A wing parachute track tracking method for complex environment

Abstract

The application provides a wing parachute track tracking method for complex environment, and belongs to the technical field of wing parachute track tracking control, and comprises the following steps: a six-degree-of-freedom model of the wing parachute is established to describe the position and posture of the wing parachute in the movement process; a reasonable structure and loss function are selected, and a long short-term memory network (LSTM) for predicting instantaneous speed is trained through a back propagation algorithm; the error between the actual track and the expected track is calculated through a lateral track error method to realize lateral control of the wing parachute; and the predicted instantaneous speed, the expected track and the actual track error are taken as inputs to realize tracking control of the wing parachute through a sliding mode controller. In the case that the measurement information is limited, the instantaneous speed of the wing parachute is predicted through the LSTM, and the track tracking of the wing parachute is realized in combination with the sliding mode control. Compared with the traditional control method, the method provided by the application has higher reaction speed and robustness, and can realize fast and stable track tracking of the wing parachute.

Description

Technical Field

[0001] This invention relates to a trajectory tracking method, and more particularly to a paraglider trajectory tracking method for complex environments. Background Technology

[0002] A paraglider is an advanced aerial energy storage device, mainly composed of a paraglider, suspension system, control system, and parachute. It features high controllability, long-duration loiter time, flexible landing, and low cost, which have driven its application and continuous improvement in the aerospace field.

[0003] Compared to traditional parachutes, the wing parachute's airfoil structure and large canopy area give it a longer loiter time. The airdrop system uses the wing parachute as a decelerator, which has good controllability and can achieve autonomous delivery of payloads at high altitudes, long distances and with high precision. It makes up for the shortcomings of traditional airdrop methods, such as poor accuracy, target dispersion and high risk, and greatly enhances the maneuverability and flexibility of airdrop missions.

[0004] The paraglider is a highly complex underactuated system with strong coupling and large time delay, controlled only by pull-down control lines. Due to its strong coupling, nonlinearity, large time delay, uncertain disturbances, and the combined effects of multiple constraints, current technologies cannot achieve high-precision trajectory tracking control, and its robustness and disturbance rejection capabilities are poor. Summary of the Invention

[0005] Purpose of the invention: The technical problem to be solved by the present invention is to provide a paraglider trajectory tracking method for complex environments, addressing the shortcomings of the existing technology.

[0006] To address the aforementioned technical problems, this invention discloses a paraglider trajectory tracking method for complex environments, comprising:

[0007] Step 1: Based on the mechanical structure of the parachute, establish a six-degree-of-freedom model of the parachute's translation and rotation.

[0008] Furthermore, the establishment of the six-degree-of-freedom model for the parachute's translation and rotation is specifically as follows:

[0009] If we consider the parachute as a rigid body, then the scalar form of the dynamic equation for the translation of the parachute's center of mass is:

[0010]

[0011] in, and- This represents the projection of the acceleration vector onto the x, y, and z axes of the velocity system;

[0012] The kinematic equations for the translation of the parachute's center of mass are:

[0013]

[0014] Where V is the velocity of the parachute, ψ v Let θ be the parachute's deflection angle, m be the parachute's inclination angle, g be the gravitational acceleration, D be the drag, L be the lift, Y be the lateral force, and γ be the lateral force. v Let (x, y, z) be the velocity tilt angle, and (x, y, z) be the position of the parachute in the ground coordinate system.

[0015] The scalar form of the dynamic equation for the rotation of the parachute's center of mass is:

[0016]

[0017] in, and This represents the angular acceleration of rotation about the x, y, and z axes of the body coordinate system;

[0018] The kinematic equation for the rotation of the parachute's center of mass is:

[0019]

[0020] in, Indicates the rate of change of tilt angle. Indicates the rate of change of pitch angle. ω represents the rate of change of yaw angle. x ω y and ω z These are the components of the rotational angular velocity along the x, y, and z axes of the body coordinate system, respectively. x M y M z J represents the components of the principal moments acting on the center of mass along the x, y, and z axes of the body coordinate system. xx J yy J zz J represents the moments of inertia of the body coordinate system along the x, y, and z axes. xz Let γ be the product of inertia of the x, y, and z axes of the body coordinate system, and γ be the tilt angle. ψ is the pitch angle, and ψ is the yaw angle.

[0021] Step 2: Construct and train a long short-term memory network to predict the instantaneous velocity of the parachute;

[0022] Furthermore, the specific method for constructing and training the Long Short-Term Memory network is as follows:

[0023] Step 2-1: Select the network structure and construct a Long Short-Term Memory (LSTM) network. The specific method is as follows:

[0024] The Long Short-Term Memory (LSTM) network includes a forget gate, an input gate, and an output gate;

[0025] Cell state C at the previous momentt-1 The updated cell state C is calculated by passing the forget gate, input gate, and output gate respectively. t ;

[0026] The forget gate is used to filter information, where the current input x is... t and the output h of the previous time step t-1 The output f after passing through the forget gate t for:

[0027] f t =relu(W f [h t-1 x t ]+b f )

[0028] Among them, W f and b f For the weights and biases of the forget gate, the mathematical expression for the ReLU function, relu(x), is:

[0029] relu(x) = max{0, x}

[0030] The input gate is used to determine the new information to be stored. It consists of a ReLU layer and a tanh layer. The ReLU layer determines the value to be updated, and the tanh layer creates a new candidate value vector. Add to status:

[0031] i t =relu(W i [h t-1 x t ]+b i )

[0032]

[0033] Updated status C t for:

[0034]

[0035] Among them, i t W represents the output vector. i and b i W represents the weights and biases of the input gate. n and b n For the weights and biases of the tanh layer, the mathematical expression for tanh, tanh(x), is:

[0036]

[0037] The output gate is used to determine the output value, and the final output is h. t for:

[0038] h t =o t tanh(C t )

[0039] Wherein, the output state o t This is determined by a ReLU layer, as follows:

[0040] o t =relu(W o [h t-1 x t ]+b o )

[0041] Among them, W o and b o The weights and biases of the output gate.

[0042] Step 2-2: Determine the loss function of the network, using the following method:

[0043] Use a sliding window to extract a length of W from the pre-collected paraglider velocity dataset. V The speed data is used to obtain the j-th input vector I of the Long Short-Term Memory Network. j for:

[0044] I j ={v k k = j, j+1, ..., W v +j-1}

[0045] Its corresponding tag is:

[0046]

[0047] The loss function L of the network is:

[0048]

[0049] in: Here, T represents the label corresponding to the predicted vector, and T represents the number of target trajectory points.

[0050] Steps 2-3 involve training the constructed Long Short-Term Memory network using the backpropagation algorithm.

[0051] Step 3: Based on the horizontal distance between the current position of the paraglider and the planning point, calculate the error between the actual trajectory and the expected trajectory of the paraglider, namely the lateral trajectory error and the heading angle tracking error, using the lateral trajectory error method, and then perform lateral control on the paraglider.

[0052] Furthermore, the error between the actual trajectory and the desired trajectory of the calculated paraglider, namely the lateral trajectory error and the heading angle tracking error, is specifically as follows:

[0053] Let the position vector of the paraglider in the two-dimensional plane be [x(t), y(t)], and the position vectors of the path points that the paraglider needs to track at the current time, the previous time, and the next time be [x(t), y(t)], respectively. r (i), y r (i)],[x r (i-1), y r (i-1)] and [x r (i+1), y r [i+1], where the heading angle of the parachute at its current position is ψ(t);

[0054] Let the positional deviations between the path tracking point at the current moment and the path tracking point at the previous moment be Δx and Δy, then:

[0055] Δx=x r (i)-x r (i-1)

[0056] Δy=y r (i)-y r (i-1)

[0057] Let the positional deviation between the current position of the parachute and the path point to be tracked be . and but:

[0058]

[0059]

[0060] trajectory line heading angle ψ r (i) is:

[0061]

[0062] The lateral trajectory tracking error Δ(t) is:

[0063]

[0064] Heading angle tracking error ψ e (t) is:

[0065] ψ e (t)=ψ(t)-ψ r (i).

[0066] Step 4: Design a sliding mode controller. Take the instantaneous velocity predicted by the long short-term memory network described in Step 2 and the lateral trajectory error and heading angle tracking error calculated in Step 3 as inputs, and use the sliding mode controller to track and control the paraglider.

[0067] Furthermore, the design of the sliding mode controller specifically includes:

[0068] Step 4-1: Define the objectives of the controller design;

[0069] Step 4-2, establish the sliding surface s as follows:

[0070] s = k Δ Δ(t)+v s sin(ψ e )

[0071] Where, ψ e Indicates the heading angle tracking error; k Δ ∈R, where, k Δ Let R be a constant, and let R represent the set of real numbers; the above equation can be further simplified to:

[0072] s = k Δ Δ(t)+v s ψ e

[0073] Among them, v s This represents the horizontal velocity of the parachute, which is the instantaneous velocity predicted by the long short-term memory network in step 2.

[0074] Step 4-3, differentiate with respect to the sliding surface s to obtain for:

[0075]

[0076] Taking the derivative of the lateral trajectory tracking error Δ(t) yields for:

[0077]

[0078] Step 4-4: A sliding mode controller based on the exponential reaching law is used for control. The control law is as follows:

[0079]

[0080] Where sgn() represents the sign function;

[0081] The saturation function sat(s) is used to replace the symbolic function sgn(s), where the saturation function has the following form:

[0082]

[0083] The replaced control law is:

[0084]

[0085] Where ε and k are gain constants, whose values ​​are required to ensure that the system tends to be stable in sliding mode, and a is a constant;

[0086] Steps 4-5, heading angle tracking error ψ e The mathematical expression is:

[0087] ψ e =ψ(t)-ψ r (i)

[0088] Where ψ(t) is the heading angle, ψ r (i) is the heading angle of the trajectory line;

[0089] Combination ψ e And the control law, to obtain the rate of change of heading angle

[0090]

[0091] Control quantity Δ and rate of change of heading angle The relationship is represented as:

[0092]

[0093] Where A1, A2, B1, and B2 represent aerodynamic conversion coefficients, v x and v y This represents the components of the parachute's horizontal velocity along the x-axis and y-axis.

[0094] Furthermore, the objective of determining the design controller in step 4-1 is to make the lateral trajectory error and heading angle error tend to be stable and minimized.

[0095] Furthermore, the constant a mentioned in step 4-4 takes the value of 0.05.

[0096] Furthermore, the control quantity Δ obtained in step 4-4 is used to control the parachute.

[0097] Beneficial effects:

[0098] By using LSTM to predict the instantaneous velocity of the paraglider, the instantaneous velocity can be obtained from the paraglider's position information even with limited measurement information. Compared with traditional methods, it has a stronger adaptability to complex environments. The instantaneous velocity information obtained by prediction can be used for more accurate tracking control, avoiding control errors caused by time delay. Furthermore, the guidance law is designed using the lateral trajectory error method, which improves the tracking accuracy of the paraglider. At the same time, the sliding mode controller makes the system highly adaptable and robust, and can effectively cope with the impact of environmental changes, wind disturbances and other factors. Attached Figure Description

[0099] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0100] Figure 1 This is a flowchart of the paraglider trajectory tracking method for complex environments according to the present invention;

[0101] Figure 2 This is a diagram of the LSTM structure;

[0102] Figure 3 This is a schematic diagram of lateral trajectory tracking;

[0103] Figure 4 This is a schematic diagram of the trajectory tracking controller structure.

[0104] Figure 5 This is a simulation diagram of parachute trajectory tracking. Detailed Implementation

[0105] This invention provides a paraglider trajectory tracking method for complex environments. Using LSTM (Long Short-Term Memory) networks, the instantaneous velocity of the paraglider can be effectively predicted. Even with limited measurement information, the instantaneous velocity of the paraglider can be obtained solely from its position information, thereby improving the timeliness and stability of trajectory tracking control. The predicted instantaneous velocity information allows for more accurate tracking control, avoiding control errors caused by time delays. Furthermore, the use of a sliding mode controller gives the system strong adaptability and robustness, effectively coping with environmental changes and disturbances. In the control of nonlinear, time-varying, and unknown systems, sliding mode control exhibits excellent control performance and can achieve high-precision control of the system. The technical solution adopted in this invention is as follows:

[0106] Step 1: By analyzing the mechanical structure of the parachute, establish a six-degree-of-freedom model of the parachute's translation and rotation.

[0107] Step 2: Select a reasonable structure and loss function, and train a Long Short-Term Memory (LSTM) network for predicting instantaneous velocity using the backpropagation algorithm;

[0108] Step 3: Based on the horizontal distance between the current position of the paraglider and the planning point, calculate the error between the actual trajectory and the desired trajectory, as well as the heading angle tracking error, using the lateral trajectory error method to achieve lateral control of the paraglider;

[0109] Step 4: Using the instantaneous velocity, lateral trajectory error, and heading angle error predicted by LSTM as inputs, design a sliding mode controller to achieve stable tracking control of the paraglider.

[0110] Step 1 above is specifically as follows:

[0111] Treating the parachute as a rigid body, we use Newton's second law to study the movement of the center of mass and the theorem of angular momentum to study the rotation about the center of mass.

[0112] The scalar form of the dynamic equation for the motion of the parachute's center of mass is:

[0113]

[0114] The kinematic equations for the motion of the parachute's center of mass are:

[0115]

[0116] Where V is the velocity of the parachute, ψ v Let θ be the parachute's deflection angle, m be the parachute's inclination angle, g be the gravitational acceleration, D be the drag, L be the lift, Y be the lateral force, and γ be the lateral force. v Let x be the velocity tilt angle, and let x, y, and z be the positions of the parachute below the ground frame.

[0117] The scalar form of the dynamic equation for the rotation of the parachute's center of mass is:

[0118]

[0119] in, and This represents the angular acceleration of rotation about the x, y, and z axes of the body coordinate system;

[0120] The kinematic equations for the motion of the parachute's center of mass are:

[0121]

[0122] in, Indicates the rate of change of tilt angle. Indicates the rate of change of pitch angle. ω represents the rate of change of yaw angle. x ω y and ω z These are the components of the rotational angular velocity along the x, y, and z axes of the body coordinate system, respectively.x M y M z J represents the components of the principal moments acting on the center of mass along the x, y, and z axes of the body coordinate system. xx J yy J zz J represents the moments of inertia of the body coordinate system along the x, y, and z axes. xz Let γ be the product of inertia of the x, y, and z axes of the body coordinate system, and γ be the tilt angle. ψ is the pitch angle, and ψ is the yaw angle.

[0123] Step 2 above is specifically as follows:

[0124] Let T be the number of points on the target trajectory, then the coordinate set L of the nth trajectory is... n ={c i |i = 1, 2, ..., T}, velocity set is V n ={v i |i = 1, 2, ..., T};

[0125] First, the forget gate filters out the information to be discarded, given the current input x. t and the output h of the previous time step t-1 The output after passing through the forget gate is:

[0126] f t =relu(W f [h t-1 x t ]+b f )

[0127] Among them, W f and b f The weights and biases for the forget gate;

[0128] Then, the input gate is used to determine the new information to be stored, the ReLU layer determines the value to be updated, and the tanh layer creates a new candidate value vector. Add to status:

[0129] i t =relu(W i [h t-1 x t ]+b i )

[0130]

[0131] The updated status is:

[0132]

[0133] Among them, W i and bi W represents the weights and biases of the input gate. n and b n The weights and biases of the tanh layer;

[0134] Next, the output state is determined through a ReLU layer:

[0135] o t =relu(W o [h t-1 x t ]+b o )

[0136] Among them, W o and b o The weights and biases of the output gate;

[0137] Finally, the output gate determines the output value, and the final output is:

[0138] h t =o t tanh(C t )

[0139] Determine the loss function: Use a sliding window to extract a loss function of length W from the velocity dataset. V From the velocity data, the j-th input vector of the LSTM model for predicting instantaneous velocity is:

[0140] I j ={v k k = j, j+1, ..., W v +j-1}

[0141] Its corresponding tag is:

[0142] The loss function is:

[0143]

[0144] in: The label is the one corresponding to the predicted vector, and T is the number of target trajectory points;

[0145] An LSTM for predicting instantaneous velocity is trained through backpropagation.

[0146] Step 3 above specifically refers to:

[0147] Let the position vector of the paraglider in the two-dimensional plane be [x(t), y(t)], and the position vectors of the path points that the paraglider needs to track at the current time, the previous time, and the next time be [x(t), y(t)], respectively. r (i), y r (i)],[x r (i-1), yr (i-1)] and [x r (i+1), y r [i+1], where the heading angle of the parachute at its current position is ψ(t);

[0148] Let the positional deviations between the path tracking point at the current moment and the path tracking point at the previous moment be Δx and Δy, then:

[0149] Δx=x r (i)-x r (i-1)

[0150] Δy=y r (i)-y r (i-1)

[0151] Let the positional deviation between the current position of the parachute and the path point to be tracked be . and but:

[0152]

[0153]

[0154] The heading angle of the trajectory line is:

[0155]

[0156] The trajectory tracking error Δ(t) is:

[0157]

[0158] Heading angle tracking error ψ e (t) is:

[0159] ψ e (t)=ψ(t)-ψ r (i)

[0160] The lateral trajectory error method can simplify a complex three-dimensional problem into a two-dimensional tracking problem, shifting the focus of the tracking problem to reducing trajectory tracking error and heading angle error. Therefore, it is only necessary to design a controller to make the error tend to be stable and minimized.

[0161] Step 4 above specifically refers to:

[0162] As shown in step 3, the trajectory tracking requirement can be met simply by designing a controller that stabilizes and minimizes the lateral trajectory error and heading angle error. Based on this, the sliding surface is established as follows:

[0163] s = k Δ Δ(t)+v s sin(ψ e )

[0164] Due to ψ e It is usually very small, so sin(ψ) can be considered as e )≈ψ e Then the above formula can be further simplified to:

[0165] s = k Δ Δ(t)+v s ψ e

[0166] Where, k Δ ∈R, and its value needs to be adjusted and optimized through experiments and simulations. If a fast system response is required, k can be increased. Δ However, an excessively large k Δ This may cause the controller output to be too large, resulting in oscillation or instability. s This represents the horizontal velocity of the parachute, which is the instantaneous velocity predicted in step 2 using the Long Short-Term Memory Network.

[0167] Differentiating with respect to s, we get for:

[0168]

[0169] Taking the derivative of Δ(t) yields for:

[0170]

[0171] A sliding mode controller based on the exponential reaching law is used for control, and its control law is as follows:

[0172]

[0173] To eliminate chattering generated by the sliding mode controller, the saturation function sat(s) is used to replace the sign function sgn(s), where the saturation function has the following form:

[0174]

[0175] The recurrence law after the replacement is:

[0176]

[0177] Where ε and k are gain constants, their values ​​should be selected by comprehensively considering factors such as system stability, response speed and robustness. The optimal value of the gain constant may need to be determined through multiple experiments and debugging, and optimized according to the requirements of the actual application. a is taken as a constant value of 0.05.

[0178] Combination From the control law, we can obtain:

[0179]

[0180] Control quantity Δ and The relationship can be represented as:

[0181]

[0182] Where A1, A2, B1, and B2 represent aerodynamic conversion coefficients, v x and v y This represents the components of the parachute's horizontal velocity along the x-axis and y-axis.

[0183]

[0184]

[0185]

[0186]

[0187] Among them, F p For the incoming flow pressure, S p For the area of ​​the umbrella canopy, Where α is the parachute drag coefficient, α is the angle of attack, and C is the parachute drag coefficient. L Where β is the lift coefficient, β is the sideslip angle, and C is the lift coefficient. Yβ For the Y-axis force coefficient associated with the sideslip angle, C Yr The Z-axis rotation-induced Y-axis aerodynamic coefficient, Let be the rate of change of yaw angle, b be the parachute span, and v be the instantaneous velocity of the parachute. w For wind speed, G is the drag coefficient of the airdropped object, G is the gravity of the parachute system, and B is the drag coefficient of the airdropped object. e-b Let m be the transformation matrix from the ground coordinate system to the body coordinate system. p For the quality of the umbrella canopy, m b For the mass of the airdropped goods, m a For added mass, C Lδ For asymmetric control of lift coefficient, C Dδ For asymmetric control drag coefficient, C Yδ The induced Y-axis force coefficient is used for asymmetric control.

[0188] Where A1 represents the first element of matrix A, A2 represents the second element of matrix A, B1 represents the first element of matrix B, and B2 represents the second element of matrix B.

[0189] The quantities after the equal sign in the expression for the control quantity Δ are all known quantities, so the value of the control quantity can be directly calculated, and finally the flight state of the paraglider can be controlled by the control quantity Δ.

[0190] By definition, a paraglider has only one control variable: pull-down Δ, with positive values ​​for the left side and negative values ​​for the right side.

[0191] Example:

[0192] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0193] like Figure 1 As shown, the present invention provides a paraglider trajectory tracking method for complex environments, comprising:

[0194] Step 1: By analyzing the mechanical structure of the parachute, establish a six-degree-of-freedom model of the parachute's translation and rotation.

[0195] Treating the parachute as a rigid body, we use Newton's second law to study the movement of the center of mass and the theorem of angular momentum to study the rotation about the center of mass.

[0196] The scalar form of the dynamic equation for the motion of the parachute's center of mass is:

[0197]

[0198] The kinematic equations for the motion of the parachute's center of mass are:

[0199]

[0200] Where V is the velocity of the parachute, ψ v Let θ be the parachute's deflection angle, m be the parachute's inclination angle, g be the gravitational acceleration, D be the drag, L be the lift, Y be the lateral force, and γ be the lateral force. v Let x be the velocity tilt angle, and let x, y, and z be the positions of the parachute below the ground frame.

[0201] The scalar form of the dynamic equation for the rotation of the parachute's center of mass is:

[0202]

[0203] in, and This represents the angular acceleration of rotation about the x, y, and z axes of the body coordinate system;

[0204] The kinematic equations for the motion of the parachute's center of mass are:

[0205]

[0206] in, Indicates the rate of change of tilt angle. Indicates the rate of change of pitch angle. ω represents the rate of change of yaw angle. x ω y and ω zThese are the components of the rotational angular velocity along the x, y, and z axes of the body coordinate system, respectively. x M y M z J represents the components of the principal moments acting on the center of mass along the x, y, and z axes of the body coordinate system. xx J yy J zz J represents the moments of inertia of the body coordinate system along the x, y, and z axes. xz Let γ be the product of inertia of the x, y, and z axes of the body coordinate system, and γ be the tilt angle. ψ is the pitch angle, and ψ is the yaw angle.

[0207] Step 2, as follows Figure 2 As shown, by selecting a reasonable structure and loss function, a Long Short-Term Memory (LSTM) network for predicting instantaneous velocity is trained through the backpropagation algorithm.

[0208] Let T be the number of points on the target trajectory, then the coordinate set L of the nth trajectory is... n ={c i |i = 1, 2, ..., T}, velocity set is V n ={v i |i=1,2,…,T}, using a sliding window, extract data of length W from the trajectory dataset and velocity dataset respectively. L Coordinate data and W V The speed data is used to directly establish a mapping relationship between the two using LSTM;

[0209] First, the forget gate filters out the information to be discarded, given the current input x. t and the output h of the previous time step t-1 The output after passing through the forget gate is:

[0210] f t =relu(W f [h t-1 x t ]+b f )

[0211] Among them, W f and b f The weights and biases for the forget gate;

[0212] Then, the input gate is used to determine the new information to be stored, the ReLU layer determines the value to be updated, and the tanh layer creates a new candidate value vector. Add to status:

[0213] i t =relu(W i [h t-1 x t ]+bi )

[0214]

[0215] The updated status is:

[0216]

[0217] Among them, W i and b i W represents the weights and biases of the input gate. n and b n The weights and biases of the tanh layer;

[0218] Next, the output state is determined through a ReLU layer:

[0219] o t =relu(W o [h t-1 x t ]+b o )

[0220] Among them, W o and b o The weights and biases of the output gate;

[0221] Finally, the output gate determines the output value, and the final output is:

[0222] h t =o t tanh(C t )

[0223] By calculating the partial derivative of the loss function with respect to each network parameter, the direction of parameter updates is determined, enabling the network to learn in the direction of minimizing the loss function until the model converges.

[0224] Step 3, as follows Figure 3 As shown, based on the horizontal distance between the current position of the paraglider and the planning point, the error between the actual trajectory and the desired trajectory, as well as the heading angle tracking error, are calculated using the lateral trajectory error method to achieve lateral control of the paraglider.

[0225] Let the position vector of the paraglider in the two-dimensional plane be [x(t), y(t)], and the position vectors of the path points that the paraglider needs to track at the current time, the previous time, and the next time be [x(t), y(t)], respectively. r (i), y r (i)],[x r (i-1), y r (i-1)] and [x r (i+1), y r [i+1], where the heading angle of the parachute at its current position is ψ(t);

[0226] Let the positional deviations between the path tracking point at the current moment and the path tracking point at the previous moment be Δx and Δy, then:

[0227] Δx=x r (i)-x r (i-1)

[0228] Δy=y r (i)-y r (i-1)

[0229] Let the positional deviation between the current position of the parachute and the path point to be tracked be . and but:

[0230]

[0231]

[0232] The heading angle of the trajectory line is:

[0233]

[0234] The trajectory tracking error Δ(t) is:

[0235]

[0236] Heading angle tracking error ψ e (t) is:

[0237] ψ e (t)=ψ(t)-ψ r (i)

[0238] The lateral trajectory error method can simplify a complex three-dimensional problem into a two-dimensional tracking problem, shifting the focus of the tracking problem to reducing trajectory tracking error and heading angle error. Therefore, it is only necessary to design a controller to make the error tend to be stable and minimized.

[0239] Step 4, as follows Figure 4 As shown, using the instantaneous velocity, lateral trajectory error, and heading angle error predicted by LSTM as inputs, a sliding mode controller is designed to achieve stable tracking control of the paraglider.

[0240] As shown in step three, the trajectory tracking requirement can be met simply by designing a controller that stabilizes and minimizes the lateral trajectory error and heading angle error. Based on this, the sliding surface is established as follows:

[0241] s = k Δ Δ(t)+v s sin(ψ e )

[0242] Due to ψ e It is usually very small, so sin(ψ) can be considered as e )≈ψ e Then the above formula can be further simplified to:

[0243] s = k Δ Δ(t)+v s ψ e

[0244] Where, k Δ ∈R, and its value needs to be adjusted and optimized through experiments and simulations. If a fast system response is required, k can be increased. Δ However, an excessively large k Δ This could lead to excessive controller output, causing oscillations or instability; v s This represents the horizontal velocity of the parachute, which is the instantaneous velocity predicted in step 2 using the Long Short-Term Memory Network.

[0245] Differentiating with respect to s, we get for:

[0246]

[0247] Taking the derivative of Δ(t) yields for:

[0248]

[0249] Since the planned path points are stationary, it is assumed that there is no change in velocity. Combination Figure 3 , but:

[0250]

[0251]

[0252] Therefore It can be simplified to:

[0253]

[0254] A sliding mode controller based on the exponential reaching law is used for control, and its control law is as follows:

[0255]

[0256] To eliminate chattering generated by the sliding mode controller, the saturation function sat(s) is used to replace the sign function sgn(s), where the saturation function has the following form:

[0257]

[0258] The replaced control law is:

[0259]

[0260] Where ε and k are gain constants, their values ​​should be selected by comprehensively considering factors such as system stability, response speed and robustness. The optimal value of the gain constant may need to be determined through multiple experiments and debugging, and optimized according to the requirements of the actual application. a is taken as a constant value of 0.05.

[0261] Combination From the control law, we can obtain:

[0262]

[0263] Control quantity Δ and The relationship can be represented as:

[0264]

[0265] Where A1, A2, B1, and B2 represent aerodynamic conversion coefficients, v x and v y This represents the components of the parachute's horizontal velocity along the x-axis and y-axis.

[0266] In another embodiment, such as Figure 5 As shown:

[0267] The initial positions of the paraglider are set as x0 = 0m, y0 = 0m, z0 = 7000m, the initial heading angle is 0°, and the final positions are x1 = 20000m, y1 = 20000m, z1 = 946m. In the figure, the solid lines represent the target trajectory and the dashed lines represent the tracking trajectory.

[0268] In its specific implementation, this application provides a computer storage medium and a corresponding data processing unit. The computer storage medium is capable of storing a computer program, which, when executed by the data processing unit, can run the invention's content regarding a paraglider trajectory tracking method for complex environments, as well as some or all of the steps in various embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0269] Those skilled in the art will clearly understand that the technical solutions in the embodiments of the present invention can be implemented using computer programs and their corresponding general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of computer programs, i.e., software products. These computer program software products can be stored in a storage medium and include several instructions to cause a device containing a data processing unit (which may be a personal computer, server, microcontroller, MUU, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0270] This invention provides a concept and method for paraglider trajectory tracking in complex environments. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A wing-sail trajectory tracking method for a complex environment, characterized in that, The application relates to a wing-sail trajectory tracking control method based on long short-term memory network and sliding mode control, and belongs to the field of trajectory tracking control of wing-sails. The method comprises the following steps: Step 1, establishing a six-degree-of-freedom model of translational and rotational motion of a wing-sail according to the mechanical structure of the wing-sail; Step 2, constructing and training a long short-term memory network for predicting the instantaneous speed of the wing-sail; Step 3, calculating the lateral trajectory error and the heading angle tracking error between the actual trajectory and the expected trajectory of the wing-sail according to the horizontal distance between the current position of the wing-sail and the planning point, and performing lateral control on the wing-sail through the lateral trajectory error method; Step 4, designing a sliding mode controller, taking the instantaneous speed predicted by the long short-term memory network in step 2 and the lateral trajectory error and the heading angle tracking error calculated in step 3 as inputs, and performing tracking control on the wing-sail by using the sliding mode controller. In step 4, the sliding mode controller is designed as follows: Step 4-1, determining the target of the designed controller; s = k Δ Δ(t) + v s sin(ψ e ) where ψ e represents the heading angle tracking error, k Δ ∈ R, where k is a constant and R represents the set of real numbers; the above equation is further simplified as: s = k Δ Δ(t) + v s ψ e where v s represents the horizontal velocity of the parafoil, i.e. the instantaneous velocity predicted by the long short-term memory network in step 2; Step 4-3, the derivative of the slip surface s is obtained as is: Taking the derivative of the lateral trajectory tracking error Δ(t) gives is: Step 4-2, establishing a sliding surface s as follows: Step 4-4, using a sliding mode controller based on an exponential reaching law for control, and the control law is as follows: Wherein, sgn() represents a sign function; The sign function sgn(s) is replaced by a saturation function sat(s), and the form of the saturation function is as follows: The control law after replacement is as follows: Step 4-5, heading angle tracking error ψ e The mathematical expression is: ψ e = ψ(t) - ψ r (i) where ψ(t) is the heading angle, ψ r (i) is the track angle; Combining Ψ e and the control law, the course angle rate of change Control quantity Δ and rate of change of heading angle The relationship is represented as: where A1, A2, B1and B2represent aerodynamic conversion coefficients, v x and v y denote the components of the horizontal velocity of the parafoil along the x and y axes.

2. The wing-sail trajectory tracking method for complex environment according to claim 1, wherein, Wherein, epsilon and k are gain constants, and a is a constant; In step 1, the six-degree-of-freedom model of translational and rotational motion of the wing-sail is established as follows: wherein and denotes the projection of the acceleration vector on the velocity system x, y and z axes; When the wing-sail is regarded as a rigid body, the scalar form of the dynamic equation of translational motion of the center of mass of the wing-sail is as follows: where V is the velocity of the parafoil, ψ is the heading angle of the parafoil, v is the track angle of the parafoil, θ is the track inclination angle of the parafoil, m is the mass of the parafoil, g is the gravitational acceleration, D is the drag, L is the lift, Y is the side force, γ v is the velocity inclination angle, and (x, y, z) is the position of the parafoil in the ground coordinate system. The kinematic equation of translational motion of the center of mass of the wing-sail is as follows: wherein and denotes the angular acceleration of the rotation around the body coordinate system x, y and z axes; The scalar form of the dynamic equation of rotational motion of the center of mass of the wing-sail is as follows: wherein denotes the rate of change of the tilt angle, denotes the rate of change of the pitch angle, denotes the rate of change of the yaw angle, x , ω y and ω z are the components of the angular velocity along the body coordinate system x, y and z axes, M x , M x , M z are the components of the principal moment acting on the center of mass along the body coordinate system x, y and z axes, J xx , J yy , J zz are the moments of inertia of the body coordinate system x, y and z axes, J xz is the product of inertia of the body coordinate system x, y and z axes, γ is the tilt angle, θ is the pitch angle, and ψ is the yaw angle.

3. The wing-sail trajectory tracking method for complex environment in claim 2, wherein, The kinematic equation of rotational motion of the center of mass of the wing-sail is as follows: In step 2, the long short-term memory network is constructed and trained as follows: Step 2-1, selecting the structure of the network to construct the long short-term memory network; Step 2-2, determining the loss function of the network; 4. The wing-sail trajectory tracking method for complex environment according to claim 3, characterized in that, Step 2-3, training the constructed long short-term memory network through a back propagation algorithm. In step 2-1, the structure of the network is selected as follows: cell state C of the previous time t-1 , respectively through the forget gate, the input gate and the output gate, the updated cell state C t ; The forget gate is used to filter information, where the current input x is... t and the output h of the previous time step t-1 The output f after passing through the forget gate t for: f t = relu(W f [h t-1 ,x t ]+b f ) where W f and b f are the weights and bias of the forget gate, and the mathematical expression of the relu function relu(x) is: The long short-term memory network comprises a forgetting gate, an input gate and an output gate; The input gate is used to determine the new information to be stored, including a relu layer and a tanh layer, the relu layer determines the value to be updated, and the tanh layer creates a new candidate value vector Joining to the state: i t = relu(W i [h t-1 ,x t ]+b i ) Updated state C t Is: where i t represents the output vector, W i and b i are the weights and bias of the input gate, W n and b n are the weights and bias of the tanh layer, and the mathematical expression of the tanh function tanh(x) is: The output gate is used to determine the output value, the final output h t is: h t = o t tanh(C t ) where the output state o t is determined by a relu layer as follows: o t = relu(W o [h t-1 ,x t ]+b o ) where W o and b o are the weights and bias of the output gate.

5. The wing-sail trajectory tracking method for complex environment according to claim 4, characterized in that, relu(x) = max{0, x} velocity data from a pre-acquired parafoil velocity dataset using a sliding window of length W V , resulting in a jth input vector I j to the long short-term memory network as: I j = {v k , k = j, j + 1,..., W v + j - 1} In step 2-2, the loss function of the network is determined as follows: The corresponding label is as follows: wherein: T is the number of target trajectory points.

6. The wing-sail trajectory tracking method for complex environment of claim 5, wherein, The loss function L of the network is as follows: Let the position vector of the paraglider in the two-dimensional plane be [x(t), y(t)], and the position vectors of the path points that the paraglider needs to track at the current time, the previous time, and the next time be [x(t), y(t)], respectively. r (i),y r (i)],[x r (i-1),y r (i-1)] and [x r (i+1),y r [i+1], where the heading angle of the parachute at its current position is ψ(t); In step 3, the lateral trajectory error and the heading angle tracking error between the actual trajectory and the expected trajectory of the wing-sail are calculated as follows: Δx = x r (i) -x r (i-1) Δy = y r (i) -y r (i-1) Let the position deviation between the current position of the parachute and the path point to be tracked be and then: Trajectory course angle ψ r (i) is: Let the position deviation of the path tracking point at the current time and the path tracking point at the last time be Delta x and Delta y, then: heading angle tracking error ψ e (t) is: ψ e (t) = ψ(t) - ψ r (i).

7. The wing-sail trajectory tracking method for complex environment of claim 6, wherein, The lateral trajectory tracking error Delta (t) is as follows:

8. The wing-sail trajectory tracking method for complex environment of claim 7, wherein, In step 4-1, the target of the designed controller is to make the lateral trajectory error and the heading angle error tend to be stable and minimum.

9. The wing-sail trajectory tracking method for complex environment of claim 8, wherein, In step 4-4, the constant a is 0.

05. The control quantity Delta obtained in step 4-4 is used for controlling the wing-sail.

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