An Optimization Method for the Trajectory of UAV Towed Aerial Recovery Based on Trajectory Mapping

Abstract

The present invention discloses a trajectory optimization method for the aerial recovery of an unmanned aerial vehicle (UAV) based on trajectory mapping, belonging to the fields of UAV navigation, guidance, and control. The present invention proposes the idea of trajectory mapping. First, a motion model of the cable-buoy-UAV combination is established, and the profile data of the recovery system is parametrically represented as the input of the trajectory mapping network. Then, based on deep learning, a precise mapping relationship between the input and the output (the recovery trajectory of the buoy-UAV combination) is established using BiGRU to obtain the trajectory mapping network. Finally, based on this trajectory mapping network, the real recovery trajectory under different recovery commands is predicted in real time, and the optimal recovery command is obtained using the grey wolf optimization algorithm, thereby obtaining the optimal recovery trajectory of the recovery system. The present invention can achieve the real-time online accurate, fast, and stable recovery of the UAV under different environmental conditions, while reducing the burden on the optimization algorithm.

Description

Technical Field

[0001] The invention belongs to the field of unmanned aerial vehicle navigation, guidance and control, and in particular relates to a method for optimizing the trajectory of a towed aerial recovery of an unmanned aerial vehicle based on trajectory mapping. Background Art

[0002] Drone towed aerial recovery refers to the process in which a small fixed-wing drone is docked and locked with a buoy towed by a cable in the air, and then the cable is recovered by the reel and the drone is recovered into the cargo hold of a transport aircraft (mother aircraft). Figure 1 As shown in the figure. UAV aerial recovery technology can eliminate the dependence of UAVs on reliable land-based / ship-based systems and effectively expand the combat range of UAVs. During the recovery process, the recovery trajectory of the UAV needs to be optimized so that the UAV can be recovered smoothly and quickly. How to achieve online optimization of the recovery trajectory of the UAV is an urgent problem to be solved.

[0003] The recovery trajectory of the UAV is not only related to the expected recovery trajectory, but also affected by the cable recovery speed and acceleration, as well as the timing and speed of wing folding. Therefore, when optimizing the recovery trajectory, it is necessary not only to optimize the expected trajectory, but also to optimize the cable recovery speed and acceleration, as well as the timing and speed of wing folding. It should be emphasized that the mapping relationship between the above optimization variables and the recovery trajectory is not analytical, and it is impossible to directly use the traditional numerical optimization algorithm for optimization. First, the relationship between the expected trajectory and the actual trajectory is not analytical. Considering the performance of the position tracking controller and the complex dynamic characteristics of the cable-buoy-UAV combination, the expected trajectory will not be strictly tracked. Secondly, the influence of the cable recovery speed and wing folding on the recovery trajectory is implicit in the recovery system model and cannot be explicitly expressed. One of the most direct methods is to use the entire recovery system model for prediction, that is, input the recovery command, and predict the recovery trajectory by numerically solving the model. This method comprehensively considers the dynamic characteristics of the cable-buoy-UAV combination and the performance of the controller, as well as the impact of cable recovery and wing folding. However, the dynamic model of the entire recovery system is very complex, containing dozens or hundreds of differential equations, which makes it difficult to make real-time predictions and cannot be used online. In order to improve the optimization efficiency, if only a simplified kinematic model is considered during trajectory optimization without fully considering the impact of various factors in the recovery system, as in the existing trajectory optimization methods, then there will inevitably be a large deviation between the actual trajectory and the optimized command trajectory, which is likely to cause the actual recovery trajectory to swing significantly, affecting the safety of the recovery mission. As an emerging technology, there is currently no research literature related to recovery trajectory optimization for towed UAV aerial recovery.

[0004] In recent years, with the development of the new generation of artificial intelligence technology, the powerful non-linear fitting ability demonstrated by deep learning has provided the possibility for solving complex non-linear problems. Through the idea of trajectory mapping, using deep learning to establish an accurate mapping relationship between the recovery instructions and the recovery trajectory in the UAV recovery system, and then realizing the online optimization of the recovery trajectory, which provides a way to solve the above problems. Summary of the Invention

[0005] To improve the stability and rapidity of the UAV recovery process, the present invention proposes a UAV towed air recovery trajectory optimization method based on trajectory mapping. The proposed method can establish an accurate mapping relationship between the UAV recovery instructions and the actual recovery trajectory, and can fully consider the tracking characteristics of the recovery system during trajectory optimization, accurately predict the true recovery trajectory corresponding to different recovery instructions in real time, greatly improve the trackability of the planned trajectory, and achieve planning and tracking.

[0006] A UAV towed air recovery trajectory optimization method based on trajectory mapping specifically includes the following steps:

[0007] Step 1: Establish a non-linear motion model of the cable and the buoy-UAV combination for the UAV recovery system;

[0008] Specifically as follows:

[0009] (1) Establish a cable motion model based on the multi-rigid body theory;

[0010] Discretize the cable into N segments of equal-length cylindrical rigid connecting rods, connect the connecting rods with frictionless spherical hinge nodes, ignore the extensibility and flexibility of the connecting rods, and assume that the weight of the connecting rods is equivalent at the two end nodes of the connecting rods, that is, consider that half of the mass of the i-th connecting rod and half of the mass of the i + 1-th connecting rod are concentrated at the hinge node at the end of the i-th connecting rod, and a multi-rigid body dynamics system is obtained. Specifically:

[0011] Model the cable in the towing coordinate system S D (O D -X D Y D Z D ), p i is the position of the i-th node, r i = p i -p i-1 is the position vector of the i-th connecting rod. Use the deflection angles λ D O D Y D and the plane X D O D Z D of the i-th connecting rod relative to the planes X i and Describe the motion of the connecting rod.

[0012] r i The calculation formula is as follows:

[0013]

[0014] Among them, \(l = L_0 / N\) is the length of the \(i\)-th connecting rod, and \(L_0\) is the total length of the cable (variable); \(n\) i is the unit direction vector of the \(i\)-th connecting rod.

[0015] λ i and The second-order dynamic equations of can be expressed as:

[0016]

[0017] Among them, a i is the acceleration of node \(i\), \(\alpha\) D and \(\omega\) D are the angular velocity and angular acceleration of the dragging system \(S\) D relative to the inertial system \(S\) g (O g -X g Y g Z g ); and are the cable retracting / extending speed and acceleration respectively.

[0018] According to Newton's second law, the acceleration of node \(i\) can be obtained from the following formula:

[0019]

[0020] Among them, \(m\) i is the mass of the connecting rod concentrated at node \(i\), and \(m\) d is the mass of the buoy; \(Q\) i is the resultant external force acting on node \(i\), including aerodynamic force and gravity; \(t\) i is the tension of the \(i\)-th section of the cable.

[0021] (2) Establish a six-degree-of-freedom buoy-UAV combined body dynamics model considering cable tension;

[0022] First, analyze the forces acting on the end node of the cable, including the gravity \(m\) of the buoy-UAV combined body A g and the aerodynamic force \(F\) A , the gravity \(m\) of node \(N\) N g, half of the aerodynamic force of the \(N\)-th section of the cable \(0.5F\) N and the cable tension \(t\) N. Therefore, the following combined body dynamics model is established in the track system:

[0023]

[0024] In the formula, and respectively represent the transformation matrices from the airflow system and the drag system to the track system; V k is the velocity of the buoy - UAV combined body; γ, χ are the track angles of the buoy - UAV combined body. The motion equations of other loops are similar to those of conventional aircraft.

[0025] Then, adopting the parametric modeling method, the buoy - UAV combined body is subjected to CFD blowing under seven cases of the wing sweep angle ξ = 0°, ξ = 15°, ξ = 30°, ξ = 45°, ξ = 60°, ξ = 75°, ξ = 90°. Assuming that the parameter change between adjacent folding angles is linear, linear interpolation is performed on the obtained parameters, and the aerodynamic parameters of the buoy - UAV combined body during the wing folding process can be obtained:

[0026]

[0027] Among them, and are the aerodynamic parameters of the buoy - UAV combined body when the sweep angles are 0°, 15°, 30°, 45°, 60°, 75° and 90° respectively.

[0028] Step 2: Based on the nonlinear motion model of the UAV recovery system, parametrically represent the profile data of the UAV recovery system and optimize it. The command variables (R l , V L , a L , t W , V W ) output by the optimization algorithm are extended into an input sequence and used as the input of the trajectory mapping network.

[0029] The profile data of the UAV recovery system includes: the expected recovery trajectory profile of the UAV the recovery speed profile of the cable and the wing folding profile Γ W ; After parametric representation, it is: the non - binding force vector and direction R l , the cable recovery speed and acceleration V L , a L , the timing and folding speed of the wing t W , V W functions. Specifically as follows:

[0030] (1) Expected recovery trajectory profile Parametric and serialization methods;

[0031] Given the non - constraint vector and direction R l , and the change of the cable length L r during the entire recovery process, it is generated through simulation That is:

[0032]

[0033] where R l * is the desired non - constraint vector and direction, t is the current time, T s is the sampling step, T is the termination time, f RLX (·) and f RLZ (·) are the fitting functions of the steady - state X - axis and Z - axis positions of the buoy - UAV combination respectively.

[0034] Given different combinations of R l and L r in the simulation environment, after the control is stabilized, record the corresponding X - axis and Z - axis positions at this time. Based on the simulation data, polynomial fitting is performed to obtain the following relationship:

[0035]

[0036] In the formula: The unit of R l is radian, and the unit of L r is meter.

[0037] It can be seen from the above formula that during the recovery process, the X - axis and Z - axis positions of the buoy - UAV combination have a linear relationship with L r and a quadratic relationship with R l .

[0038] (2) Cable recovery speed profile Parameterization and serialization methods;

[0039] The cable recovery speed profile is determined by its maximum recovery speed and acceleration. Assuming that the cable length moves at a constant speed or with a uniform acceleration during recovery, its recovery speed profile is trapezoidal. Since the trapezoidal area is equal to the cable length L r to be recovered, it can be deduced that:

[0040]

[0041] In the formula, V L and a L are the maximum speed and acceleration of cable recovery respectively. When V L and a L are determined, the recovery time T is also determined, and thus the entire recovery speed profile is uniquely determined. Therefore, regarding V L and aL As an optimization variable for the cable recovery speed profile.

[0042] Based on Equation (8), the cable recovery speed sequence can be expressed as:

[0043]

[0044]

[0045] Where t1 is the moment when the cable recovery speed reaches the maximum value, and t2 is the moment when the cable recovery speed starts to decelerate from the uniform speed.

[0046] (3) Wing folding profile Γ W Parameterization and serialization method;

[0047] The sweep angle profile of the wing is determined by the wing folding time t W and the speed V W jointly. Assuming the wing folds at a uniform speed, the wing folding sequence is expressed as:

[0048]

[0049] Γ W =[ξ(t), ξ(t + T s ),..., ξ(T)] T (12)

[0050] (4) Generation of the tracking error sequence Γ exN , Γ ezN ;

[0051] By continuously repeating the current tracking error e Udx , e Udz to construct the tracking error sequence Γ exN , Γ ezN , to more accurately predict the recovery trajectory, that is:

[0052]

[0053] Step 3: Based on deep learning, use a bidirectional gated recurrent unit (BiGRU) neural network to establish an accurate mapping relationship between the input and output of the entire recovery system, that is, the trajectory mapping network;

[0054] The input of the trajectory mapping network includes the expected position of the buoy - UAV combination, the cable recovery speed and acceleration, the wing folding time and speed of the UAV, etc.; the output includes the recovery trajectory of the buoy - UAV combination.

[0055] The specific steps for establishing the trajectory mapping network are as follows:

[0056] Step 301: Design a trajectory mapping network structure based on BiGRU;

[0057] BiGRU contains GRU structures in both forward and backward directions. In terms of the structural dimension, both the forward and backward GRUs have multiple layers, and a Dropout layer is added between each GRU layer during training. In terms of the time dimension, the input profiled information is arranged in time sequence and input to the forward and backward GRUs, and the outputs of the two are stacked. Finally, after passing through a fully connected layer, the outputs of the fully connected layer are integrated in time sequence, which is the final network output profile.

[0058] The BiGRU combines the outputs of the last layers of the forward and backward GRUs and Finally, through the integration of the fully connected layer, we can obtain:

[0059]

[0060] Among them, is the set of the outputs of the last layers of the forward and backward GRUs, N L is the number of GRU layers, and are the weight vector and bias vector of the last layer of the network respectively, Y t is the final network output, that is, the buoy - UAV combination recovery trajectory profile predicted by the trajectory mapping network, represents the mapped buoy - UAV combination recovery trajectory.

[0061] Then, the forward propagation process of the trajectory mapping network is defined as the following function:

[0062]

[0063] Among them, f TMN (·) is the forward propagation function of the trajectory mapping network.

[0064] Step 302: Use the closed - loop model of the UAV recovery system to generate training data;

[0065] Input data of different intensities of atmospheric turbulence, different parameter perturbation data, and different command data into the UAV recovery system model to generate several trajectory data, and divide the trajectory data into training data and test data according to a ratio of 10:1.

[0066] The specific input data is:

[0067] ① The atmospheric turbulence intensity is randomly selected between mild turbulence and moderate turbulence.

[0068] ② The random given method of parameter perturbation is as follows:

[0069] c′ Ud = c Ud ·U(0.8, 1.2) (16)

[0070] Among them, U(0.8, 1.2) is a uniform distribution between 0.8 and 1.2, indicating that the aerodynamic parameters of the combined body are perturbed between [-20%, +20%].

[0071] ③ The method for randomly generating command data is as follows:

[0072]

[0073] Normalize the training data:

[0074] data train = (data ori - μ data ) / σ data (18)

[0075] Among them, data ori is the original data, data train is the normalized data, μ data and σ data are the mean and variance of the original data respectively.

[0076] Step 303: Use the Adam optimizer to calculate the gradient according to the loss value to update the parameters of the trajectory mapping network. After sufficient training iterations with the training data, a trajectory mapping network that accurately maps the recovery trajectory is obtained.

[0077] Use the mean square error to measure the loss value during training:

[0078]

[0079] Among them, Y i * is the output label value, Y i (W, b) is the predicted value of the trajectory mapping network, W is the weight vector of the network, b is the bias vector of the network, and I is the number of samples of the training data.

[0080] Step Four: Use the trajectory mapping network to predict the actual recovery trajectories corresponding to different recovery commands in real time, evaluate the predicted actual recovery trajectories according to the designed cost function, and use the Grey Wolf Optimization (GWO) algorithm to select the optimal recovery command, so as to achieve the stable and rapid recovery of the UAV;

[0081] The specific steps are as follows:

[0082] Step 401: Design a cost function considering stability and rapidity;

[0083] The cost function needs to reflect the swing amplitude and recovery speed of the recovery trajectory. The recovery speed is characterized by the time required for the end of the recovery and the swing amplitude of the recovery trajectory is characterized by using the predicted length of the recovery trajectory minus the length L of the cable to be recovered r In the completely stable state, the length of the recovery trajectory is equal to the length of the cable to be recovered. The larger the is, the greater the degree of sway of the recovery trajectory.

[0084] Based on the above analysis, the cost function for optimizing the trajectory during the recovery process is designed as follows:

[0085]

[0086] In the formula: K d and K l are the weight coefficients of the swing amplitude term and the recovery time term respectively; represents the time sequence length of, multiplied by T s is the recovery time, and is obtained through the following formula:

[0087]

[0088] Step 402: Use the GWO algorithm to optimize and obtain the optimal recovery command, and then obtain the optimal recovery trajectory;

[0089] First, initialize the population and randomly generate multiple sets of recovery commands.

[0090] Then, predict the recovery trajectories corresponding to different recovery commands through the above trajectory mapping network.

[0091] Next, calculate the cost of each recovery trajectory according to the cost function. After multiple rounds of iteration, the recovery command corresponding to the minimum cost is the optimal recovery command.

[0092] Finally, input the optimal command into the UAV recovery system to obtain the optimal recovery trajectory of the UAV.

[0093] The advantages of the present invention are as follows:

[0094] (1) A method for optimizing the UAV towed aerial recovery trajectory based on trajectory mapping can achieve rapid and stable recovery of the UAV under different initial states, parameter perturbations, and multiple wind disturbances.

[0095] (2) A method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed air recovery based on trajectory mapping, which establishes an accurate mapping relationship between the recovery instructions and the recovery trajectory in the air recovery system based on deep learning. While fully considering the dynamic characteristics and tracking performance of the recovery system, it has high computational efficiency and can accurately predict the recovery trajectory corresponding to different recovery instructions in real-time online.

[0096] (3) A method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed air recovery based on trajectory mapping, which parametrically represents the profile parameters of the recovery instructions to be optimized as several instruction parameters and uses the Grey Wolf Optimization algorithm to optimize them, thereby greatly reducing the burden of the optimization algorithm and facilitating engineering implementation. Brief Description of the Drawings

[0097] Figure 1 is a schematic diagram of the UAV towed air recovery of the present invention;

[0098] Figure 2 is a flowchart of the method for optimizing the trajectory of the UAV towed air recovery of the present invention;

[0099] Figure 3 is a schematic diagram of the dynamic modeling of the cable-buoy combination of the present invention;

[0100] Figure 4 is a schematic diagram of the cable recovery speed profile of the present invention;

[0101] Figure 5 is a schematic diagram of the trajectory mapping network structure based on BiGRU of the present invention;

[0102] Figure 6 is a schematic diagram of the method for generating training data and training the network of the present invention;

[0103] Figure 7 is a schematic diagram of the framework for optimizing the UAV recovery trajectory based on trajectory mapping of the present invention;

[0104] Figure 8 is a diagram of the trajectory mapping results of the present invention under different situations; among them, Figure 8a is the situation where the command trajectory is appropriate, the true recovery trajectory and the predicted recovery trajectory curves; Figure 8b and Figure 8c is the situation where the command trajectory is inappropriate, the true recovery trajectory and the predicted recovery trajectory curves;

[0105] Figure 9 is a comparison chart of the operation time of the present invention and other mapping models;

[0106] Figure 10 is a comparison chart of the command and the actual recovery trajectory of the present invention and the case without adopting the optimization method;

[0107] Figure 11It is the diagram of the cable configuration change during the UAV recovery process under the trajectory optimization of the present invention;

[0108] Figure 12 It is the diagram of the cable configuration change during the UAV recovery process without optimization of the present invention; Detailed implementation manners

[0109] For the convenience of those of ordinary skill in the art to understand and implement the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and examples.

[0110] A method for optimizing the trajectory of a UAV towed aerial recovery based on trajectory mapping according to the present invention proposes the idea of trajectory mapping, and based on deep learning, an accurate mapping relationship between the input (desired position, cable recovery speed and acceleration, UAV wing folding timing and speed, etc.) and the output (recovery trajectory of the buoy-UAV combination) of the entire recovery system (including position tracking controller, cable-buoy-UAV combination motion model, etc.) is established. Based on this trajectory mapping network, the real recovery trajectory under different recovery instructions can be predicted in real time, and the gray wolf optimization algorithm is used to obtain the optimal recovery instructions.

[0111] A method for optimizing the trajectory of a UAV towed aerial recovery based on trajectory mapping, as Figure 2 shown, the detailed implementation manners include the following steps:

[0112] Step 1. Establish a non-linear motion model of the cable and the buoy-UAV combination for the UAV recovery system;

[0113] The specific steps are as follows:

[0114] Step 101. Establish a cable motion model based on the multi-rigid body theory;

[0115] The present invention discretizes the cable into N segments of equal-length cylindrical rigid connecting rods, which are connected by frictionless spherical hinge joints. The extensibility and flexibility of the connecting rods are ignored, and it is assumed that the weight of the connecting rods is equivalent at the two end nodes of the connecting rods, that is, half of the mass of the i-th connecting rod and half of the mass of the i+1-th connecting rod are concentrated at the hinge joint at the end of the i-th connecting rod. Based on the above assumptions and approximations, the cable can be regarded as a multi-rigid body dynamics system.

[0116] As Figure 3 shown, the present invention performs cable modeling in the towing coordinate system S D (O D -X D Y D Z D ), p i is the position of the i-th node, r i = p i - p i-1is the position vector of the i-th link. Since the rolling motion of the cable can be ignored, the present invention uses the deflection angles λ of the i-th link relative to the plane X D O D Y D and the plane X D O D Z D to describe the link motion. i and The r can be calculated by the following formula:

[0117] r i where l = L0 / N is the length of the i-th link, L0 is the total length (variable) of the cable, and n

[0118]

[0119] is the unit direction vector of the i-th link. i The second-order dynamic equations of λ

[0120] λ i and can be expressed as:

[0121]

[0122] where a i is the acceleration of node i, and α D and ω D are the angular velocity and angular acceleration of the dragging system S D relative to the inertial system S g (O g -X g Y g Z g ), respectively; and are the cable retracting and releasing speed and acceleration, respectively.

[0123] According to Newton's second law, the acceleration of node i can be obtained by the following formula:

[0124]

[0125] where m i is the mass of the link concentrated at node i, and m d is the mass of the buoy; Q i is the resultant external force acting on node i, including aerodynamic force and gravity; t i is the tension force on the i-th section of the cable.

[0126] Based on (1)-(3), the kinematic model of the cable can be established.

[0127] Step 102: Establish a six-degree-of-freedom buoy-UAV combined body dynamics model considering cable tension;

[0128] After the UAV is docked and locked with the buoy, the buoy-UAV combined body, as the end point of the cable, its gravity and aerodynamic force will have a greater impact on the movement of the cable, which will in turn affect the tension of the cable, and the tension of the cable will also affect the movement of the buoy-UAV combined body. Therefore, there is a close coupling relationship between the buoy-UAV combined body and the cable in dynamics. In order to more accurately describe the movement of the buoy-UAV combined body, the present invention models it by referring to the six-degree-of-freedom dynamics modeling method of aircraft.

[0129] First, analyze the forces acting on the end node of the cable, including the gravity mg of the buoy-UAV combined body A and the aerodynamic force F A , the gravity mg of node N N , half of the aerodynamic force of the Nth section of the cable 0.5F N , and the tension t of the cable N . Therefore, the following combined body dynamics model is established in the flight path system:

[0130]

[0131] In the formula, and respectively represent the transformation matrices from the airflow system and the drag system to the flight path system; V k is the speed of the buoy-UAV combined body; γ, χ are the flight path angles of the buoy-UAV combined body. The motion equations of other loops are similar to those of conventional aircraft and will not be elaborated.

[0132] During the recovery process of the UAV, the wings need to be folded in the form of variable sweep angles for recovery. During the wing folding process, the geometric parameters, mass distribution and aerodynamic force of the buoy-UAV combined body will change. The present invention adopts a parametric modeling method, conducts CFD blowing on the buoy-UAV combined body in seven cases where the sweep angle of the wing ξ = 0°, ξ = 15°, ξ = 30°, ξ = 45°, ξ = 60°, ξ = 75°, ξ = 90°, and assumes that the parameter changes between adjacent folding angles are linear, and linearly interpolates the obtained parameters to obtain the aerodynamic parameters of the buoy-UAV combined body during the wing folding process:

[0133]

[0134] Among them, and are the aerodynamic parameters of the buoy-UAV combined body when the sweep angles are 0°, 15°, 30°, 45°, 60°, 75° and 90° respectively.

[0135] Step 2: Parametrize and optimize the profile data of the UAV recovery system, and expand the instruction variables (R l , V L , a L , t W , V W ) output by the optimization algorithm into an input sequence as the input of the trajectory mapping network.

[0136] The recovery trajectory of the UAV is not only related to the expected recovery trajectory profile , but also affected by the recovery speed profile of the cable and the wing folding profile Γ W . Therefore, it is necessary to optimize the above profiles to make the actual recovery trajectory of the UAV optimal. First, to reduce the burden of the optimization algorithm and facilitate engineering implementation, the above profiles to be optimized are respectively parameterized as a non-binding vector and direction R l , the cable recovery speed and acceleration V L , a L , and the timing and folding speed t of the wing folding W , V W functions, so that the optimization object of the optimization algorithm changes from the entire profile to several instruction parameters. Then, to map out the entire recovery trajectory profile, it is necessary to expand the instruction variables (R l , V L , a L , t W , V W ) output by the optimization algorithm into an input sequence to meet the input format of the trajectory mapping network.

[0137] The specific steps are as follows:

[0138] Step 201: Parametrization and serialization method of the recovery trajectory profile ;

[0139] During the recovery process, the cable length is constantly changing, and the steady-state X-axis and Z-axis positions of the buoy-UAV combination should be determined by the non-binding vector and direction R l and the cable length L r . Therefore, R l can be given, as well as the change of L r during the entire recovery process, and the following can be generated through simulation That is:

[0140]

[0141] where R l * is the expected non-binding vector and direction, t is the current time, T s is the sampling step, T is the termination time, fRLX (·) and f RLZ (·) are the fitting functions of the X-axis and Z-axis positions respectively.

[0142] In the simulation environment, different combinations of R l and L r are given. After the control is stable, record the corresponding X-axis and Z-axis positions at this time. Based on a large amount of simulation data, polynomial fitting is performed to obtain the following relationship:

[0143]

[0144] In the formula: The unit of R l is radian, and the unit of L r is meter. It can be seen that during the recovery process, the X-axis and Z-axis positions of the buoy-UAV combination have a basically linear relationship with L r and a quadratic relationship with R l .

[0145] Step 202, Cable recovery speed profile Parameterization and serialization method;

[0146] The cable recovery speed profile is determined by its maximum recovery speed and acceleration. Considering the actual recovery situation and operability, it is assumed in this paper that the cable length moves at a constant speed or with a uniform acceleration during recovery, and its recovery speed profile is trapezoidal, as shown in Figure 4 .

[0147] Since the trapezoidal area is equal to the cable length L r to be recovered, the following can be deduced:

[0148]

[0149] In the formula, V L and a L are the maximum speed and acceleration of the cable recovery respectively. When V L and a L are determined, the recovery time T is also determined, and thus the entire recovery speed profile is uniquely determined. Therefore, V L and a L can be used as the optimization variables of the cable recovery speed profile.

[0150] Based on Equation (8), the cable recovery speed sequence can be expressed as:

[0151]

[0152]

[0153] where t1 is the moment when the cable recovery speed reaches the maximum value, and t2 is the moment when the cable recovery speed starts to decelerate from the uniform speed. For details, please refer to Figure 4 .

[0154] Step 203, Wing folding profile Γ W Parameterization and serialization method;

[0155] The swept angle profile of the wing is determined by the wing folding time t W and the speed V W jointly. The present invention assumes that the wing folds uniformly. Therefore, the wing folding sequence can be expressed as:

[0156]

[0157] Γ W =[ξ(t),ξ(t+T s ),...,ξ(T)] T (12)

[0158] Step 204, Generation of tracking error sequences Γ exN ,Γ ezN ;

[0159] To more accurately predict the recovery trajectory, the tracking error sequences Γ exN ,Γ ezN are also used as inputs to the trajectory mapping network. Since the position of the buoy-UAV combination at future times cannot be obtained, therefore, Γ exN ,Γ ezN is constructed by continuously repeating the current tracking error e Udx ,e Udz , that is:

[0160]

[0161] The sectionalization method expressed by Equation (13) is also reasonable because the purpose of Γ exN ,Γ ezN is to reflect the current tracking state of the combination. Combining with other instruction profiles, the prediction of the recovery trajectory is completed. The purpose of sectionalizing e Udx ,e Udz is only to meet the input format requirements of the trajectory mapping network.

[0162] Step 3. Based on deep learning, utilize the non-linear approximation ability and the ability to extract temporal features of the bidirectional gated recurrent unit (BiGRU) neural network to establish an accurate mapping relationship between the inputs (the expected positions of the buoy-UAV combination, the cable recovery speed and acceleration, the timing and speed of UAV wing folding, etc.) and the output (the recovery trajectory of the buoy-UAV combination) of the entire recovery system (including the tracking controller, the motion model of the cable-buoy-UAV combination, etc.), that is, the trajectory mapping network;

[0163] The specific steps are as follows:

[0164] Step 301. Design the trajectory mapping network structure based on BiGRU;

[0165] Based on the deep learning method, propose the UAV recovery trajectory mapping network. And use BiGRU as the network structure. BiGRU contains GRU structures in both the forward and backward directions. By integrating the outputs of the GRUs in the two directions, BiGRU has better context understanding ability compared to GRU.

[0166] The trajectory mapping network structure based on BiGRU is as Figure 5 shown. In terms of the structure dimension, both the forward and backward GRUs have a multi-layer structure to better extract temporal features. Each layer of GRU can be called a GRU cell. In the time dimension, the input sectionalized information is arranged in time series and input to the forward and backward GRUs, and the outputs of the two are stacked and arranged. Finally, through the fully connected layer, the outputs of the fully connected layer are integrated in time series, which is the final network output section.

[0167] The forward propagation process of GRU will not be elaborated in this invention. BiGRU combines the outputs of the last layers of the forward and backward GRUs and Finally, through the integration of the fully connected layer, we can obtain:

[0168]

[0169] Among them, is the set of the outputs of the last layers of the forward and backward GRUs, N L is the number of GRU layers, and are the weight vector and bias vector of the last layer of the network respectively, Y t is the final network output, that is, the recovery trajectory section of the buoy-UAV combination predicted by the trajectory mapping network, represents the mapped recovery trajectory of the buoy-UAV combination.

[0170] Then, the forward propagation process of the trajectory mapping network can be defined as the following function:

[0171]

[0172] where f TMN (·) is the forward propagation function of the trajectory mapping network.

[0173] Step 302, data generation and network training;

[0174] The present invention uses the closed-loop model of the UAV recovery system to generate training data, and then completes the training of the trajectory mapping network, as Figure 6 shown.

[0175] The turbulence intensity is randomly selected between mild turbulence and moderate turbulence.

[0176] The random given method of parameter perturbation is as follows:

[0177] c′ Ud = c Ud ·U(0.8, 1.2) (16)

[0178] where U(0.8, 1.2) is a uniform distribution from 0.8 to 1.2, indicating that the aerodynamic parameters of the composite body are perturbed between [-20%, +20%].

[0179] The random given method of command data is as follows:

[0180]

[0181] Based on the above method, 22,000 trajectory data are generated, of which 20,000 are used for training and 2,000 are used for testing. To accelerate network training, the training data are normalized:

[0182] data train =(data ori - μ data ) / σ data (18)

[0183] where data ori is the original data, data train is the normalized data, μ data and σ data are the mean and variance of the original data respectively.

[0184] The mean square error is used to measure the loss during training:

[0185]

[0186] where Yi * For the output tag value, Y i (W, b) is the predicted value of the trajectory mapping network, W is the weight vector of the network, b is the bias vector of the network, and I is the number of samples of the training data.

[0187] The Adam optimizer is used to calculate the gradient according to the loss value to update the parameters of the trajectory mapping network. To prevent overfitting, a Dropout layer is added between each GRU layer during training to reduce the dependence between nodes. After sufficient training iterations, a trajectory mapping network that can accurately map the recovery trajectory can be finally obtained.

[0188] Step 4: Use the trajectory mapping network to predict the actual recovery trajectory corresponding to different recovery instructions in real time, evaluate the predicted actual recovery trajectory according to the designed cost function, and use the Grey Wolf Optimization (GWO) algorithm to select the optimal recovery instruction, so as to achieve the stable and rapid recovery of the UAV;

[0189] The specific steps are as follows:

[0190] Step 401: Design a cost function considering stability and rapidity;

[0191] The desired recovery process is both stable and rapid, so the cost function needs to reflect the swing amplitude and recovery speed of the recovery trajectory. The recovery speed can be characterized by the time required for the end of recovery while the swing amplitude of the recovery trajectory is characterized by the length of the predicted recovery trajectory minus the length L of the cable to be recovered r In the completely stable state, the length of the recovery trajectory is equal to the length of the cable to be recovered, and indicates that the recovery trajectory has an unnecessary increase and flutter occurs. Therefore, the larger, the greater the degree of flutter of the recovery trajectory.

[0192] Based on the above analysis, the cost function for optimizing the recovery process trajectory is designed as follows:

[0193]

[0194] In the formula: K d and K l are the weight coefficients of the swing amplitude term and the recovery time term respectively; represents the time series length of, multiplied by T s is the recovery time, and is obtained by the following formula:

[0195]

[0196] Step 402: Optimize using the GWO algorithm to obtain the optimal recovery instruction, and then obtain the optimal recovery trajectory;

[0197] First, initialize the population and randomly generate multiple sets of recovery instructions.

[0198] Then, predict the recovery trajectories corresponding to different recovery instructions through the above trajectory mapping network.

[0199] Next, calculate the cost of each recovery trajectory according to the cost function. After multiple rounds of iteration, the recovery instruction corresponding to the minimum cost is the optimal recovery instruction.

[0200] Finally, input the optimal instruction into the recovery system to obtain the optimal recovery trajectory of the UAV.

[0201] After the above design, the overall block diagram of the UAV recovery trajectory optimization is as Figure 7 shown.

[0202] To verify the effectiveness and superiority of the present invention, a certain type of UAV air recovery system is taken as an example for simulation verification. First, verify the prediction performance of the proposed trajectory mapping network and compare it with the GRU network. The parameter selections of the two network structures are shown in Table 1:

[0203] Table 1

[0204] Network model BiGRU GRU Number of nodes in each layer 80 80 <![CDATA[Number of layers N of BiGRU / GRU L > 3 3 Size of training set (number of trajectories) 20000 20000 Training batch size (number of trajectories) 20 20 Number of training epochs 10000 10000 Initial learning rate 0.001 0.001 Optimizer Adam Adam Size of test set (number of trajectories) 2000 2000 Root mean square error (RMSE) of test set 0.1073 0.2100

[0205] As can be seen from Table 1, under the condition of basically the same parameters, the RMSE of BiGRU is half of the RMSE of GRU. Therefore, the trajectory mapping network based on BiGRU of the present invention has better prediction performance than GRU, which is because BiGRU has better time series feature extraction ability.

[0206] The trajectory mapping results of some typical test sets are shown in Figure 8. It can be seen that the trajectory mapping network based on BiGRU proposed by the present invention can well predict the real recovery trajectory, laying a foundation for subsequent trajectory optimization. It should be noted that the instruction trajectories in the test set are randomly generated. When the given instruction trajectories are not appropriate, there will inevitably be a large deviation between the actual trajectory and the instruction trajectory, as Figure 8b and Figure 8c shown, which is also the reason why trajectory mapping and optimization are needed.

[0207] The comparison of the running times of the recovery system closed-loop model, BiGRU, and GRU in the test set is as Figure 9As shown in the figure. The operation time of the closed-loop model is the longest and the operation efficiency is the lowest. This is because the closed-loop model includes the complex dynamic model of the combined body, the actuator, the controller, etc., with more differential equations and a longer integration time. The operation times of BiGRU and GRU are similar. Due to its more complex structure, the operation time of BiGRU is slightly longer than that of GRU. The average operation time of the closed-loop model is 29.22 seconds, and the average operation time of BiGRU is 0.13 seconds. The trajectory mapping network has improved the computing efficiency by more than 200 times, making online optimization a reality.

[0208] After verifying the prediction performance of the trajectory mapping network, the recovery trajectory optimization performance based on the trajectory mapping network is further verified. To demonstrate the superiority of the method proposed in the present invention, a recovery method without trajectory optimization is used for comparison, that is, the recovery command adopts a constant value, and the command input of the comparison method is selected according to the median value of the optimization range of the proposed method. The recovery process considers mild turbulence and the wake of the mother ship. The comparison between the command and the actual recovery trajectory is as Figure 10 shown. The comparison method does not consider the tracking performance of the position controller and the comprehensive influence of other recovery commands when generating the command trajectory. Therefore, the actual recovery trajectory shows a large swing after the start of recovery, seriously affecting the recovery safety. On the basis of comprehensively considering the comprehensive influence of all elements of the entire recovery system, the method proposed in the present invention optimizes the recovery command. Through trajectory mapping, the actual recovery trajectory has been predicted during optimization, and the influence of each command on the actual recovery trajectory has been considered in advance. Therefore, an appropriate command trajectory, the wing folding and cable recovery speed commands, etc. have been optimized. Under the action of these commands, the actual trajectory swing amplitude of the buoy-UAV combined body is small.

[0209] The change in the cable configuration under the action of the trajectory optimization method proposed in the present invention during the recovery process is as Figure 11 shown. The change in the cable configuration is very stable and the swing amplitude is very small. In comparison, the change in the cable configuration under the action of the comparison method is large and the swing amplitude is also large, as Figure 12 shown, which is not conducive to the stable recovery of the UAV.

[0210] The comparison of the recovery trajectory indexes and costs under the condition of aerodynamic parameter perturbation (-20% to 20%) is shown in Table 2. The total cost is calculated by Equation (20), where K d = 2, K l = 1. The swing amplitude, recovery time, and total cost of the trajectory optimization method proposed in the present invention are all better than those of the comparison method. And under different aerodynamic parameter perturbations, the method proposed in the present invention does not change much and is better than the comparison method in all cases. This verifies the effectiveness of the trajectory optimization method proposed in the present invention and its adaptability to parameter changes.

[0211] Table 2

[0212]

[0213] Based on the above simulation verification of the embodiments, the effectiveness of the method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed aerial recovery based on trajectory mapping according to the present invention is proved.

[0214] The content not described in detail in the specification of the present invention belongs to the prior art well known to those skilled in the art.

Claims

1. A method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed aerial recovery based on trajectory mapping, characterized in that, Specifically, it includes the following steps: Step 1: Establish a non-linear motion model of the cable and the buoy-UAV combination for the UAV recovery system; Specifically, it includes establishing a cable motion model based on the multi-rigid body theory and a six-degree-of-freedom dynamics model of the buoy-UAV combination considering the cable tension; Step 2: Based on the non-linear motion model of the UAV recovery system, parameterize and optimize the profile data of the UAV recovery system, and expand the command variables (R l , V L , a L , t W , V W ) output by the optimization algorithm into an input sequence as the input of the trajectory mapping network; The profile data of the UAV recovery system includes: the expected recovery trajectory profile of the UAV The recovery speed profile Γ of the cable VL And the wing folding profile Γ W ; After parametric representation: the non-binding vector and direction R l 、The cable recovery speed and acceleration V L ,a L 、The timing and folding speed t of wing folding W ,V W Function of; Step 3: Based on deep learning, use the Bidirectional Gated Recurrent Unit Neural Network (BiGRU) to establish an accurate mapping relationship between the input and output of the entire recovery system, that is, the trajectory mapping network; The input of the trajectory mapping network includes the desired position of the buoy-UAV combination, the cable recovery speed and acceleration, the timing and speed of the UAV wing folding; the output includes the recovery trajectory of the buoy-UAV combination; The specific steps for establishing the trajectory mapping network are as follows: Step 301: Design a trajectory mapping network structure based on BiGRU; BiGRU contains GRU structures in both the forward and backward directions. In terms of the structural dimension, both the forward and backward GRUs have a multi-layer structure, and a Dropout layer is added between each GRU layer during training; in terms of the time dimension, the input sectionalized information is arranged in time sequence and input to the forward and backward GRUs, and the outputs of the two are stacked and arranged. Finally, after passing through the fully connected layer, the outputs of the fully connected layer are integrated in time sequence to obtain the final network output section; The output of the last layer of the BiGRU combines the forward and backward GRUs and Finally, it is integrated through a fully connected layer to obtain: Among them, is the set of outputs of the last layers of the forward and reverse GRUs, N L is the number of GRU layers, and are the weight vector and bias vector of the last layer of the network respectively, Y t is the final network output, that is, the buoy - UAV combined body recovery trajectory profile predicted by the trajectory mapping network, represents the mapped buoy - UAV combined body recovery trajectory; Then, the forward propagation process of the trajectory mapping network is defined as the following function: where, f TMN (·) is the forward propagation function of the trajectory mapping network; Γ exN , Γ ezN is the tracking error sequence; Step 302: Use the closed-loop model of the UAV recovery system to generate training data; Input different intensities of atmospheric turbulence data, different parameter perturbation data, and different command data into the UAV recovery system model to generate several trajectory data, and divide the trajectory data into training data and test data according to a ratio of 10:1; Step 303: Use the Adam optimizer to calculate the gradient according to the loss value to update the parameters of the trajectory mapping network. After sufficient training iterations with the training data, obtain a trajectory mapping network that accurately maps the recovery trajectory; Step 4: Use the trajectory mapping network to predict the actual recovery trajectories corresponding to different recovery commands in real time, evaluate the predicted actual recovery trajectories according to the designed cost function, and use the Grey Wolf Optimization algorithm (GWO) to select the optimal recovery command, so as to achieve the stable and fast recovery of the UAV; The specific steps are as follows: Step 401: Design the cost function for trajectory optimization in the recovery process as follows: where: K d and K l are the weight coefficients of the swing amplitude term and the recovery time term respectively; denotes the timing length of s multiplied by T r is the recovery time; L is obtained by the following formula: Step 402: Use the GWO algorithm to optimize and obtain the best recovery command, and then obtain the optimal recovery trajectory; First, initialize the population and randomly generate multiple groups of recovery commands; Then, predict the recovery trajectories corresponding to different recovery commands through the above trajectory mapping network; Next, calculate the cost of each recovery trajectory according to the cost function. After multiple rounds of iteration, the recovery command corresponding to the minimum cost is the optimal recovery command; Finally, input the optimal command into the UAV recovery system to obtain the optimal recovery trajectory of the UAV.

2. The method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed aerial recovery based on trajectory mapping according to claim 1, characterized in that, The establishment of the cable motion model based on the multi-rigid body theory in Step 1 is specifically as follows: In the dragging coordinate system S D (O D -X D Y D Z D ), cable modeling is carried out, where p i is the position of the i-th node, and r i = p i - p i-1 is the position vector of the i-th link; the angular deflections λ D O D Y D of the i-th link relative to the plane X D O D Z D and i are used to describe the link motion; ​ r i The calculation formula is as follows: where l = L0 / N is the length of the i-th link, L0 is the total length of the cable, and N is the number of discrete equally long cylindrical rigid links of the cable; n i is the unit direction vector of the i-th link; λ i and The second-order dynamic equation of is expressed as: Among them, a i is the acceleration of node i, α D and ω D are respectively the angular velocity and angular acceleration of the dragging system S D relative to the inertial system S g (O g -X g Y g Z g ); and are the cable retracting / extending speed and acceleration respectively.

5. A method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed aerial recovery based on trajectory mapping according to claim 1, wherein, The six-degree-of-freedom dynamics model of the buoy-UAV combination considering the cable tension in Step 1 is specifically as follows: First, analyze the forces acting on the end node of the cable, including the gravity mg of the buoy-UAV combination A and the aerodynamic force F A , the gravity mg of node N N , half of the aerodynamic force of the Nth section of the cable 0.5F N and the tension t of the cable N ; Therefore, establish the following combined body dynamics model in the track system: In the formula, and respectively represent the transformation matrices from the air flow system and the drag system to the track system; V k is the speed of the buoy-UAV combination; γ and χ are the track angles of the buoy-UAV combination; the motion equations of other loops are similar to those of conventional aircraft; Then, adopt the parametric modeling method to conduct CFD air blowing on the buoy-UAV combination under seven cases where the wing sweep angle ξ = 0°, ξ = 15°, ξ = 30°, ξ = 45°, ξ = 60°, ξ = 75, and ξ = 90°. Assume that the parameter change between adjacent folding angles is linear, and linearly interpolate the obtained parameters, that is, obtain the aerodynamic parameters of the buoy-UAV combination during the wing folding process.

6. A method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed aerial recovery based on trajectory mapping according to claim 3, wherein, The aerodynamic parameters of the buoy-UAV combination during the wing folding process are expressed by the formula: Among them, and are the aerodynamic parameters of the buoy-UAV combination when the sweep angle ξ is 0, 15°, 30°, 45°, 60°, 75°, and 90°, respectively.

7. A method for optimizing the trajectory of an unmanned aerial vehicle (UAV) towed aerial recovery based on trajectory mapping according to claim 1, wherein, In the second step, the parameterization of each section data is specifically as follows: (1) Desired recovery trajectory profile Parameterization and serialization method; Given the non-constrained vector and direction R l , and the change in the cable length L r during the entire recovery process, generated by simulation That is: where, R l * is the desired non-binding vector sum and direction, t is the current moment, T s is the sampling step, T is the termination moment, f RLX (·) and f RLZ (·) are the fitting functions of the steady-state X-axis and Z-axis positions of the buoy-UAV combination, respectively; Given different combinations of R l , L r in the simulation environment, after the control stabilizes, record the corresponding X-axis and Z-axis positions at this time, and perform polynomial fitting based on the simulation data to obtain the following relationship: As can be seen from the above formula, during the recovery process, the X-axis and Z-axis positions of the buoy-UAV combination are linearly related to L r and quadratically related to R l . (2) Cable recovery speed profile Parameterization and serialization methods; The recovery speed profile of the cable is determined by its maximum recovery speed and acceleration. Assuming that the cable length moves at a constant speed or with a uniform acceleration during recovery, its recovery speed profile is trapezoidal. Since the area of the trapezoid is equal to the length of the cable L to be recovered r , it follows that: where V L , a L are respectively the maximum speed and acceleration of cable recovery; Based on Equation (7), the cable recovery speed sequence is expressed as: In the formula, t1 is the moment when the cable recovery speed reaches the maximum value, and t2 is the moment when the cable recovery speed starts to decelerate from uniform speed; (3) Wing folding section Γ W Parametrization and serialization method; The swept angle profile of the wing is determined by the time t W and the speed V W jointly. Assuming the wing folds at a constant speed, the wing folding sequence is expressed as: Γ W = [ξ(t), ξ(t + T s ),..., ξ(T)] T (11) (4) Generation of the tracking error sequence Γ exN , Γ ezN ; By continuously repeating the current tracking error e Udx , e Udz to construct the tracking error sequence Γ exN , Γ ezN , to more accurately predict the recovery trajectory, i.e.:

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