An adaptive tracking control method for large-curvature path of underactuated underwater vehicle

Abstract

The present application relates to a kind of underactuated underwater vehicle large curvature path adaptive tracking control method, comprising: the mathematical model of underactuated underwater vehicle is established, the position, attitude of underwater vehicle is initialized, the parameter equation of path to be tracked is determined;Kinematics control law is designed using improved line-of-sight method, curvature adaptive update rate, expected yaw angle and pitch angle are calculated;Based on underwater vehicle model, the position of underwater vehicle at next time is predicted, target function about speed is established;Based on improved particle swarm optimization algorithm, target speed is optimized;Adaptive sliding mode controller based on width learning system is constructed, the speed of underwater vehicle is controlled to reach expected speed, and estimation and compensation to external disturbance and model parameter uncertainty are realized.The present application can improve the path tracking accuracy of underactuated underwater vehicle based on adaptive speed mechanism, especially reduce the tracking error to large curvature path, improve the precision of underactuated underwater vehicle navigation.

Description

Technical Field

[0001] This invention relates to the field of underwater vehicle path tracking control technology, and in particular to an adaptive tracking control method for underactuated underwater vehicles with large curvature paths. Background Technology

[0002] Autonomous underwater vehicles (AUVs) are efficient and autonomous marine exploration equipment. They are simple to operate, flexible in deployment, and low in manufacturing cost, possessing high mobility and autonomy. They can replace manual labor in tasks such as marine environmental exploration, autonomous underwater operations, underwater search and rescue, and fishing, demonstrating enormous application potential. Path tracking is a key technology for AUVs, playing a crucial role in tasks such as seabed search and pipeline inspection. Curve path tracking refers to the AUV following a smooth curved path. Compared to straight-line path tracking, curve path tracking can adapt to more complex tasks and environments. Therefore, researching curve path tracking algorithms for AUVs has significant practical implications.

[0003] In complex obstacle environments, curved paths exhibit significant curvature. If the maximum curvature of the path exceeds the curvature corresponding to the minimum turning radius of an underactuated underwater vehicle (AUV), this path is considered a high-curvature path. AUVs achieve safe maneuverability in complex obstacle environments by tracking high-curvature paths. However, due to the lack of lateral drive, underactuated AUVs have limited steering capabilities, leading to significant deviations when tracking high-curvature paths, reducing the accuracy and safety of AUV path tracking. Existing underactuated AUV curved path tracking methods primarily use the line-of-sight (LOS) method to design the desired heading angle of the AUV, thereby enabling the AUV to track the desired path. Building upon the LOS method, the paper "Direct and indirect adaptive integral line-of-sight path-following controllers for marine craft exposed to ocean currents" proposes adaptive LOS, which estimates and compensates for drift angles, improving path tracking accuracy. However, due to limited turning capabilities, AUVs struggle to quickly reach the designed desired heading angle, resulting in substantial tracking errors. The steering ability of an underactuated AUV is coupled with its speed, but most existing curve path tracking methods set the speed of the AUV to a constant value, ignoring the influence of speed on the steering ability of the AUV and lacking adaptability to path curvature.

[0004] To address the issue of large tracking errors during high curvature path tracking in underactuated AUVs, this invention proposes an adaptive tracking control method for high curvature paths in underactuated AUVs. By designing an adaptive speed mechanism, the tracking accuracy of high curvature paths is improved. Summary of the Invention

[0005] Based on the above background, this invention addresses the problem of large tracking errors in existing underactuated underwater vehicle (AUV) curve path tracking methods, and proposes an adaptive tracking control method for large curvature paths of underactuated AUVs to improve the tracking accuracy of underactuated AUVs for large curvature paths.

[0006] The technical solution of this invention: an adaptive tracking control method for a large curvature path of an underactuated underwater vehicle, comprising the following steps:

[0007] S1. Establish a mathematical model of the underactuated underwater vehicle, initialize the position and attitude of the underactuated underwater vehicle, and determine the parametric equations of the path to be tracked.

[0008] S2. Calculate the curvature adaptive update rate, forward sight distance, and desired yaw and pitch angles using the improved line-of-sight method;

[0009] S3. Predict the position of the underwater vehicle at the next moment based on the underwater vehicle model, and establish the objective function;

[0010] S4. Optimize the target speed based on the improved particle swarm optimization algorithm;

[0011] S5. Construct an adaptive sliding mode controller based on a Broad Learning System (BLS) to control the underwater vehicle to reach the desired speed and to estimate and compensate for external disturbances and model parameter uncertainties.

[0012] In one embodiment, in S1, the five-degree-of-freedom kinematic model of the underactuated underwater vehicle is:

[0013] ,

[0014] in, x , y , z The coordinates of the AUV in the inertial coordinate system. θ、ψ These are pitch angle and yaw angle, respectively. u For longitudinal velocity, v For lateral velocity, w Vertical velocity, q The pitch angular velocity, r Yaw angular velocity;

[0015] In the dynamic model, considering the uncertainty of the hydrodynamic coefficients, the dynamic model is as follows:

[0016] ,

[0017] in, m 11 , m 22 , m 33 , m 44 , m 55 The inertia of the AUV, t u The thrust provided to the longitudinal thruster, t q For pitching moment, t r For yaw moment, f u , f v , f w , f q , f r The uncertain hydrodynamic term and external disturbance at each degree of freedom are specifically in the form of: f u = X u u + X u|u| u|u| -( W - B sin i + d u , f v = Y v v + Y v|v| v|v| - mz b rq + d v , f w = Z w w + Z w|w| w|w| +( W - B cos i + d w , f r = N r r + N r|r| r|r| + d r , f q = M q q + M q|q| q|q|+mz b ( rv - qw ) - Wz b sin i + d q ,in, X u , X u|u| , Y v , Y v|v| , Z w , Z w|w| , M q , M q|q| , N r , N r|r| For hydrodynamic coefficient, m For the mass of the underwater vehicle, W Let B be the weight of the underwater vehicle, and let B be the buoyancy force acting on the underwater vehicle. z b This is the distance between the center of buoyancy and the center of gravity of the underwater vehicle. d u , d v , d w , d q , d r This is due to external interference.

[0018] In one embodiment, S2 includes the following steps:

[0019] S21. The parametric equation of the path to be tracked is expressed as follows: The path tracking error is expressed as:

[0020] ,

[0021] in, , , x , y , z The coordinates of the underwater vehicle in the geodetic coordinate system. x e , y e , z e For tracking error;

[0022] S22. Taking the derivative with respect to the tracking error, we get:

[0023] ,

[0024] in, , , , , u , v , w These are the longitudinal velocity, lateral velocity, and vertical velocity of the underwater vehicle. i , ψ These are the pitch angle and yaw angle of the underwater vehicle in the geodetic coordinate system, respectively.

[0025] S23. Define the Lyapunov function as follows: Taking the derivative, we get

[0026] ,

[0027] To make the system asymptotically stable, that is Update law for path variables and desired pitch angular velocity i d yaw rate ψ d Design;

[0028] S24. The update rate of path variables affects the tracking accuracy of underwater vehicles. A curvature adaptive term is introduced into the path variable update law, specifically:

[0029] ,

[0030] in, k x , k κ , aκ Let κ be a constant greater than 0, and let κ be the curvature at the path point, which is calculated as follows: ;

[0031] The desired pitch and yaw angles are as follows:

[0032] , ,

[0033] Where, Δ z Δ y The forward sight distances are for the pitch and yaw degrees of freedom, respectively:

[0034] ,

[0035] Where, Δ zmin Δ ymin This is the minimum forward sight distance. d 1. d 2 is a constant greater than 0. k θ , k ψ The curvature of the path in the pitch and yaw degrees of freedom is calculated as follows:

[0036] ;

[0037] S25, will Substitution When the pitch angle and yaw angle are equal to the designed desired pitch angle and yaw angle,

[0038]

[0039] Obviously, when | i e |< hour, And only if x e , y e , z e When both are 0, Therefore, when the initial pitch angle error is less than At that time, the system asymptotically stabilizes, and the tracking error... x e , y e , z e All tend to 0.

[0040] In one embodiment, S3 includes the following steps:

[0041] S31. Based on the desired pitch angle i d and yaw angle ψ d Design desired pitch angular velocity q d and yaw rate r d :

[0042] ,

[0043] in, k q and k r A constant greater than 0 i t and ψ t These are the pitch and yaw angles of the underwater vehicle at the current moment.

[0044] S32. Predict the pitch angle of the underwater vehicle at the next moment. and yaw angle :

[0045] ,

[0046] in, q t and r t Let Δ be the pitch and yaw rates of the underwater vehicle at the current moment. t For time intervals.

[0047] S33. Based on the kinematic model of the underwater vehicle, predict the velocity of the underwater vehicle at the next moment:

[0048] ,

[0049] in, , , These represent the velocities of the underwater vehicle along the x, y, and z axes in the Earth coordinate system at the next moment. u t , v t , w t The current longitudinal velocity, lateral velocity, and vertical velocity of the underwater vehicle are... u d The longitudinal velocity at the next moment is to be determined;

[0050] S34. Predict the position of the underwater vehicle at the next moment:

[0051] ,

[0052] in, , , The coordinates of the underwater vehicle in the geodetic coordinate system are predicted for the next moment. x t , y t , z t The coordinates of the underwater vehicle in the geodetic coordinate system at the current moment;

[0053] S35. Establish the longitudinal velocity at the next moment. u d Objective function:

[0054]

[0055] in, l It is a constant. u min , u max They are respectively u d The minimum and maximum values.

[0056] In one embodiment, S4 includes the following steps:

[0057] S41. Initialize particle swarm parameters, including the number of particles. N Initial particle position, maximum number of iterations M Global optimal position G Global optimal fitness, where the position of the particle is the target speed to be optimized, and the relevant number of particles is set. n The fitness function is set to the objective function established in step S3, and the initial fitness of each particle's position is calculated.

[0058] S42. Initialize t=0;

[0059] S43. Initialize i=0;

[0060] S44, Regarding the first i There are 1 particle with positions and velocities of 1 and 2, respectively. X i (t), V i (t), the optimal position of this particle is P i (t), based on the set number of relevant particles n Except for the first i Randomly select from all particles except for that particle. n -1 particle, with the firsti Each particle together forms a subgroup;

[0061] S45. Based on the individual fitness of all particles in this subgroup, select the m particles with the smallest individual fitness values ​​as the dominant particle set, where the set of indices of each particle is: Using the average optimal position of the dominant particle set in the subgroup to guide the first i The position and velocity of each particle are updated to avoid getting trapped in local optima. i The velocity and position of each particle are updated as follows:

[0062] ,

[0063] ;

[0064] in, oh , c 1. c 2 is a positive constant. r 1. r 2 is a random number between 0 and 1.

[0065] S46, Update No. i Fitness value of each particle J ( X i (t+1)), if J ( X i (t+1))< J ( P i (t)), then P i (t+1)= X i (t+1); if J ( X i (t+1))> J ( P i (t)), then P i (t+1)= P i (t), if J ( X i (t+1))< J ( G ),but G = X i (t+1);

[0066] S47 i = i+1, if i < N Return to S44; if i ≥ N ,but t = t +1;

[0067] S48, if t < M Return to S43; if t ≥ M Then the iteration ends, and the global optimal position is found. G That is, the optimal target speed obtained. u d .

[0068] In one embodiment, S5 includes the following steps:

[0069] S51, Target speed u d Desired pitch angular velocity q d Desired yaw rate r d Through a first-order low-pass filter:

[0070] ,

[0071] in, oh 1. oh 2. oh 3 is a constant greater than 0. u cf , q cf , r cf The control law is filtered;

[0072] S52, Define speed error: e u = u - u cf , e q = q - q cf , e r = r - r cf ;

[0073] S53. Define the integral sliding surface:

[0074] ,

[0075] in,s u , s q , s r These are the sliding surfaces for the longitudinal velocity, pitch angular velocity, and yaw angular velocity of the underwater vehicle, respectively. k u , k q , k r , l u , l q , l r All are constants greater than 0;

[0076] S54. The specific design control law is as follows:

[0077] ,

[0078] in, or 11 , or 12 , or 21 , or 22 , or 31 , or 32 , c 11 , c 12 , c 21 , c 22 , c 31 , c 32 All are positive constants. , , The output of the wide-range learning system serves as an estimate of external disturbances and model uncertainty, and its form is: , For the actual weights between the feature layer and the output layer of the width learning system, the adaptive law for updating is:

[0079] ,

[0080] A l ( l ) represents the augmented matrix of the feature layer and enhancement layer of the width learning system, in the form of: ,in,Z =[ Z 1, Z 2, …, Z p ], Z i For feature nodes, p The number of feature nodes, H =[ H 1, H 2, …, H q ], H j To enhance the nodes, q To increase the number of nodes;

[0081] The method for constructing feature nodes is as follows:

[0082] ,

[0083] in, f (·) represents a nonlinear mapping function. W fi For random weights, β fi For random bias;

[0084] The method for constructing enhanced nodes is as follows:

[0085] ,

[0086] in, x (·) represents a nonlinear mapping function. W ei The weights are random. β ei For random bias. Attached Figure Description

[0087] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0088] Figure 1 A flowchart of an adaptive tracking control method for a large curvature path of an underactuated underwater vehicle according to an embodiment of the present invention;

[0089] Figure 2 This is a framework diagram of an adaptive tracking control method for a large curvature path of an underactuated underwater vehicle according to an embodiment of the present invention.

[0090] Figure 3 This is a diagram showing the results of high curvature path tracking in an embodiment of the present invention;

[0091] Figure 4This is a large curvature path tracking error diagram according to an embodiment of the present invention. Detailed Implementation

[0092] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0093] Now combined Figure 1 to Figure 4 The preferred embodiments of the present invention will be described herein. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0094] like Figure 1 and 2 As shown, a method for adaptive tracking control of a large curvature path for an underactuated underwater vehicle includes the following steps:

[0095] S1. Underwater Vehicle Model Establishment and Parameter Initialization: Specifically, establish a mathematical model of the underactuated underwater vehicle (AUV), initialize the position, attitude, and velocity of the underactuated underwater vehicle, and provide the parametric equations for the path to be tracked.

[0096] (1) The five-degree-of-freedom kinematic model of the underactuated underwater vehicle is established as follows:

[0097] ,

[0098] in, x , y , z The coordinates of the AUV in the inertial coordinate system. θ、ψ These are pitch angle and yaw angle, respectively. u For longitudinal velocity, v For lateral velocity, w Vertical velocity, q The pitch angular velocity, r This is the yaw rate.

[0099] In the dynamic model, considering the uncertainty of the hydrodynamic coefficients, the dynamic model is established as follows:

[0100] ,

[0101] in, m 11 , m 22 ,m 33 , m 44 , m 55 The inertia of the AUV, t u The thrust provided to the longitudinal thruster, t q For pitching moment, t r For yaw moment, f u , f v , f w , f q , f r The uncertain hydrodynamic term and external disturbance at each degree of freedom are specifically in the form of: f u = X u u + X u|u| u|u| -( W - B sin i + d u , f v = Y v v + Y v|v| v|v| - mz b rq + d v , f w = Z w w + Z w|w| w|w| +( W - B cos i + d w , f r = N r r + N r|r| r|r| +d r , f q = M q q + M q|q| q|q|+mz b ( rv - qw ) - Wz b sin i + d q ,in, X u , X u|u| , Y v , Y v|v| , Z w , Z w|w| , M q , M q|q| , N r , N r|r| For hydrodynamic coefficient, m For the mass of the underwater vehicle, W Let B be the weight of the underwater vehicle, and let B be the buoyancy force acting on the underwater vehicle. z b This is the distance between the center of buoyancy and the center of gravity of the underwater vehicle. d u , d v , d w , d q , d r This is due to external interference.

[0102] S2. Design an improved line-of-sight method incorporating the curvature adaptive update law and forward look distance. Specifically, the improved line-of-sight method is used to design the kinematic control law, calculate the curvature adaptive update law, the desired yaw angle, and the pitch angle, including the following steps:

[0103] (1) The parametric equation of the path to be tracked is expressed as follows: The path tracking error is expressed as

[0104] ,

[0105] in, , , x , y , z The coordinates of the underwater vehicle in the geodetic coordinate system. x e , y e , z e This is for tracking error.

[0106] (2) Taking the derivative with respect to the tracking error, we get:

[0107] ,

[0108] in, , , , .

[0109] (3) Define the Lyapunov function as Taking the derivative, we get

[0110] ,

[0111] To make the system asymptotically stable, that is Update law for path variables and desired pitch angular velocity i d yaw rate ψ d To carry out the design.

[0112] (4) The update rate of path variables affects the tracking accuracy of underwater vehicles. A curvature adaptive term is introduced into the path variable update law, specifically:

[0113] ,

[0114] in, k x , k κ , a κ Let κ be a constant greater than 0, and let κ be the curvature at the path point, which is calculated as follows: .

[0115] The desired pitch and yaw angles are as follows:

[0116] , ,

[0117] Where, Δ z Δ yThese are the forward sight distances for the pitch and yaw degrees of freedom, respectively. Specifically:

[0118] ,

[0119] Where, Δ zmin Δ ymin This is the minimum forward sight distance. d 1. d 2 is a constant greater than 0. k θ , k ψ The curvature of the path in the pitch and yaw degrees of freedom is calculated as follows:

[0120] .

[0121] (5) Substitution When the pitch angle and yaw angle are equal to the designed desired pitch angle and yaw angle,

[0122] ,

[0123] Obviously, when | i e |< hour, And only if x e , y e , z e When both are 0, Therefore, when the initial pitch angle error is less than At that time, the system asymptotically stabilizes, and the tracking error... x e , y e , z e All tend to 0.

[0124] S3. Predict the position of the underwater vehicle at the next moment based on the underwater vehicle's kinematic model, and establish the objective function. The specific steps are as follows:

[0125] (1) Based on the desired pitch angle i d and yaw angle ψ d Design desired pitch angular velocity q d and yaw rate r d :

[0126] ,

[0127] in, k q and k r A constant greater than 0 i t and ψ t These are the pitch and yaw angles of the underwater vehicle at the current moment.

[0128] (2) Predict the pitch angle of the underwater vehicle at the next moment and yaw angle :

[0129] ,

[0130] in, q t and r t Let Δ be the pitch and yaw rates of the underwater vehicle at the current moment. t For time step.

[0131] (3) Based on the kinematic model of the underwater vehicle, predict the speed of the underwater vehicle at the next moment:

[0132] ,

[0133] in, , , These represent the velocities of the underwater vehicle along the x, y, and z axes in the Earth coordinate system at the next moment. u t , v t , w t The current longitudinal velocity, lateral velocity, and vertical velocity of the underwater vehicle are... u The longitudinal velocity is to be determined at the next moment.

[0134] (4) Predict the position of the underwater vehicle at the next moment:

[0135] ,

[0136] in, , , The coordinates of the underwater vehicle in the geodetic coordinate system are predicted for the next moment. x t , y t , z tThe coordinates of the underwater vehicle in the geodetic coordinate system at the current moment are given.

[0137] (5) Establish the longitudinal velocity at the next moment. u d Objective function:

[0138] ,

[0139] in, l It is a constant. u min , u max They are respectively u d The minimum and maximum values.

[0140] S4. Based on the improved particle swarm optimization algorithm, the target speed is optimized. The algorithm steps are as follows:

[0141] (1) Initialize particle swarm parameters, including the number of particles. N Initial particle position, maximum number of iterations M Global optimal position G The global optimal fitness is determined by the particle's position, which represents the target speed to be optimized. The number of relevant particles is set. n The fitness function is set to the objective function established in step S3, and the initial fitness of each particle's position is calculated.

[0142] (2) Initialization t =0.

[0143] (3) Initialization i =0.

[0144] (4) For the first i There are 1 particle with positions and velocities of 1 and 2, respectively. X i (t), V i (t), the optimal position of this particle is P i (t), based on the set number of relevant particles n Randomly select from all particles except the i-th particle. n -1 particle, with the first i Each particle together forms a subgroup.

[0145] (5) Based on the individual fitness of all particles in the subgroup, select the m particles with the smallest individual fitness values ​​as the dominant particle set, where the set of indices of each particle is: Using the average optimal position of the dominant particle set in the subgroup to guide the first iThe position and velocity of each particle are updated to avoid getting trapped in local optima. i The velocity and position of each particle are updated as follows:

[0146] ,

[0147] .

[0148] in, oh , c 1. c 2 is a positive constant. r 1. r 2 is a random number between 0 and 1.

[0149] (6) Update the first i Fitness value of each particle J ( X i (t+1)). If J ( X i (t+1))< J ( P i (t)), then P i (t+1)= X i (t+1); if J ( X i (t+1))> J ( P i (t)), then P i (t+1)= P i (t). If J ( X i (t+1))< J ( G ),but G = X i (t+1).

[0150] (7) i = i +1. If i < N Return to step (4); if i ≥ N ,but t = t +1.

[0151] (8) If t < MReturn to step (3); if t ≥ M The iteration ends when the global optimal position is reached. G That is, the optimal target speed obtained. u d .

[0152] S5. Construct an adaptive sliding mode controller based on a Broad Learning System (BLS) to enable the underwater vehicle to reach the desired speed and to estimate and compensate for external disturbances and model parameter uncertainties.

[0153] S51, Target speed u d Desired pitch angular velocity q d Desired yaw rate r d Through a first-order low-pass filter:

[0154] ,

[0155] in, oh 1. oh 2. oh 3 is a constant greater than 0. u cf , q cf , r cf This is the filtered control law.

[0156] S52, Define speed error: e u = u - u cf , e q = q - q cf , e r = r - r cf .

[0157] S53. Define the integral sliding surface as follows:

[0158] ,

[0159] in, s u , s q , s rThese are the sliding surfaces for the longitudinal velocity, pitch angular velocity, and yaw angular velocity of the underwater vehicle, respectively. l u , l q , l r All are constants greater than 0.

[0160] S54. The specific design control law is as follows:

[0161] ,

[0162] in, or 11 , or 12 , or 21 , or 22 , or 31 , or 32 , c 11 , c 12 , c 21 , c 22 , c 31 , c 32 All are positive constants. , , The output of the wide-range learning system serves as an estimate of external disturbances and model uncertainty, and its form is: , For the actual weights of the width-learning system, the adaptive law for updating is:

[0163] ,

[0164] A l ( l ) represents the augmented matrix of the feature layer and enhancement layer of the width learning system, in the form of: ,in, Z =[ Z 1, Z 2, …, Z p ], Z i For feature nodes, p The number of feature nodes, H =[ H 1, H2, …, H q ], H j To enhance the nodes, q To increase the number of nodes.

[0165] The method for constructing feature nodes is as follows:

[0166]

[0167] in, f (·) represents a nonlinear mapping function. W fi For random weights, β fi For random bias.

[0168] The method for constructing enhanced nodes is as follows:

[0169]

[0170] in, x (·) represents a nonlinear mapping function. W ei The weights are random. β ei For random bias.

[0171] Simulation verification:

[0172] Set the time step for each step in the simulation. The time is 0.01s. The dynamic parameters of the AUV are: m 11 =27.68, m 22 =55.34, m 33 =55.34, m 44 =30.84, m 55 =30.84, X u =-7.70, X u|u| =-3.71, Y v =-58.92, Y v|v| =-124.45, Z w =-58.62, Z w|w| =-124.45, M q =-40.51, M q|q|=-178.6, N r =-46.34, N r|r| =-89.3, z b =0.02, B =264, m =26.94, W =264.01, d u =3+2.5sin(0.8t+π / 8), d v =1.2 sin(0.8t+π / 8)+0.6sin(0.5πt), d v =0.5+0.5sin(0.8t+π / 8)-0.6sin(0.5πt),d q = sin(0.8t+π / 8)-0.5sin(0.3t), d r = sin(0.8t+π / 8)+0.5sin(0.3πt). The parameters of the curvature adaptive line-of-sight method are: k x =1, a 1= a 2 = 0.2, D ymin = D zmin =0.12, k κ =2, a κ =20, k q = k r =10. The parameters in the improved particle swarm optimization algorithm are: N =100, M =100, n= 20, m=5, oh =0.7, c 1 = 0.6 c 2=1. The controller parameters are: oh 1= oh 2= oh 3=5, k u =10, k q = k r =1, l u = l q = l r =0.01, or11 = or 21 = or 31 =1, or 12 = or 22 = or 32 =10, c 11 = c 21 = c 31 =2, c 12 = c 22 = c 32 =10, p =3, q =5. Compared with existing adaptive line-of-sight (ALOS) navigation methods, its parameters are: c =-0.01, Δ=0.2, , , c 0 = 1.

[0173] The parametric equation of the curve path to be tracked is:

[0174]

[0175] in, α For path variables, α ∈[0,1].

[0176] Figure 3 and Figure 4 This section compares the simulation results of the method of this invention with those of the ALOS method. From... Figure 3 It can be seen that the method of this invention can track the desired path more accurately, while the ALOS method shows significant deviations at locations of high curvature on the path. From Figure 4 As can be seen, the tracking error of the method of this invention remains below 0.25 meters, while the maximum tracking error of the ALOS method exceeds 0.4 meters. The ALOS method has an average tracking error of 0.153 meters and a maximum tracking error of 0.472 meters, while the method of this invention has an average tracking error of 0.124 meters and a maximum tracking error of 0.226 meters, representing a 52% reduction in the maximum tracking error. Therefore, this invention can effectively address the problem of underactuated AUVs tracking paths with large curvatures, and compared with existing methods, it can significantly reduce deviation from the path and improve tracking accuracy.

[0177] The foregoing has shown and described the basic principles, main features, and application effects of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for adaptive tracking control of a large curvature path for an underactuated underwater vehicle, characterized in that, The steps are as follows: S1. Establish the mathematical model of the underwater vehicle, initialize the position and attitude of the underactuated underwater vehicle, and determine the parametric equations of the path to be tracked. The five-degree-of-freedom kinematic model of the underactuated underwater vehicle is as follows: ， in, x , y , z The coordinates of the AUV in the inertial coordinate system. θ、ψ These are pitch angle and yaw angle, respectively. u For longitudinal velocity, v For lateral velocity, w Vertical velocity, q The pitch angular velocity, r Yaw angular velocity; In the dynamic model, considering the uncertainty of the hydrodynamic coefficients, the dynamic model is as follows: ， in, m 11 , m 22 , m 33 , m 44 , m 55 The inertia of the AUV, τ u The thrust provided to the longitudinal thruster τ q For pitching moment, τ r For yaw moment, f u , f v , f w , f q , f r The uncertain hydrodynamic term and external disturbance at each degree of freedom are specifically in the form of: f u = X u u + X u|u| u|u| -( W - B sin θ + d u , f v = Y v v + Y v|v| v|v| - mz b rq + d v , f w = Z w w + Z w|w| w|w| +( W - B cos θ + d w , f r = N r r + N r|r| r|r| + d r , f q = M q q + M q|q| q|q|+mz b ( rv - qw ) - Wz b sin θ + d q ,in, X u , X u|u| , Y v , Y v|v| , Z w , Z w|w| , M q , M q|q| , N r , N r|r| For hydrodynamic coefficient, m For the mass of the underwater vehicle, W Let B be the weight of the underwater vehicle, and let B be the buoyancy force acting on the underwater vehicle. z b This is the distance between the center of buoyancy and the center of gravity of the underwater vehicle. d u , d v , d w , d q , d r External interference; S2. Calculate the curvature adaptive update rate, forward sight distance, and desired yaw and pitch angles using the improved line-of-sight method, including: S21. Express the parametric equation of the path to be tracked as follows: The path tracking error is expressed as: ， in, , , x , y , z The coordinates of the underwater vehicle in the geodetic coordinate system. x e , y e , z e For tracking error; S22. Taking the derivative with respect to the tracking error, we get: ， in, , , , u, v, and w represent the longitudinal velocity, lateral velocity, and vertical velocity of the underwater vehicle, respectively. θ , ψ These are the pitch angle and yaw angle of the underwater vehicle in the geodetic coordinate system, respectively. S23. Define the Lyapunov function as follows: Taking the derivative, we get ， To make the system asymptotically stable, that is Update law for path variables and desired pitch angular velocity θ d yaw rate ψ d Design; S24. The update rate of path variables affects the tracking accuracy of underwater vehicles. A curvature adaptive term is introduced into the path variable update law, specifically: ， in, k x , k κ , a κ Let κ be a constant greater than 0, and let κ be the curvature at the path point, which is calculated as follows: , The desired pitch and yaw angles are as follows: ， ， Where, Δ z Δ y These are the forward sight distances for pitch and yaw degrees of freedom, respectively; specifically: ， Where, Δ zmin Δ ymin This is the minimum forward sight distance. δ 1. δ 2 is a constant greater than 0. κ θ , κ ψ The curvature of the path in the pitch and yaw degrees of freedom is calculated as follows: ； S25, will Substitution When the pitch angle and yaw angle are equal to the designed desired pitch angle and yaw angle, ， Obviously, when | θ e |< hour, And only if x e , y e , z e When both are 0, Therefore, when the initial pitch angle error is less than At that time, the system asymptotically stabilizes, and the tracking error... x e , y e , z e All tend to 0; S3. Based on the underwater vehicle model, predict the position of the underwater vehicle at the next moment and establish the objective function; S4. Optimize the target speed based on the improved particle swarm optimization algorithm; S5. Construct an adaptive sliding mode controller based on a width learning system to control the speed of the underwater vehicle to reach the desired speed, and to estimate and compensate for external disturbances and model parameter uncertainties.

2. The adaptive tracking control method for large curvature path of an underactuated underwater vehicle according to claim 1, characterized in that, S3 include: S31. Based on the desired pitch angle θ d and yaw angle ψ d Design desired pitch angular velocity q d and yaw rate r d : ， in, k q and k r A constant greater than 0 θ t and ψ t These are the pitch and yaw angles of the underwater vehicle at the current moment. S32. Predict the pitch angle of the underwater vehicle at the next moment. and yaw angle : ， in, q t and r t Let Δ be the pitch and yaw rates of the underwater vehicle at the current moment. t For time intervals; S33. Based on the kinematic model of the underwater vehicle, predict the velocity of the underwater vehicle at the next moment: ， in, , , These represent the predicted velocities of the underwater vehicle along the x, y, and z axes in the Earth coordinate system for the next moment. u t , v t , w t The current longitudinal velocity, lateral velocity, and vertical velocity of the underwater vehicle are... u d The longitudinal velocity at the next moment is to be determined; S34. Predict the position of the underwater vehicle at the next moment: ， in, , , The coordinates of the underwater vehicle in the geodetic coordinate system are predicted for the next moment. x t , y t , z t The coordinates of the underwater vehicle in the geodetic coordinate system at the current moment; S35. Establish the longitudinal velocity at the next moment. u d Objective function: ， in, λ It is a constant. u min , u max They are respectively u d The minimum and maximum values.

3. The adaptive tracking control method for large curvature path of an underactuated underwater vehicle according to claim 2, characterized in that, S4 include: S41. Initialize particle swarm parameters, including the number of particles. N Initial particle position, maximum number of iterations M Global optimal position G The global optimal fitness is determined by the particle's position, which represents the target speed to be optimized. The number of relevant particles is set. n The fitness function is set to the objective function established in step S3, and the initial fitness of each particle's position is calculated. S42. Initialize t=0; S43, Initialization i =0; S44, Regarding the first i There are 1 particle with positions and velocities of 1 and 2, respectively. X i (t), V i (t), the optimal position of this particle is P i (t), based on the set number of relevant particles n Except for the first i Randomly select from all particles except for that particle. n -1 particle, with the first i Each particle together forms a subgroup; S45. Based on the individual fitness of all particles in this subgroup, select the m particles with the smallest individual fitness values ​​as the dominant particle set, where the set of indices of each particle is... Using the average optimal position of the dominant particle set in the subgroup to guide the first i The position and velocity of each particle are updated to avoid getting trapped in local optima; the position and velocity of the first particle are updated. i The velocity and position of each particle are updated as follows: ， ； in, ω , c 1. c 2 is a positive constant. r 1. r 2 is a random number between 0 and 1; S46, Update No. i Fitness value of each particle J ( X i (t+1)); if J ( X i (t+1))< J ( P i (t)), then P i (t+1)= X i (t+1); if J ( X i (t+1))> J ( P i (t)), then P i (t+1)= P i (t); if J ( X i (t+1))< J ( G ),but G = X i (t+1); S47 i = i +1 if i< N Return to S44; if i ≥ N ,but t = t +1; S48, if t < M Return to S43; if t ≥ M Then the iteration ends, and the global optimal position is found. G That is, the optimal target speed obtained. u d .

4. The adaptive tracking control method for large curvature path of an underactuated underwater vehicle according to claim 3, characterized in that, S5 include: S51, Target speed u d Desired pitch angular velocity q d Desired yaw rate r d Through a first-order low-pass filter: ， in, ω 1. ω 2. ω 3 is a constant greater than 0. u cf , q cf , r cf The control law is filtered; S52, Define speed error: e u = u - u cf , e q = q - q cf , e r = r - r cf ; S53. Define the integral sliding surface as follows: ， in, s u , s q , s r These are the sliding surfaces for the longitudinal velocity, pitch angular velocity, and yaw angular velocity of the underwater vehicle, respectively. k u , k q , k r , λ u , λ q , λ r All are constants greater than 0; S54. The specific design control law is as follows: ， in, η 11 , η 12 , η 21 , η 22 , η 31 , η 32 , c 11 , c 12 , c 21 , c 22 , c 31 , c 32 All are positive constants. , , The output of the wide-range learning system serves as an estimate of external disturbances and model uncertainty, and its form is: , For the actual weights between the feature layer and the output layer of the width learning system, the adaptive law for updating is: ， A l ( l ) represents the augmented matrix of the feature layer and enhancement layer of the width learning system, in the form of: ,in, Z =[ Z 1, Z 2, …, Z p ], Z i For feature nodes, p The number of feature nodes, H =[ H 1, H 2, …, H q ], H j To enhance the nodes, q To increase the number of nodes; The method for constructing feature nodes is as follows: ， in, φ (·) represents a nonlinear mapping function. W fi For random weights, β fi For random bias; The method for constructing enhanced nodes is as follows: ， in, ξ (·) represents a nonlinear mapping function. W ei The weights are random. β ei For random bias.

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