Unmanned ship trajectory tracking control method based on optimized backstepping method

Abstract

The invention discloses an unmanned ship trajectory tracking control method based on an optimized backstepping method, which belongs to the technical field of trajectory tracking control, is used for unmanned ship trajectory tracking control, and comprises the following steps of: generating an expected motion trajectory meeting kinematics constraints among a plurality of target waypoints through a monotonic cubic Hermite spline interpolation method; and the real-time state vector of the unmanned ship under the ECEF is obtained, the real-time state vector of the unmanned ship and the expected state vector are input into an optimal controller based on an optimization backstepping method, a nonlinear expansion state observer is adopted to carry out feed-forward compensation on the wind wave disturbance torque, and optimal control over path tracking of the unmanned ship is achieved. Compared with the prior art, the method has the advantages that the robustness is high, the optimal control thought is adopted, and the control quantity is minimized under the condition that the minimum error amount is guaranteed, so that the energy consumption can be effectively reduced, online reinforcement learning is realized, the optimized control strategy can be updated in real time, and the measurement precision is high.

Description

Technical Field

[0001] The present invention discloses an unmanned ship trajectory tracking control method based on an optimized backstepping method, belonging to the technical field of trajectory tracking control. Background Art

[0002] In scenarios where certain special tasks are executed, it is required that the unmanned ship intelligently sails to multiple specified target points for data collection and other work. This requires the unmanned ship to be able to intelligently generate a navigation trajectory according to the target waypoints and maintain stable navigation along the generated desired trajectory. However, due to the high uncertainty of the marine environment, traditional trajectory tracking methods still face many challenges in terms of control accuracy, stability, and robustness. The backstepping method is a traditional control method commonly used for unmanned ship trajectory tracking. It makes the system state gradually tend to be stable by recursively designing virtual control quantities. However, when applied in the actual marine environment, due to the existence of environmental uncertainty interference, a single backstepping method is difficult to ensure global stability, which may lead to increased energy consumption or degraded control performance. Summary of the Invention

[0003] The purpose of the present invention is to provide an unmanned ship trajectory tracking control method based on an optimized backstepping method to solve the problem in the prior art that a single backstepping method in unmanned ship trajectory tracking control is difficult to ensure global stability, which may lead to increased energy consumption or degraded control performance.

[0004] An unmanned ship trajectory tracking control method based on an optimized backstepping method includes:

[0005] S1. Set multiple target waypoints in the Earth-Centered Earth-Fixed (ECEF) coordinate system, and generate a desired motion trajectory that satisfies kinematic constraints between the multiple target waypoints through the monotonic cubic Hermite spline interpolation method;

[0006] S2. According to the GNSS satellite signals received by the satellite receiver carried on the unmanned ship, the position coordinates of the unmanned ship in the ECEF are calculated in real time and , and according to the data of the on-board Inertial Measurement Unit (IMU) and the data of the GNSS satellite receiver, the real-time heading angle in the ECEF is obtained , and the real-time state vector of the unmanned ship in the ECEF is combined to obtain ;

[0007] S3. Input the of the unmanned ship and the desired state vector into an optimal controller based on an optimized backstepping method, and use a non-linear Extended State Observer (ESO) to perform feed-forward compensation on the wind and wave disturbance torque to achieve the optimal control of the unmanned ship path tracking.

[0008] S1 includes: S1.1, set target waypoints, the number of target waypoints is N, and the input target waypoint set is , the th waypoint's position coordinates are ;

[0009] S1.2, introduce independent parameter , and express in terms of the parameter as , and decompose the two-dimensional path interpolation into two independent one-dimensional interpolation problems;

[0010] S1.3, in the one-dimensional interval , use the monotonic cubic Hermite spline interpolation method for interpolation;

[0011] S1.4, obtain the fitting path function between two points by interpolation between two adjacent waypoints , is 's horizontal and vertical coordinates. Let be the partition of the interval , is 's corresponding two-dimensional waypoint;

[0012] S1.5, output the expected position and heading angle.

[0013] S1.3 includes: S1.3.1, , divide the interval into a total of nodes, , define as the monotonic data set corresponding to the nodes, or ;

[0014] S1.3.2, is the monotonic cubic polynomial function for interpolation within , with continuous first derivative. The node corresponds to the function value . For each sub-interval , is:

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] wherein, is the cubic Hermite basis function on the interval , , , , , are intermediate variables, is the time.

[0026] S1.3 includes S1.3.3, adjusting the tangent at the node to maintain monotonicity. Let the slope of the piecewise linear interpolation of the th waypoint be :

[0027] ;

[0028] When and have opposite signs or one of them is 0, is a local maximum or minimum, and set ;

[0029] When and have the same sign, and the corresponding intervals have the same length:

[0030] ;

[0031] When and have the same sign, and the corresponding intervals have different lengths:

[0032] ;

[0033] ;

[0034] ;

[0035] wherein, , are intermediate variables.

[0036] S1.4 includes the data between adjacent waypoints and is:

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] Among them, , , , are intermediate parameters, is the local interval, , are the piecewise linear interpolation slopes;

[0046] Deriving the function gives :

[0047] ;

[0048] ;

[0049] At the point on the fitted path, the corresponding heading angle is:

[0050] .

[0051] S1.5 includes introducing the cumulative distance and time of the unmanned ship. Assuming the unmanned ship sails forward at a constant speed of , the cumulative distance corresponding to is calculated recursively as . At the point on the fitted path, the corresponding distance is:

[0052] ;

[0053] Calculate the corresponding parameters at the solved time to obtain the corresponding position and heading angle, and output them in the form of a matrix vector : ;

[0054] ;

[0055] In the formula, is the expected position obtained by the solution, is the expected heading angle obtained by the solution.

[0056] S3 includes S3.1, setting the sampling frequency , and solving the relevant state vector of the unmanned ship;

[0057] S3.1.1, calculating the expected speed and heading angular velocity of the unmanned ship, and directly decomposing the speed of the unmanned ship in the ECEF coordinate system into , and the expected heading angular velocity is:

[0058] ;

[0059] Combining them to obtain the expected state vector of the unmanned ship:

[0060] ;

[0061] In the formula, is the position and heading angle of the expected state vector of the unmanned ship.

[0062] S3 includes S3.1.2, solving the actual speed and heading angular velocity of the unmanned ship. Assume that the state vector of the unmanned ship containing the position and heading angle received at time is , and the state vector of the unmanned ship received at the previous time is , and the state vector of the unmanned ship actually containing the speed and heading angular velocity is :

[0063] ;

[0064] S3.2, designing a nonlinear extended state observer;

[0065] S3.3, using the optimized backstepping method to achieve the path tracking of the unmanned ship.

[0066] S3.2 includes defining the extended variable :

[0067] ;

[0068] In the formula, is the wind and wave disturbing torque, and the observer model is:

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] In the formula, is the observation error, is the control input, is the state transition matrix, is the control input matrix, is the gain matrix, is the observer parameter, used to adjust the observation speed, is 's estimation value;

[0075] The control input after feedforward compensation is:

[0076] ;

[0077] In the formula, is the control input generated by the optimal controller of the optimized backstepping method, is 's estimation value.

[0078] S3.3 includes S3.3.1, solving the unique solution of the HJB equation to obtain the update law of the neural network;

[0079] S3.3.2, re-obtaining the update law of the neural network according to the optimal solution;

[0080] S3.3.3, updating the weights of the Actor-Critic neural network in real time according to the update law, approximating the ideal network weights, obtaining the optimal control solution of the HJB equation, and realizing the optimal control of the unmanned ship path planning.

[0081] Compared with the prior art, the present invention has the following beneficial effects: By means of a non-linear extended state observer, the present invention estimates the unknown disturbances in the real marine environment and performs feed-forward compensation for the disturbances in the control input part, so it has strong robustness; The optimal control idea is adopted, and while ensuring the minimum error, the minimization of the control quantity is also taken into account, so the energy consumption can be effectively reduced; The Actor-Critic architecture is integrated to realize online reinforcement learning, and the optimized control strategy can be updated in real time, so it has high measurement accuracy. Description of the Drawings

[0082] Figure 1 is the heading angle tracking error graph;

[0083] Figure 2 is the tracking error graph in the y direction;

[0084] Figure 3 is the tracking error graph in the x direction;

[0085] Figure 4 is the waypoint and motion trajectory graph;

[0086] Figure 5 is the heading angle change graph;

[0087] Figure 6 is the motion trajectory graph in the y direction;

[0088] Figure 7 is the motion trajectory graph in the x direction;

[0089] Figure 8 is the technical flow chart of the present invention. Detailed Embodiments

[0090] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0091] A trajectory tracking control method for an unmanned ship based on an optimized backstepping method, comprising:

[0092] S1. Set multiple target waypoints in the Earth-Centered Earth-Fixed (ECEF) coordinate system, and generate an expected motion trajectory that satisfies the kinematic constraints between the multiple target waypoints by using the monotonic cubic Hermite spline interpolation method;

[0093] S2. According to the GNSS satellite signals received by the satellite receiver carried on the unmanned ship, the position coordinates of the unmanned ship in the ECEF are calculated in real time And , obtain the real-time heading angle in ECEF according to the data of the shipborne inertial measurement unit (IMU) and the data of the GNSS satellite receiver , and combine to obtain the real-time state vector of the unmanned ship in ECEF ;

[0094] S3. Input the of the unmanned ship and the desired state vector into the optimal controller based on the optimized backstepping method, and use a non-linear extended state observer to perform feedforward compensation on the wind and wave disturbance torque to achieve the optimal control of the unmanned ship path tracking.

[0095] S1 includes: S1.1. Set the target waypoints, the number of target waypoints is N, and input the set of target waypoints as , the position coordinates of the -th waypoint are ;

[0096] S1.2. Introduce the independent parameter , and express in terms of the parameter as , and decompose the two-dimensional path interpolation into two independent one-dimensional interpolation problems;

[0097] S1.3. In the one-dimensional interval , use the monotonic cubic Hermite spline interpolation method for interpolation;

[0098] S1.4. Use interpolation between two adjacent waypoints to obtain the fitting path function between the two points , is the horizontal and vertical coordinates of , let be the partition of the interval , and is corresponding two-dimensional waypoint;

[0099] S1.5. Output the desired position and heading angle.

[0100] S1.3 includes: S1.3.1. , divide the interval into a total of nodes, , define as the monotonic data set corresponding to the nodes, or ;

[0101] S1.3.2. is the monotonic cubic polynomial function for interpolation within , with continuous first derivative, and the nodes The corresponding function value is , for each sub - interval , is:

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] In the formula, is the cubic Hermite basis function on the interval , , , , , are intermediate variables, is the time.

[0113] S1.3 includes S1.3.3, adjusting the tangent at the node to maintain monotonicity. Let the slope of the piece - wise linear interpolation of the th waypoint be :

[0114] ;

[0115] When and have opposite signs or one of them is 0, is a local maximum or minimum, set ;

[0116] When and have the same sign and the corresponding intervals have the same length:

[0117] ;

[0118] When and have the same sign, and the corresponding intervals have different lengths:

[0119] ;

[0120] ;

[0121] ;

[0122] wherein, and are intermediate variables.

[0123] S1.4 includes the data between adjacent waypoints and as:

[0124] ;

[0125] ;

[0126] ;

[0127] ;

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] wherein, and and and are intermediate parameters, is the local interval, and are the piecewise linear interpolation slopes;

[0133] Deriving the function gives :

[0134] ;

[0135] ;

[0136] At the point on the fitted path, the corresponding heading angle is:

[0137] 。

[0138] S1.5 includes introducing the cumulative distance traveled by the unmanned ship and the moment , assuming that the unmanned ship maintains a speed magnitude of and moves forward. At the position , the cumulative distance is recursively calculated as . At the point on the fitted path, the corresponding distance is:

[0139] ;

[0140] Solve for the parameter corresponding to the time , and obtain the corresponding position and heading angle, which are output in the matrix vector form:

[0141] ;

[0142] In the formula, is the expected position obtained by the solution, is the expected heading angle obtained by the solution.

[0143] S3 includes S3.1, setting the sampling frequency , and solving the relevant state vector of the unmanned ship;

[0144] S3.1.1, finding the expected speed and heading angular velocity of the unmanned ship, and directly decomposing the speed of the unmanned ship in the ECEF coordinate system into . The expected heading angular velocity is:

[0145] ;

[0146] Combine to obtain the expected state vector of the unmanned ship:

[0147] ;

[0148] In the formula, is the position and heading angle of the expected state vector of the unmanned ship.

[0149] S3 includes S3.1.2, solving the actual speed and heading angular velocity of the unmanned ship. Assume that the state vector of the unmanned ship containing the position and heading angle received at the moment is , and the state vector of the unmanned ship received at the previous moment is . The state vector of the unmanned ship actually containing the speed and heading angular velocity is :

[0150] ;

[0151] S3.2. Design a non - linear extended state observer;

[0152] S3.3. Implement the path tracking of the unmanned ship using the optimized backstepping method.

[0153] S3.2 includes defining the extended variable :

[0154] ;

[0155] In the formula, is the wind - wave disturbance torque, and the observer model is:

[0156] ;

[0157] ;

[0158] ;

[0159] ;

[0160] ;

[0161] In the formula, is the observation error, is the control input, is the state transition matrix, is the control input matrix, is the gain matrix, is the observer parameter used to adjust the observation speed, is 's estimate;

[0162] The control input after feed - forward compensation is:

[0163] ;

[0164] In the formula, is the control input generated by the optimized backstepping optimal controller, is 's estimate.

[0165] S3.3 includes, S3.3.1. Solve the unique solution of the HJB equation to obtain the update law of the neural network;

[0166] S3.3.2. Re - obtain the update law of the neural network according to the optimal solution;

[0167] S3.3.3. Update the weights of the Actor-Critic neural network in real time according to the update law to approximate the ideal network weights, obtain the optimal control solution of the HJB equation, and achieve the optimal control of the unmanned ship path planning.

[0168] The unique solution to solving the HJB equation includes defining the position error vector as:

[0169] ;

[0170] ;

[0171] where is the estimate of , and the virtual control quantity of the subsystem is represented by the three-dimensional vector , , is the admissible control strategy of the system;

[0172] Define the local value function as:

[0173] ;

[0174] where represents the magnitude of the control quantity, and represents the magnitude of the error quantity;

[0175] Define the value function of the infinite time domain as:

[0176] ;

[0177] To achieve the optimal virtual control and minimize the cost consumed by the subsystem, minimize the value function of this infinite time domain. The corresponding optimal virtual control quantity is , and the optimal value function is as:

[0178] ;

[0179] Construct the HJB equation as:

[0180] ;

[0181] Assume that the HJB equation has a solution and the solution is unique, then there is:

[0182] ;

[0183] ;

[0184] Substitute the unique solution back into the HJB equation to obtain:

[0185] ;

[0186] The update law of the neural network is obtained, including introducing the Actor-Critic neural network algorithm to optimize the algorithm. Among them, the Actor network is used to execute the control strategy, and the Critic network is used to evaluate the optimization performance. The optimal value function is rewritten as:

[0187] ;

[0188] ;

[0189] where is a positive design constant, is the scalar value function, is approximately expressed by the neural network as:

[0190] ;

[0191] where is the ideal neural network weight, is the basis function vector, is the approximation error of the neural network. Reconstruct the optimal value function and solve for the optimal control quantity:

[0192] ;

[0193] ;

[0194] The original HJB equation is rewritten as:

[0195] ;

[0196] ;

[0197] where is a term bounded by a positive constant, is 's estimate;

[0198] When the error of the neural network used to approximate the optimal control is approximately zero, there is:

[0199] ;

[0200] ;

[0201] where 、 is 、 the approximation of, and are the weights of the Critic network and the Actor network respectively;

[0202] The approximate HJB equation obtained is:

[0203] ;

[0204] Calculate the Bellman residual :

[0205] ;

[0206] The Lyapunov function is:

[0207] ;

[0208] Apply the gradient descent method to the Lyapunov positive definite function to obtain the update law of the neural network. The update law of the Critic network is:

[0209] ;

[0210] ;

[0211] In the formula, is the learning rate, is the intermediate parameter;

[0212] The update law of the Actor network is:

[0213] ;

[0214] In the formula, is the learning rate;

[0215] S3.3.2 includes that the three-degree-of-freedom dynamic equation of the unmanned ship is:

[0216] ;

[0217] ;

[0218] In the formula, is the mass matrix of the unmanned ship, which is a positive definite constant matrix, is the Coriolis centripetal matrix, is the damping matrix, is the restoring force vector in the presence of gravity and buoyancy;

[0219] Let the input control variable be:

[0220] ;

[0221] ;

[0222] Define the control error variable as :

[0223] ;

[0224] ;

[0225] In the formula, is the unique solution, is 's estimate;

[0226] The optimal value function is:

[0227] ;

[0228] Among them, represents the optimal control of the subsystem;

[0229] Construct the HJB equation as:

[0230] ;

[0231] The optimal value function estimate and the corresponding optimal solution are:

[0232] ;

[0233] ;

[0234] In the formula, , are , 's estimates, is the basis function vector;

[0235] Critic network update law is:

[0236] ;

[0237] ;

[0238] In the formula, is the learning rate, is the intermediate parameter, and The weights of the Critic network and the Actor network, respectively;

[0239] Actor network update law is:

[0240] ;

[0241] In the formula, is the learning rate.

[0242] Based on the traditional backstepping control, the present invention introduces the optimal control idea to optimize the design of the controller, that is, on the basis of backstepping, it integrates the Actor-Critic neural network architecture, continuously optimizes the control strategy through the "evaluation-execution" mechanism, and at the same time adds a non-linear extended state observer to estimate the unknown environmental disturbances and perform feedforward compensation. Based on this, an optimal controller for the trajectory tracking of an unmanned ship based on the optimized backstepping method is designed, which can optimize the control input, reduce energy consumption and improve the tracking accuracy while meeting the stability conditions. The unmanned ship is equipped with a GNSS antenna to receive satellite signals and transmit data to the satellite receiver, and at the same time obtains the attitude data of the unmanned ship from the on-board IMU sensor, and transmits the obtained raw data to the controller part together. The data processing algorithms including GNSS satellite signal solution and IMU attitude data parsing, the optimal controller based on the optimized backstepping method and the relevant control algorithms of the disturbance observer are written into a Python file, and the ROS system is built on the JETSON development board. In the built system, the relevant position and heading angle data of the unmanned ship are subscribed through nodes, and the obtained relevant data are used to complete the parsing of the raw data and the intelligent generation and tracking control of the expected path of the unmanned ship movement with the help of the written Python code.

[0243] In the embodiment of the present invention, the heading angle tracking error is as Figure 1 shown, the y-direction tracking error is as Figure 2 shown, the x-direction tracking error is as Figure 3 shown, the waypoint and the movement trajectory are as Figure 4 shown, the change of the heading angle is as Figure 5 shown, the y-direction movement trajectory is as Figure 6 shown, the x-direction movement trajectory is as Figure 7 shown, and the longitude, latitude and elevation of the key position points of the movement trajectory are shown in Table 1. The technical process of the present invention is as Figure 8As shown, the actual position of the unmanned ship is obtained by resolving the GNSS satellite signal. The IMU sensor collects the heading angle, and the actual position of the unmanned ship is combined to generate the actual motion trajectory. The desired motion trajectory is obtained by performing monotonic cubic spline interpolation on the waypoints. The ocean disturbances (sea wind, ocean current, ocean) are combined with the actual motion trajectory and the desired motion trajectory, and then input into the optimal controller based on the optimized backstepping method, and cyclic feedback is performed through disturbance control.

[0244] Table 1. Latitude, longitude and elevation of key position points of the motion trajectory

[0245] ;

[0246] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting it. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An unmanned ship trajectory tracking control method based on an optimized backstepping method, characterized in that Including: S1. Set multiple target waypoints in the Earth-Centered Earth-Fixed (ECEF) coordinate system, and generate an expected motion trajectory that satisfies kinematic constraints between the multiple target waypoints through the monotonic cubic Hermite spline interpolation method; S2. Based on the GNSS satellite signals received by the satellite receiver carried on the unmanned ship, the position coordinates of the unmanned ship in ECEF are calculated in real time and , based on the data of the on-board inertial measurement unit IMU and the data of the GNSS satellite receiver, the real-time heading angle in ECEF is obtained , and the real-time state vector of the unmanned ship in ECEF is combined ; S3. Input the of the unmanned ship and the desired state vector into the optimal controller based on the optimized backstepping method, and use a non-linear extended state observer to perform feed-forward compensation on the wind and wave disturbance torque to achieve the optimal control of the unmanned ship path tracking.

2. The method for controlling the trajectory tracking of an unmanned ship based on the optimized backstepping method according to claim 1, characterized in that S1 includes S1.1, setting target waypoints. The number of target waypoints is N, and the input target waypoint set is , the th waypoint has a position coordinate of ; S1.

2. Introduce independent parameters , express using parameters as , and decompose the two-dimensional path interpolation into two independent one-dimensional interpolation problems; S1.

3. Interpolate using the monotonic cubic Hermite spline interpolation method in a one-dimensional interval Interpolate using the monotonic cubic Hermite spline interpolation method S1.

4. Obtain the fitting path function between two points by interpolation between two adjacent waypoints , is the horizontal and vertical coordinates of. Let be the partition of the interval , be the corresponding two-dimensional waypoint; S1.

5. Output the expected position and heading angle.

3. The method for trajectory tracking control of an unmanned ship based on an optimized backstepping method according to claim 2, characterized in that, S1.3 includes S1.3.1, Divide the interval into a total of nodes, Define as the monotonic data set corresponding to the node, or ; S1.3.2、 is a monotonic cubic polynomial function for the interpolated value, with a continuous first derivative, and the nodes corresponding function values are , for each subinterval , is: ； ； ； ； ； ； ； ； ； ； wherein, is the cubic Hermite basis function on the interval , , , , , are intermediate variables, is the time.

4. A trajectory tracking control method for an unmanned ship based on an optimized backstepping method according to claim 3, characterized in that, S1.3 includes S1.3.3, adjusting the tangents at the nodes to maintain monotonicity. Let the slope of the piecewise linear interpolation of the th waypoint be : ； When and have opposite signs or one of them is zero, is a local maximum or minimum, set ; When and have the same sign and the corresponding intervals have the same length: ； When and the symbols are the same and the corresponding intervals have different lengths: ； ； ； In the formula, , are intermediate variables.

5. A trajectory tracking control method for an unmanned ship based on an optimized backstepping method according to claim 4, characterized in that, S1.4 includes adjacent waypoints and The data between them is: ； ； ； ； ； ； ； ； Among them, , , , are intermediate parameters, is the local interval, , are the piecewise linear interpolation slopes; Derive the function to obtain : ； ； Points on the fitting path The corresponding heading angle at is as follows: 。 6. The method for trajectory tracking control of an unmanned ship based on an optimized backstepping method according to claim 5, characterized in that S1.5 includes introducing the cumulative distance traveled by the unmanned ship and the moment , assuming that the unmanned ship maintains a speed of and moves forward. At , the corresponding cumulative distance is calculated recursively as . At the point on the fitted path, the corresponding distance is: ； Calculate the time and the corresponding parameters , and obtain the corresponding position and heading angle, and output in the form of a matrix vector as follows: ； wherein, is the calculated desired position, is the calculated desired heading angle.

7. A trajectory tracking control method for an unmanned ship based on an optimized backstepping method according to claim 6, characterized in that S3 includes S3.1, setting the sampling frequency , and solving the state vectors related to the unmanned ship; S3.1.

1. Calculate the expected speed and heading angular velocity of the unmanned ship. Decompose the ship speed of the unmanned ship directly in the ECEF coordinate system into , and the expected heading angular velocity is: ； Combine to obtain the desired state vector of the unmanned ship : ； In the formula, is the position and heading angle of the desired state vector of the unmanned ship.

8. A trajectory tracking control method for an unmanned ship based on an optimized backstepping method according to claim 7, characterized in that, S3 includes S3.1.2, solving the actual speed and heading angular velocity of the unmanned ship, assuming the moment The received state vector of the unmanned ship containing position and heading angle is , at the previous moment The received state vector of the unmanned ship is , and the state vector of the unmanned ship actually containing speed and heading angular velocity is : ； S3.

2. Design a nonlinear extended state observer; S3.

3. Use the optimized backstepping method to achieve path tracking of the unmanned ship.

9. A trajectory tracking control method for an unmanned ship based on an optimized backstepping method according to claim 8, characterized in that, S3.2 includes defining expansion variables : ； In the formula, is the disturbing moment of wind and wave, and the observer model is: ； ； ； ； ； wherein, is the observation error, is the control input, is the state transition matrix, is the control input matrix, is the gain matrix, is the observer parameter for adjusting the observation speed, is the estimate of; The control input after feedforward compensation is: ； wherein, is the control input generated by the optimized backstepping optimal controller, is the estimate of.

10. A trajectory tracking control method for an unmanned ship based on an optimized backstepping method according to claim 9, characterized in that S3.3 includes S3.3.

1. Solve the unique solution of the Hamilton-Jacobi-Bellman (HJB) equation to obtain the update law of the neural network; S3.3.

2. Re-obtain the update law of the neural network according to the optimal solution; S3.3.

3. Update the weights of the Actor-Critic neural network in real time according to the update law, approximate the ideal network weights, obtain the optimal control solution of the HJB equation, and achieve the optimal control of the unmanned ship path planning.

Images