euler angles of the earth coordinate system to the parachute body coordinate system are described by the yaw angle , the pitch angle , and the roll angle , and the conversion matrix is denoted as ; the conversion matrix of the load coordinate system and the earth coordinate system is denoted as , and the conversion matrix of the load coordinate system to the parachute body coordinate system is denoted as . The aerodynamic force and moment acting on the parachute are denoted as , ; the aerodynamic force and moment acting on the load are denoted as , Gravitational acceleration is denoted as The aerodynamic forces and moments at the center of mass of the canopy are expressed using polynomials, namely:
[0071] ;
[0072] ;
[0073] in, p Atmospheric density, For the area of the umbrella canopy, The velocity of the umbrella's center of mass. For the angle of attack, Sideslip angle, The drag coefficient, This is the lift coefficient of the parachute. and These are the drag coefficients induced by symmetrical and asymmetrical underbias, respectively. delta s and delta a For symmetrical rudder deflection and antisymmetrical rudder deflection, , , and The lift coefficient, , , and This is the lateral force coefficient. , , , , This is the rolling moment coefficient. , , , , This is the pitch moment coefficient. , , , This is the yaw moment coefficient. p , q and r These are the roll, pitch, and yaw angular velocities of the parachute canopy. V The magnitude of the velocity of the umbrella canopy's center of mass relative to the airflow. b To extend the length of the umbrella canopy, c For the length of the umbrella canopy;
[0074] To avoid the relative constraint forces between the parachute and the load, this embodiment establishes the origin of the parachute coordinate system at the hinge point. According to the Newton-Euler equation, at the hinge point By establishing the translational dynamic equations, the generalized mass matrix can be obtained. and generalized force matrix The statement is as follows:
[0075] ;
[0076] ;
[0077] in, For load mass, It is a 3×3 identity matrix. It is a 3×3 zero matrix. For the quality of the umbrella canopy, It is the acceleration due to gravity. For the parachute-load system at the hinge point The velocity of the point, and These are the rotational angular velocities of the umbrella body and the load, respectively. Load relative to hinge point Moment of inertia, The relative hinge points of the umbrella canopy The projection of the inertia tensor onto the umbrella system. hinge point to the load center of mass , For its antisymmetric matrix, hinge point To the center of umbrella clothing vector, To add a mass matrix, To add the rotational inertia tensor, and Let the aerodynamic forces and aerodynamic moments acting on the parachute be... and These are the aerodynamic forces and aerodynamic moments acting on the load.
[0078] The final nine-degree-of-freedom dynamic equations of the parachute / load system can be obtained as follows:
[0079] .
[0080] Displacement of the hinge point between the parachute and the load during homing The kinematic equations are:
[0081]
[0082] in, This is the transformation matrix from the geodetic coordinate system to the umbrella coordinate system.
[0083] Spline functions are widely used in related numerical fields due to their simple structure, ease of use, and many other desirable properties. Let finite intervals... Then a finite interval can be constructed. Sobolev space ,Right now:
[0084] ;
[0085] in, For function The second derivative, It is a space of square-integrable functions;
[0086] If we introduce the inner product ,but For the Hilbert space, the function space is further defined as follows:
[0087] .
[0088] because exist It is dense inside, so The basis functions can also be used as The basis functions. Therefore, we can... The interpolation operator on can be generalized to The orthogonal projection operator on the surface. Based on this, we can construct... The cubic spline wavelet function on the space. The above constructs a multi-scale analysis, and this embodiment is in space. The above construction constructs an internal scaling function. and boundary scaling function ,for:
[0089] ;
[0090] ;
[0091] in, x For normalized time coordinates, This is to truncate the power function.
[0092] Further based on the scaling function and boundary scaling function Construct the corresponding internal interval wavelet function and boundary wavelet function ,for:
[0093] ;
[0094] .
[0095] In specific function fitting calculations, it is usually necessary to combine predetermined collocation points to represent the function fitting. For any function... First, define the space. Internal distribution points on:
[0096] ;
[0097] in, N Let this be the initial interval partition number. Then, for the detail space... In the interval Choose the following points to allocate, i.e.
[0098] ;
[0099] in, . Figure 3 With interval For example, a schematic diagram of a 5-layer point configuration is given, from... Figure 3 This shows the distribution of points on each spatial level. In subsequent calculations, within the height range... Similar point allocation can be performed on the above.
[0100] All collocations as defined Above, function If the values of all values are known, then the function can be derived from... Perform wavelet approximation, i.e.:
[0101] ;
[0102] in, The coefficients of the left boundary scaling function are... For the first The coefficients of the internal functions, The coefficients of the right boundary scaling function For the first Layer, First The coefficients of the wavelet function ( ).
[0103] For ease of description, this embodiment will... This can be written as a simplified mathematical expression:
[0104] ;
[0105] in, Including all wavelet scaling coefficients and wavelet coefficients, This includes the corresponding boundary scaling function, scaling function, wavelet function, and wavelet scaling function. The number of points to be selected for the wavelet.
[0106] In this embodiment, the state variables of the parafoil system trajectory planning process Specifically, the state variables of the parafoil system trajectory planning process are set as follows:
[0107] wherein, is the position of the hinge point in the earth coordinate system, is the hinge point velocity, is the roll angle, pitch angle and yaw angle of the parafoil body, is the angular velocity of the parafoil body.
[0108] The control variables of the parafoil system trajectory planning process Specifically, the control variables of the parafoil system trajectory planning process are set as follows:
[0109] ;
[0110] wherein, is the symmetric control variable, is the asymmetric control variable.
[0111] The performance index of the parafoil system trajectory planning process Specifically, the performance index of the parafoil system trajectory planning process is set as minimizing the terminal time or minimizing the terminal state error, i.e.:
[0112] or ;
[0113] wherein, is the terminal time, is the terminal landing point position, is the desired landing point position, is the velocity term weight coefficient, is the terminal velocity.
[0114] In the specific implementation process of step 2, the constraint conditions include:
[0115] The differential constraint condition is: wherein, is the time derivative of the state variable, is the nonlinear dynamics equation of the parafoil system;
[0116] The path constraint condition is: wherein, is the lower limit of the path constraint, is the path constraint function, is the upper limit of the path constraint;
[0117] The boundary constraint condition is: wherein, is the lower limit of the boundary constraint, is the boundary constraint function, is the upper limit of the boundary constraint.
[0118] In the specific implementation of step 3, all collocation points are defined as follows: , N j Given the number of collocation points, and based on this, the state variables are expanded using interval spline wavelet basis functions on the collocation points as follows:
[0119] ;
[0120] in, For the state variable One portion, State variables The Wavelet coefficients, For interval spline wavelet basis functions, The number of dimensions of the state variables;
[0121] The control variables, based on the interval spline wavelet basis function expansion for collocation, are as follows:
[0122] ;
[0123] in, To control component number One portion, For control variables The Wavelet coefficients, For interval spline wavelet basis functions, To control the number of dimensions of the variable.
[0124] The optimal control problem is transformed into a nonlinear programming problem as follows:
[0125] use matrix , Store the wavelet coefficients and discrete values of the state variables separately, i.e.:
[0126] ;
[0127] ;
[0128] Among them, matrix Each element in the matrix represents the discrete value of the state variable at the collocation point. Each element in the matrix represents the wavelet coefficient matrix of the state variables;
[0129] Similarly, it can be adopted matrix , Store the wavelet coefficients and discrete values of the control variables at the collocation points, respectively;
[0130] Finally, the optimal control problem is transformed into a nonlinear programming problem by wavelet transform and For the nonlinear programming problem of optimization parameters, further, all optimization parameters are expressed as a decision vector denoted as i.e.
[0131] ;
[0132] In the above formula denotes arranging the matrix in a column. Through the above processing, the original optimal control problem is transformed into a nonlinear programming problem, and the optimization objective function is:
[0133] .
[0134] The process of transforming the constraint conditions into the form of wavelet coefficients is:
[0135] Discretize the differential constraint conditions into an equality constraint matrix expressed by wavelet coefficients, i.e. wherein is a differential constraint residual vector, is a coordinate conversion matrix of the time derivative of the wing parachute Euler angle to its body angular velocity, and the wavelet differential operator matrix is ;
[0136] Transform the path constraint conditions into the expression of wavelet coefficients, i.e. ;
[0137] Discretize the boundary constraint conditions into the expression of wavelet coefficients, i.e. .
[0138] Correspondingly, the constraint conditions
[0139] ;
[0140] ;
[0141] wherein is a nonlinear programming constraint lower limit vector, is an aggregated constraint function, is a nonlinear programming constraint upper limit vector, is a lower limit of the decision variable , and is an upper limit of the decision variable .
[0142] This transforms the trajectory planning process of the paraglider system from the original optimal control problem into a nonlinear programming problem. The trajectory planning result of the paraglider system can then be obtained by using nonlinear programming optimization algorithms, such as successive quadratic programming, interior point method, and sequential convex optimization method.
[0143] In the specific implementation process, the solution process for the trajectory planning results of the paraglider system is as follows:
[0144] Step 101, Initialize decision variables ;
[0145] Step 102, Construct the current decision variables Constrained Jacobian matrix Hessian matrix :
[0146] ;
[0147] ;
[0148] in, Let Lagrange multiplier vectors be used. The total number of constraints, Let the dimension of the decision variables be... For the constraint function vector, For the objective function F The Hessian matrix, For the first A constrained Hessian matrix;
[0149] Step 103, based on the current decision variables Solving quadratic programming subproblems using the Jacobian and Hessian matrices yields the search direction. The process is as follows:
[0150] ;
[0151] in, Let be the gradient vector of the objective function;
[0152] Step 104: Perform a one-dimensional search along the search direction to determine the step size. The process is as follows:
[0153] ;
[0154] in, The attenuation coefficient;
[0155] Step 105, update the decision variables based on the search step size, as follows:
[0156]
[0157] wherein, is the updated decision variable, is the pre-updated decision variable, is the step size, is the search direction;
[0158] Step 106, based on the current decision variable calculating the gradient of the Lagrange function and the differential constraint residual vector ;
[0159] Step 107, determining whether to meet wherein, is the optimality tolerance, is the dynamics constraint tolerance:
[0160] if yes, outputting each decision variable in the iteration process, completing the trajectory planning of the parafoil system;
[0161] otherwise, returning to step 102.
[0162] The interval spline wave-based parafoil system trajectory planning method in the embodiment will be further described below in combination with specific examples.
[0163] The interval spline wave-based parafoil system trajectory planning method in the embodiment is adopted, the initial height of the system is 1500 meters, the planar case of 0m / s, 2m / s, 4m / s wind speed is considered as shown in Figure 4 , the initial shape and the terminal shape of the system are given by using the interval spline wave, the optimal control law can be obtained by using the successive quadratic programming optimization algorithm, and the three-dimensional trajectory of the parafoil system at 4m / s wind speed is shown in Figure 5 . It can be known from Figure 5 that the method in the embodiment can significantly reduce the calculation dimension, can strictly meet the end point constraint, can adaptively capture the trajectory mutation, and can effectively realize the coordinated breakthrough of the parafoil trajectory planning in speed, accuracy and robustness.
[0164] The above only describes the preferred embodiments of the present application, and does not limit the protection scope of the present application, any equivalent structure transformation made according to the content of the present application specification and drawings, or direct / indirect application in other related technical fields under the inventive concept of the present application are included in the protection scope of the present application.
Claims
1. A paragliding system trajectory planning method based on interval spline wavelet, characterized in that, Comprising the following steps: Step 1, establishing a wing parachute dynamics model, and constructing an interval spline wavelet basis function; Step 2, define the trajectory planning process of the parafoil system as an optimal control problem, i.e. find the control variables and the state variables , a fixed initial time , a free final time , such that the performance index is minimized, subject to constraints, where is the performance index function, is the state of the parafoil system at the initial time, is the state of the parafoil system at the final time; State variable is: wherein, is the position of the hinge point in the earth coordinate system, is the velocity of the hinge point, is the roll, pitch and yaw angles of the parachute body, is the angular velocity of the parachute body; Controlled variables are: wherein is a symmetric steering amount, is an asymmetric steering amount; Performance indicators minimizing the terminal time or minimizing the terminal state error, i.e.: Or wherein, is a terminal landing point position, is a desired landing point position, is a velocity term weight coefficient, is a terminal velocity; Step 3, time interval discretized into multi-layer collocation points, and the state variables and control variables are expanded on the collocation points based on the interval spline wavelet basis functions, and the constraint conditions are converted into wavelet coefficient forms, and the optimal control problem is converted into a nonlinear programming problem; Step 4, solving the nonlinear programming problem by using a nonlinear programming optimization algorithm to obtain the trajectory planning result of the wing parachute system, and the specific solving process is: Step 101, initialize decision variable ; Step 102, construct current decision variable Constraint Jacobian matrix and Hessian matrix : wherein, is a Lagrange multiplier vector, is the total number of constraints, is the dimension of the decision variable, is a constraint function vector, is the objective function F is the Hessian matrix of the objective function, is the Hessian matrix of the th constraint; Step 103, solving a quadratic programming subproblem based on the Jacobian matrix of the current decision variable and the Hessian matrix to obtain a search direction The process is as follows: wherein, is the gradient vector of the objective function; Step 104, one-dimensional search is performed along the search direction to determine the step size The process is as follows: wherein is the attenuation coefficient; Step 105, updating the decision variable based on the search step length, and the specific solving process is: wherein, is the updated decision variable, is the pre-updated decision variable, is the step size, is the search direction; Step 106, based on the current decision variable the gradient of the Lagrangian function and the differential constraint residual vector ; Step 107, determining whether the following is satisfied wherein, is the optimality tolerance, is the dynamics constraint tolerance: If yes, output each decision variable in the iteration process, and complete the trajectory planning of the wing parachute system; Otherwise, return to step 102.
2. The interval-spline-wavelet-based parafoil system trajectory planning method according to claim 1, wherein, The parafoil dynamics model includes nine degrees of freedom dynamics equations of the parafoil / load system, and the kinematics equations of the displacement of the hinge point between the parafoil and the load during the homing process ; The nine-degree-of-freedom dynamics equation of the wing parachute / load system is: wherein, is a generalized mass matrix, is a generalized force matrix, is the velocity of the hinge point between the parafoil and the payload in the parafoil body coordinate system, is the rotational angular velocity of the payload, is the rotational angular velocity of the parafoil; The hinge point between the parafoil and the load moves during homing The kinematic equation is: wherein, is the transformation matrix from the earth coordinate system to the umbrella body coordinate system.
3. The interval-spline wavelet based parafoil system trajectory planning method of claim 1, wherein, The interval spline wavelet base function comprises an internal interval wavelet function and a boundary wavelet function , in particular: wherein is an internal scale function, is a boundary scale function, represented as: wherein x is a normalized time coordinate, is a truncated power function.
4. The interval-spline-wavelet based parafoil system trajectory planning method according to claim 1 or 2 or 3, characterized in that, In step 3, define all the points as where, N j is the number of points. The state variable is expanded based on the interval spline wavelet basis function at the collocation point, and the specific expansion process is: wherein, is the i-th vector of the state vector, is the i-th wavelet coefficient of the state variable is the interval spline wavelet basis function, is the dimension number of the state variable; The control variable is expanded based on the interval spline wavelet basis function at the collocation point, and the specific expansion process is: wherein is the i-th component of the control vector, is the i-th wavelet coefficient of the control variable is the interval spline wavelet basis function, is the dimension number of the control variable. 5. The interval-spline wavelet based parafoil system trajectory planning method of claim 4, wherein, The optimal control problem is converted into a nonlinear programming problem, and the specific conversion process is: The wavelet coefficients of the state variables and the discrete values are stored in matrices The wavelet coefficients of the state variables and the discrete values are stored in matrices , The wavelet coefficients of the control variables and the discrete values are stored in matrices The wavelet coefficients of the control variables and the discrete values are stored in matrices , The optimal control problem is transformed by wavelet transform to and a nonlinear programming problem for optimization parameters.
6. The interval-spline-wavelet-based parafoil system trajectory planning method of claim 5, wherein, The constraint condition includes: Differential constraint conditions: where, is the state variable time derivative, is the parafoil system nonlinear dynamics equation; path constraints: wherein, is a path constraint lower bound, is a path constraint function, is a path constraint upper bound; Boundary constraint condition: wherein, is a boundary constraint lower limit, is a boundary constraint function, is a boundary constraint upper limit; The process of converting the constraint condition into the wavelet coefficient form is: The differential constraint condition is discretized as an equality constraint matrix represented by wavelet coefficients, i.e., wherein, is a differential constraint discretization residual vector, is a wavelet differential operator matrix; and is a coordinate transformation matrix of the wing parachute Euler angle time derivative to its body angular velocity. The path constraint condition is converted into an expression of the wavelet coefficient, i.e. ; The boundary constraint condition is discretized into an expression of wavelet coefficients, i.e. .
7. An apparatus for trajectory planning of a parafoil system based on interval-spline wavelets, characterized by, The device comprises: A model construction unit, configured to establish a wing parachute dynamics model, and construct an interval spline wavelet basis function; a planning definition unit for defining a trajectory planning process of the parafoil system as an optimal control problem, i.e. finding control variables and state variables , a fixed initial time , a free final time , minimizing a performance index and determining constraints, wherein is a performance index function, is a state of the parafoil system at the initial time, is a state of the parafoil system at the final time; a problem transformation unit for transforming a time interval into a plurality of layers of collocation points, expanding the state variables and control variables at the collocation points based on the interval spline wavelet basis functions, and transforming the constraints into wavelet coefficient form, transforming the optimal control problem into a nonlinear programming problem; A trajectory planning unit, configured to solve the nonlinear programming problem by using a nonlinear programming optimization algorithm to obtain the trajectory planning result of the wing parachute system.
8. A terminal device, comprising: The terminal device is provided with: A memory, configured to store a program; A processor, configured to execute the program stored in the memory, and when the program is executed, the processor is configured to execute the method according to any one of claims 1 to 6.