CN113820956B - High-speed AUV motion control method - Google Patents

High-speed AUV motion control method Download PDF

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CN113820956B
CN113820956B CN202111393837.3A CN202111393837A CN113820956B CN 113820956 B CN113820956 B CN 113820956B CN 202111393837 A CN202111393837 A CN 202111393837A CN 113820956 B CN113820956 B CN 113820956B
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CN113820956A (en
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郭军军
连文康
范彦福
顾建军
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Zhejiang Lab
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Abstract

The invention discloses a motion control method of an Autonomous Underwater Vehicle (AUV), which improves the control precision of the AUV during high-speed motion and effectively inhibits buffeting of a control system by integrating a radial basis function neural network and a boundary layer method into the traditional sliding mode control. Compared with the traditional AUV model simplification method, the high-speed AUV motion control method adds a parameter model with self-adaptive change during model simplification, so that the established model is closer to the actual situation; compared with the traditional AUV sliding mode control method, the method adds the compensation of the radial basis function neural network in the sliding mode control, and improves the switching surface of the sliding mode through a boundary layer method, so that the sliding mode control system can keep higher control precision and inhibit buffeting.

Description

High-speed AUV motion control method
Technical Field
The invention relates to the field of Autonomous Underwater Vehicle (AUV) control, in particular to a high-speed AUV motion control method.
Background
An Autonomous Underwater Vehicle (AUV) is one of powerful tools for exploring ocean space, and is increasingly widely applied to the fields of military ocean technology, oil field survey, seabed salvage, pipeline overhaul, seabed survey and the like. However, the conventional underwater robot generally has the problems of low navigational speed, poor environmental adaptability and the like, and the exploration of the motion control method of the high-speed AUV is an important direction for research around the urgent needs of quick emergency search in deep sea, quick underwater environment evaluation and the like.
PID Control (performance Integration Differentiation Control), backstepping Control (Back Stepping Control), Fuzzy Control (Fuzzy Control), Sliding Mode Control (Sliding Mode Control), Neural network Control (Neural network Control), and the like are some Control methods commonly used in current AUVs, and in recent years, the application of Deep Learning (Deep Learning) in the Control field has also greatly promoted the development of Control technology. The PID control is only suitable for simple control under some AUV weak maneuvers, but is sensitive to environmental parameter change, and setting optimization is troublesome; the backstepping control depends on an accurate mathematical model, but the accurate model of the novel high-speed AUV is difficult to obtain; the sliding mode variable structure control has the characteristic of high response speed, but the sliding mode variable structure control is easy to cause buffeting; fuzzy controllers rely on a priori knowledge; although the neural network control has strong nonlinear approximation capability, the number of network layers and the number of nodes of each layer are difficult to determine; deep learning has powerful complex nonlinear modeling capability, but training thereof is time-consuming, and model correctness verification is complex and cumbersome.
Disclosure of Invention
The invention aims to provide a high-speed AUV motion control method aiming at the defects of the prior art.
The purpose of the invention is realized by the following technical scheme: a high-speed AUV motion control method comprises the following steps:
(1) obtaining a functional relation between system parameters and the navigational speed through polynomial fitting, and obtaining a high-speed AUV simplified motion model according to the functional relation; taking the navigational speed as the input of a high-speed AUV simplified motion model;
(2) selecting a radial basis function, defining a sliding mode function, designing a sliding mode control law and a self-adaptive law, calculating a sliding mode surface switching function based on a boundary layer method, and improving the sliding mode control law;
(3) and (3) performing motion control on the high-speed AUV by using the improved sliding mode control law obtained in the step (2).
Further, the high-speed AUV simplified motion model in step (1) is specifically:
Figure 634249DEST_PATH_IMAGE001
wherein, it is provided with
Figure 791692DEST_PATH_IMAGE002
Is provided with
Figure 758511DEST_PATH_IMAGE003
，
Figure 123633DEST_PATH_IMAGE004
Is the longitudinal speed of the AUV and,
Figure 651435DEST_PATH_IMAGE005
the vertical velocity is the velocity of the gas,
Figure 2782DEST_PATH_IMAGE006
in order to be at a longitudinal-inclination angle,
Figure 948742DEST_PATH_IMAGE007
as to the speed of the pitch angle,
Figure 94552DEST_PATH_IMAGE008
for the purpose of the depth value,
Figure 876695DEST_PATH_IMAGE009
in order to be a pitching moment,
Figure 625208DEST_PATH_IMAGE010
is the rudder angle of the stern rudder,
Figure 566619DEST_PATH_IMAGE011
is a positive number, and the number of the positive number,
Figure 522811DEST_PATH_IMAGE012
、
Figure 916884DEST_PATH_IMAGE013
taking the hydrodynamic coefficient of AUV
Figure 734667DEST_PATH_IMAGE014
，
Figure 999426DEST_PATH_IMAGE015
The density of the seawater is shown as the density of the seawater,
Figure 627985DEST_PATH_IMAGE016
is the length of the high-speed AUV,
Figure 509353DEST_PATH_IMAGE017
and
Figure 130827DEST_PATH_IMAGE018
is a polynomial coefficient.
Further, the sliding mode function in the step (2) is obtained based on a stability theory, and specifically includes:
Figure 781251DEST_PATH_IMAGE019
wherein,
Figure 548088DEST_PATH_IMAGE020
is a positive number, and the number of the positive number,
Figure 41386DEST_PATH_IMAGE021
is an error.
Further, the sliding mode control law in the step (2) is as follows:
Figure 76338DEST_PATH_IMAGE022
wherein,
Figure 722214DEST_PATH_IMAGE023
，
Figure 286051DEST_PATH_IMAGE024
、
Figure 266645DEST_PATH_IMAGE025
is a positive number, and the number of the positive number,
Figure 105288DEST_PATH_IMAGE026
is a target value;
the adaptive law is as follows:
Figure 844486DEST_PATH_IMAGE027
wherein,
Figure 969437DEST_PATH_IMAGE028
，
Figure 47114DEST_PATH_IMAGE029
in order to be the pitch angle,
Figure 564815DEST_PATH_IMAGE030
is the output of the gaussian-based function,
Figure 44337DEST_PATH_IMAGE031
in order to be a coefficient of hydrodynamic force,
Figure 605769DEST_PATH_IMAGE032
is the weight of the neural network;
further, the sliding mode surface switching function in the step (2) is as follows:
Figure 905163DEST_PATH_IMAGE033
in the formula,
Figure 459510DEST_PATH_IMAGE034
in order to be a function of the sign,
Figure 793539DEST_PATH_IMAGE035
is a natural constant and is a natural constant,
Figure 525872DEST_PATH_IMAGE036
is a positive number.
Further, the step (3) is specifically: and (3) obtaining a depth error by subtracting the expected depth from the feedback depth, inputting the depth error into a sliding mode function to perform sliding mode control, improving a sliding mode control law by using a radial basis function and a boundary layer method, obtaining an output rudder angle through the sliding mode control law, and finishing the feedback control by changing the depth of the high-speed AUV through the rudder angle.
The sliding mode switching method has the advantages that the sliding mode switching method is used for switching functions through the sliding mode
Figure 578142DEST_PATH_IMAGE037
And replacement is carried out, buffeting of the sliding mode control system is effectively weakened under the condition that strong robustness of the system is ensured, and practicability of a control algorithm is improved. In the method, the influence of internal and external disturbance of the high-speed AUV during high-speed maneuvering can be effectively inhibited through the compensation of the radial basis function neural network on the sliding mode control, so that the control precision of the high-speed AUV at different navigational speeds is ensured, and the working performance of the system is improved.
In order to realize the motion Control of the high-speed AUV, the invention improves the AUV Control system by applying a radial basis function neural network and a nonlinear switching surface to a Sliding Mode Control (SMC) Mode, so as to achieve the purposes of weakening the buffeting of the system and improving the motion Control precision.
Drawings
FIG. 1 is a schematic diagram of the working principle of high-speed AUV depth control;
FIG. 2 is a schematic diagram showing depth comparison before and after improvement of the high-speed AUV diving algorithm at the speed of 10 knots;
FIG. 3 is a schematic diagram showing a comparison of rudder angles before and after the improvement of the high-speed AUV by the 10-joint cruise latency algorithm.
Detailed Description
The invention is further illustrated by the following figures and examples. The invention provides a high-speed AUV motion control method, which specifically comprises the following steps:
(1) obtaining a functional relation between system parameters and the navigational speed through polynomial fitting, and obtaining a high-speed AUV simplified motion model according to the functional relation; and taking the navigational speed as the input of the high-speed AUV simplified motion model. The method specifically comprises the following steps:
fig. 1 is a schematic diagram of a high-speed AUV inertial coordinate system and a carrier coordinate system, and simplifies a dynamic model of the high-speed AUV. The method is characterized in that the depth control is carried out on the high-speed AUV under different navigation speeds, and when the AUV maneuvers according to the depth, the longitudinal speed is assumed
Figure 906486DEST_PATH_IMAGE038
The longitudinal speed being provided solely by the thrust system and being able to be maintained at a stable value
Figure 485235DEST_PATH_IMAGE038
Is constant, neglecting the effect of rolling, then there are
Figure 529414DEST_PATH_IMAGE039
，
Figure 177302DEST_PATH_IMAGE040
Is a positive number, and the number of the positive number,
Figure 699550DEST_PATH_IMAGE038
in order to achieve a longitudinal navigational speed,
Figure 867227DEST_PATH_IMAGE041
the speed of the ship is vertical to the ship,
Figure 816728DEST_PATH_IMAGE042
is the pitch angle. The high-speed AUV is assumed to have symmetrical shape structure left and right and approximately symmetrical up and down, and under the condition of high-speed motion, the high-speed AUV has longitudinal speed
Figure 453377DEST_PATH_IMAGE038
Compared with the heave motion speed
Figure 779316DEST_PATH_IMAGE041
Much smaller, no possibility of making the heave movement speed
Figure 801499DEST_PATH_IMAGE041
Seen as a small perturbation, say
Figure 295803DEST_PATH_IMAGE043
。
The simplified dynamic model of the vertical plane motion is as follows:
Figure 809961DEST_PATH_IMAGE044
wherein,
Figure 798645DEST_PATH_IMAGE002
，
Figure 816280DEST_PATH_IMAGE045
is provided with
Figure 982950DEST_PATH_IMAGE046
For the influence of internal and external disturbances on the uncertainty of the modeling model,
Figure 718825DEST_PATH_IMAGE038
is the longitudinal speed of the AUV and,
Figure 511200DEST_PATH_IMAGE041
the vertical velocity is the velocity of the gas,
Figure 383341DEST_PATH_IMAGE042
in order to be at a longitudinal-inclination angle,
Figure 479168DEST_PATH_IMAGE007
as to the speed of the pitch angle,
Figure 702339DEST_PATH_IMAGE008
for the purpose of the depth value,
Figure 32826DEST_PATH_IMAGE047
in order to be a pitching moment,
Figure 25053DEST_PATH_IMAGE010
is the rudder angle of the stern rudder,
Figure 799105DEST_PATH_IMAGE011
is a positive number, and the number of the positive number,
Figure 103047DEST_PATH_IMAGE048
、
Figure 112592DEST_PATH_IMAGE049
hydrodynamic coefficient of AUV, their and speed
Figure 598806DEST_PATH_IMAGE038
The functional relationship of (A) can be obtained by polynomial fitting, preferably
Figure 137234DEST_PATH_IMAGE050
Wherein
Figure 459631DEST_PATH_IMAGE038
Is the longitudinal speed of the high-speed AUV,
Figure 7287DEST_PATH_IMAGE015
the density of the seawater is shown as the density of the seawater,
Figure 583893DEST_PATH_IMAGE051
is the length of the high-speed AUV,
Figure 683436DEST_PATH_IMAGE052
and
Figure 368496DEST_PATH_IMAGE018
is a polynomial coefficient;
Figure 93744DEST_PATH_IMAGE053
the same is true. In this example, take
Figure 915069DEST_PATH_IMAGE054
、
Figure 185514DEST_PATH_IMAGE055
、
Figure 92290DEST_PATH_IMAGE056
、
Figure 857115DEST_PATH_IMAGE057
And
Figure 798526DEST_PATH_IMAGE058
。
(2) selecting a radial basis function neural network, defining a sliding mode surface, calculating the self-adaption rate of the neural network, calculating a sliding mode surface switching function, and designing a sliding mode control law and a self-adaption law; the method specifically comprises the following steps:
(2.1) selecting a radial basis function neural network:
because the Radial Basis Function (RBF) neural network has the capability of infinite approximation, the RBF neural network is adopted for approximation
Figure 239871DEST_PATH_IMAGE046
Network input fetch
Figure 633944DEST_PATH_IMAGE059
The network output is:
Figure 700994DEST_PATH_IMAGE060
then, there are:
Figure 355967DEST_PATH_IMAGE061
wherein
Figure 109159DEST_PATH_IMAGE062
。
(2.2) defining a sliding mode function:
in order to reduce the number of the parameters of the controller, the parameter adjusting efficiency is improved. Based on the Hurwitz stability theory, a characteristic equation of a Hurwitz criterion is set as follows:
Figure 865894DEST_PATH_IMAGE063
wherein
Figure 831576DEST_PATH_IMAGE064
For Laplace operators, i.e. requiring polynomials
Figure 606634DEST_PATH_IMAGE065
The real part of the eigenvalue of (d) is negative. Is not to take
Figure 530727DEST_PATH_IMAGE066
I.e. by
Figure 13573DEST_PATH_IMAGE067
Get it
Figure 173159DEST_PATH_IMAGE068
The requirements of Hurwitz can be met, wherein
Figure 678090DEST_PATH_IMAGE069
，
Figure 648451DEST_PATH_IMAGE070
，
Figure 97887DEST_PATH_IMAGE071
，
Figure 936530DEST_PATH_IMAGE072
，
Figure 669868DEST_PATH_IMAGE073
Is a positive number. The sliding mode function can be expressed as:
Figure 935765DEST_PATH_IMAGE074
wherein
Figure 138076DEST_PATH_IMAGE021
Is an error.
(2.3) designing a sliding mode control law and an adaptive law:
according to the Lyapunov function (Lyapunov function)
Figure 514831DEST_PATH_IMAGE075
And step ofThe sliding mode control law of the sliding mode function defined in the step (2.2) is as follows:
Figure 869720DEST_PATH_IMAGE076
wherein,
Figure 306517DEST_PATH_IMAGE077
，
Figure 996125DEST_PATH_IMAGE024
、
Figure 910991DEST_PATH_IMAGE025
is a positive number, and the number of the positive number,
Figure 884501DEST_PATH_IMAGE078
is the target value.
The self-adaptation law is designed as follows:
Figure 492200DEST_PATH_IMAGE079
wherein,
Figure 403524DEST_PATH_IMAGE080
，
Figure 731868DEST_PATH_IMAGE081
in order to be the pitch angle,
Figure 185983DEST_PATH_IMAGE082
is the output of the gaussian-based function,
Figure 823638DEST_PATH_IMAGE031
in order to be a coefficient of hydrodynamic force,
Figure 737105DEST_PATH_IMAGE083
is the weight of the neural network.
Based on the controller design of the sliding mode control law and the self-adaptive law, the system stability can be simply proved as follows:
based on the stability of Lyapunov:
Figure 259353DEST_PATH_IMAGE084
let N be
Figure 692609DEST_PATH_IMAGE085
Maximum value of (1), then
Figure 376531DEST_PATH_IMAGE086
Get it
Figure 13180DEST_PATH_IMAGE087
Then, then
Figure 339119DEST_PATH_IMAGE088
The system Lyapunov is stable.
(2.4) designing a sliding mode surface switching function by using a boundary layer method, and improving a sliding mode control law:
the switching function of the boundary layer in the traditional sliding mode control is a sign function
Figure 361302DEST_PATH_IMAGE034
The discontinuity is liable to cause a buffeting phenomenon of the system. In order to weaken the buffeting phenomenon of the traditional sliding mode control, the sliding mode control law designed in the step (2.3) is improved by utilizing a boundary layer method, and a nonlinear function (namely a sliding mode surface switching function) with smooth continuous characteristic is adopted
Figure 873184DEST_PATH_IMAGE089
Function of substitution sign
Figure 387342DEST_PATH_IMAGE034
K is a positive number for adjusting the non-linear function
Figure 376026DEST_PATH_IMAGE037
At the switching speed near the zero point, the switching characteristics can be improved. The post-replacement control law is:
Figure 128082DEST_PATH_IMAGE090
wherein,
Figure 560331DEST_PATH_IMAGE091
，
Figure 296206DEST_PATH_IMAGE024
、
Figure 823002DEST_PATH_IMAGE025
is a positive number, and the number of the positive number,
Figure 537886DEST_PATH_IMAGE092
is the target value.
(3) And (3) performing motion control on the high-speed AUV by using the improved sliding mode control law obtained in the step (2):
referring to the attached drawing 1, the working principle of the high-speed AUV depth control in the scheme of the invention is schematically shown.
And obtaining a depth error by subtracting the expected depth from the feedback depth, inputting the depth error into a sliding mode function to perform sliding mode control, improving a sliding mode control law by using a Radial Basis Function (RBF) neural network and a boundary layer method, obtaining an output rudder angle through the sliding mode control law (namely a rudder angle control law), and changing the depth through the rudder angle by using a high-speed AUV (autonomous underwater vehicle). And finally, outputting the actual depth to realize a negative feedback control process.
In order to verify the effectiveness of the method, assuming that the high-speed AUV 10 is submerged at a navigational speed of 10 meters (5.145 meters/second), the sliding mode control method based on the radial basis function neural network (after improvement) and the traditional sliding mode control method (before improvement) of the invention are verified to be effective in improving the control precision, as shown in fig. 2 and 3, it can be seen that after the improvement based on the idea of the invention, the steady-state error is reduced, the control precision is improved, and the buffeting is effectively weakened.
In summary, the present invention is applicable to a sliding mode switching function
Figure 124725DEST_PATH_IMAGE037
And replacement is carried out, buffeting of the sliding mode control system is effectively weakened under the condition that strong robustness of the system is ensured, and practicability of a control algorithm is improved. In the method, the influence of internal and external disturbance of the high-speed AUV during high-speed maneuvering can be effectively inhibited through the compensation of the radial basis function neural network on the sliding mode control, so that the control precision of the high-speed AUV at different navigational speeds is ensured, and the working performance of the system is improved. The invention utilizes a sliding mode control method based on a radial basis function neural network to carry out depth control on the high-speed AUV under the conditions of different navigational speeds and different loads, thereby realizing depth maneuver under different tasks.

Claims (1)

1. A high-speed AUV motion control method is characterized by comprising the following steps:
(1) obtaining a functional relation between system parameters and the navigational speed through polynomial fitting, and obtaining a high-speed AUV simplified motion model according to the functional relation; taking the navigational speed as the input of a high-speed AUV simplified motion model;
the high-speed AUV simplified motion model specifically comprises the following steps:
Figure DEST_PATH_IMAGE001
wherein, it is provided with
Figure 737103DEST_PATH_IMAGE002
Is provided with
Figure DEST_PATH_IMAGE003
，
Figure 202719DEST_PATH_IMAGE004
Is the longitudinal speed of the AUV and,
Figure DEST_PATH_IMAGE005
the vertical velocity is the velocity of the gas,
Figure 759865DEST_PATH_IMAGE006
in order to be at a longitudinal-inclination angle,
Figure DEST_PATH_IMAGE007
as to the speed of the pitch angle,
Figure 576511DEST_PATH_IMAGE008
for the purpose of the depth value,
Figure DEST_PATH_IMAGE009
in order to be a pitching moment,
Figure 110261DEST_PATH_IMAGE010
is the rudder angle of the stern rudder,
Figure DEST_PATH_IMAGE011
is a positive number, and the number of the positive number,
Figure 695963DEST_PATH_IMAGE012
、
Figure DEST_PATH_IMAGE013
taking the hydrodynamic coefficient of AUV
Figure 922545DEST_PATH_IMAGE014
，
Figure DEST_PATH_IMAGE015
The density of the seawater is shown as the density of the seawater,
Figure 725022DEST_PATH_IMAGE016
is the length of the high-speed AUV,
Figure DEST_PATH_IMAGE017
and
Figure 62463DEST_PATH_IMAGE018
is a polynomial coefficient;
(2) selecting a radial basis function, defining a sliding mode function, designing a sliding mode control law and a self-adaptive law, calculating a sliding mode surface switching function based on a boundary layer method, and improving the sliding mode control law;
the sliding mode function is obtained based on a stability theory, and specifically comprises the following steps:
Figure DEST_PATH_IMAGE019
wherein,
Figure 502671DEST_PATH_IMAGE020
is a positive number, and the number of the positive number,
Figure DEST_PATH_IMAGE021
is an error;
the sliding mode control law is as follows:
Figure 900155DEST_PATH_IMAGE022
wherein,
Figure DEST_PATH_IMAGE023
，
Figure 927279DEST_PATH_IMAGE024
、
Figure DEST_PATH_IMAGE025
is a positive number, and the number of the positive number,
Figure 802831DEST_PATH_IMAGE026
is a target value;
the adaptive law is as follows:
Figure DEST_PATH_IMAGE027
wherein,
Figure 363125DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE029
in order to be the pitch angle,
Figure 931510DEST_PATH_IMAGE030
is the output of the gaussian-based function,
Figure DEST_PATH_IMAGE031
in order to be a coefficient of hydrodynamic force,
Figure 678886DEST_PATH_IMAGE032
is the weight of the neural network;
the sliding mode surface switching function is as follows:
Figure DEST_PATH_IMAGE033
in the formula,
Figure 139822DEST_PATH_IMAGE034
in order to be a function of the sign,
Figure DEST_PATH_IMAGE035
is a natural constant and is a natural constant,
Figure 289043DEST_PATH_IMAGE036
is a positive number;
(3) performing motion control on the high-speed AUV by using the improved sliding mode control law obtained in the step (2); the method specifically comprises the following steps: and (3) obtaining a depth error by subtracting the expected depth from the feedback depth, inputting the depth error into a sliding mode function to perform sliding mode control, improving a sliding mode control law by using a radial basis function and a boundary layer method, obtaining an output rudder angle through the sliding mode control law, and finishing the feedback control by changing the depth of the high-speed AUV through the rudder angle.
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