CN113110532A - Benthonic AUV self-adaptive terminal sliding mode trajectory tracking control method based on auxiliary dynamic system - Google Patents

Benthonic AUV self-adaptive terminal sliding mode trajectory tracking control method based on auxiliary dynamic system Download PDF

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CN113110532A
CN113110532A CN202110500855.0A CN202110500855A CN113110532A CN 113110532 A CN113110532 A CN 113110532A CN 202110500855 A CN202110500855 A CN 202110500855A CN 113110532 A CN113110532 A CN 113110532A
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CN113110532B (en
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万磊
孙超伟
孙延超
张宇昂
秦洪德
曹禹
夏光庆
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Harbin Engineering University
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Abstract

The invention discloses a benthonic AUV self-adaptive terminal sliding mode trajectory tracking control method based on an auxiliary dynamic system, and relates to a benthonic AUV self-adaptive terminal sliding mode trajectory tracking control method. The invention aims to solve the problem that the existing method has low track tracking control precision on the benthonic AUV. The method for controlling the benthonic AUV self-adaptive terminal sliding mode trajectory tracking based on the auxiliary dynamic system comprises the following steps: step one, establishing an AUV kinematic equation; secondly, defining a pose error model variable based on the AUV kinematic equation established in the first step; step three, establishing an AUV error model based on the AUV kinematic equation established in the step one and the pose error model variable defined in the step two; and step four, designing the AUV error model established in the control law control step three. The method is used for the field of AUV trajectory tracking control.

Description

Benthonic AUV self-adaptive terminal sliding mode trajectory tracking control method based on auxiliary dynamic system
Technical Field
The invention relates to a benthonic AUV self-adaptive terminal sliding mode trajectory tracking control method.
Background
As a typical representative of the current marine Autonomous intelligent agent, an Autonomous Underwater Vehicle (AUV) has the advantages of light weight, strong autonomy, flexible movement, high control accuracy and the like, and has been widely used in the civil, military and industrial fields. The benthonic AUV is an AUV which can sit on the seabed, can autonomously sail to a designated position on the seabed after being released, and can sit on the seabed for a long time to acquire data such as seabed earthquake and the like; after the operation is finished, the floating bodies can float to the designated sea area automatically, and the mother ship carries out unified salvage and recovery. When the benthonic AUV sails to a height of 200m from the sea bottom, a curve track tracking control task is started. Besides being influenced by external interference, the tracking process is also influenced by other factors, so that the track tracking control precision of the benthonic AUV is low. The benthonic AUV is a strong nonlinear system, and the model has model parameter uncertainty; considering the actual system operation, the control execution structure is influenced by physical factors, namely the system is limited by input saturation. The AUV motion control method which considers external interference, model parameter uncertainty and input saturation conditions during research is more consistent with the actual working condition of the bentable AUV.
Therefore, aiming at the problem of benthonic AUV trajectory tracking control under the influence of multiple conditions, the invention designs an AUV trajectory tracking controller based on an Auxiliary Dynamic System (ADS) adaptive terminal sliding mode control method, proves that the designed controller is converged in limited time, and verifies the control algorithm through a simulation contrast test.
Disclosure of Invention
The invention aims to solve the problem that the track tracking control precision of the existing method for the benthonic AUV is low, and provides a sliding mode track tracking control method of the benthonic AUV self-adaptive terminal based on an auxiliary dynamic system.
The method for controlling the benthonic AUV self-adaptive terminal sliding mode trajectory tracking based on the auxiliary dynamic system comprises the following specific processes:
step one, establishing an AUV kinematic equation;
secondly, defining a pose error model variable based on the AUV kinematic equation established in the first step;
step three, establishing an AUV error model based on the AUV kinematic equation established in the step one and the pose error model variable defined in the step two;
and step four, designing the AUV error model established in the control law control step three.
The invention has the beneficial effects that:
the controller designed by the invention has higher convergence speed and better robustness, and the pose convergence time is shortened by 43% compared with that of an NFFTMC controller. Compared with a controller without considering input saturation, the controller has the advantages that when the output of the actuator is close to the critical value by applying the ADS control method, the transition is more gradual, and the output of the actuator is more stable in the whole convergence stage. Therefore, compared with the existing method, the controller designed by the invention can achieve a better control effect, can better realize the control target of the benthonic AUV trajectory tracking, and improves the trajectory tracking control precision of the benthonic AUV.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is an AUV three-dimensional trajectory tracking curve
FIG. 3 is a graph of AUV longitudinal tracking error response;
FIG. 4 is a graph of AUV lateral tracking error response;
FIG. 5 is a graph of AUV vertical tracking error response;
FIG. 6 is a graph of AUV yaw angle tracking error response;
FIG. 7 is a AUV pitch angle tracking error response graph;
FIG. 8 is a graph of AUV longitudinal velocity response;
FIG. 9 is a graph of AUV lateral velocity response;
FIG. 10 is a graph of AUV vertical velocity response;
FIG. 11 is an AUV yaw rate response graph;
FIG. 12 is a graph of AUV pitch angular velocity response;
FIG. 13 is a graph of the sliding mode variable s response;
FIG. 14 is a graph of AUV longitudinal thrust response;
FIG. 15 is a graph of AUV thrust response;
FIG. 16 is a graph of AUV vertical thrust response;
FIG. 17 is an AUV yaw moment response plot;
FIG. 18 is an AUV pitching moment response plot;
FIG. 19 is a block diagram of ADS adaptive sliding mode control.
Detailed Description
The first embodiment is as follows: the embodiment is described with reference to fig. 1, and the specific process of the bentable AUV adaptive terminal sliding mode trajectory tracking control method based on the auxiliary dynamic system in the embodiment is as follows:
step one, establishing an AUV kinematic equation;
secondly, defining a pose error model variable based on the AUV kinematic equation established in the first step;
step three, establishing an AUV error model based on the AUV kinematic equation established in the step one and the pose error model variable defined in the step two;
and step four, designing the AUV error model established in the control law control step three.
The second embodiment is as follows: the difference between the first embodiment and the first embodiment is that an AUV kinematic equation is established in the first step; the specific process is as follows:
the autonomous robot generally establishes a mathematical model based on a Newton-Euler equation during motion analysis, and the establishment of the model generally adopts two coordinate systems, namely an inertial coordinate system (Earth-fixed frame) and a carrier coordinate system (Body-fixed frame);
the AUV kinematic equation expresses the conversion relation between an inertial coordinate system and a carrier coordinate system; when the AUV moves, the change of speed and angular speed occurs, if the position and the posture of the AUV under an inertial coordinate system are observed, the AUV is converted between the two coordinate systems, and referring to relevant documents, the AUV kinematic equation expression is as follows:
Figure BDA0003056457250000031
in the formula, R (eta) is a transformation matrix between a carrier coordinate system and an inertia coordinate system, eta represents the AUV actual pose,
Figure BDA0003056457250000032
is the first derivative of η, and upsilon is the velocity and angular velocity of AUV;
the six-degree-of-freedom kinetic equation of the AUV under the carrier coordinate system is in the form as follows:
Mυ+C(υ)υ+D(υ)υ+g(η)＝τ+τd (2)
in the formula, M represents an inertia matrix,
Figure BDA0003056457250000033
c (υ) represents the coriolis centripetal force matrix,
Figure BDA0003056457250000034
d (υ) represents the fluid damping torque,
Figure BDA0003056457250000035
g (η) represents a restoring force (moment) vector generated by gravity and buoyancy,
Figure BDA0003056457250000036
tau represents the force or moment vector produced by the control law,
Figure BDA0003056457250000037
τdrepresenting the external disturbance force (moment) vector,
Figure BDA0003056457250000038
other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the difference between the embodiment and the first or second embodiment is that in the second step, based on the AUV kinematic equation established in the first step, a pose error model variable is defined; the expression is as follows:
ηe＝η-ηd (3)
in the formula, eta represents AUV actual pose, etadRepresenting a desired pose in tracking control; etaeAnd (4) representing AUV pose errors.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between the embodiment and one of the first to third embodiments is that in the third step, an AUV error model is established based on the AUV kinematic equation established in the first step and the pose error model variable defined in the second step; the specific process is as follows:
according to the formulas (1), (2) and (3), an AUV error model with the following form is established:
Figure BDA0003056457250000041
in the formula, F represents a comprehensive interference item superimposed by external time-varying interference and perturbation of model parameters in the AUV error model,
Figure BDA0003056457250000042
r denotes a transformation matrix between the carrier coordinate system and the inertial coordinate system,
Figure BDA0003056457250000043
representing a comprehensive interference term under an inertial coordinate system;
Figure BDA0003056457250000044
expression ηeThe first derivative of (a) is,
Figure BDA0003056457250000045
the first derivative of η is represented as,
Figure BDA0003056457250000046
expression ηdThe first derivative of (a) is,
Figure BDA0003056457250000047
expression ηeThe second derivative of (a) is,
Figure BDA0003056457250000048
the second derivative of η is represented as,
Figure BDA0003056457250000049
expression ηdThe second derivative of (a) is,
Figure BDA00030564572500000410
the first derivative of R is indicated and τ is the control law.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between the present embodiment and one of the first to fourth embodiments is that the fourth step is to design an AUV error model established in the first control law control step; the specific process is as follows:
the nonsingular fast terminal sliding mode control switching function is as follows:
Figure BDA00030564572500000411
in the formula, s is a sliding mode variable;
Figure BDA00030564572500000412
is a positive integer, l and p are positive odd numbers, and satisfy 0 < l/p < 1,
Figure BDA00030564572500000413
α1、α2in order for the diagonal matrix to be known,
Figure BDA00030564572500000414
the control law is designed based on the AUV error model of the formula (4) and the sliding mode control switching function of the formula (5) as follows:
τ＝τc+Δτ (6)
wherein τ represents the force or moment vector generated by the control law (actual input to the controller); tau iscThe expected control law is obtained after the controller is operated; and delta tau is the difference between the actual AUV control input and the control law obtained by the control algorithm.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is that the controller obtains the desired control law τ through calculationcThe expression of (a) is:
τc＝τ0+τ1+τ2 (7)
Figure BDA0003056457250000051
Figure 100002_1
Figure BDA0003056457250000053
in the formula, τ0To disregard the control law under various disturbances, τ1For handling the adaptive term of the integrated interference (F), tau2To handle the adaptive term of input saturation, Θ is an intermediate symbolic variable, k, that is easy to understand and derive1Is a known normal number; k is a radical ofζIs a known constant, kζ＝diag[kζ1kζ2kζ3kζ4kζ5kζ6]，kζiIs a known constant, i ═ 1.., 6; k is a radical ofλIs a known constant, kλ＝diag[kλ1kλ2kλ3kλ4kλ5kλ6]，kλiIs a known positive number, i ═ 1.., 6; gamma raymin(kλ) Is the sign of the minimum value, γmin(kλ)＝min{kλ1,kλ2,kλ3,kλ4,kλ5,kλ6}; ζ is the auxiliary variable, T is the transpose, and λ is a known constant.
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is that the expression of the intermediate symbolic variable Θ is:
Figure BDA0003056457250000054
in the formula (I), the compound is shown in the specification,
Figure BDA0003056457250000055
are intermediate symbolic variables that are easy to understand and deduce.
Other steps and parameters are the same as those in one of the first to sixth embodiments.
The specific implementation mode is eight: this embodiment is different from one of the first to seventh embodiments in that the intermediate symbol variable
Figure BDA0003056457250000056
The expression of (a) is:
designing a self-adaptive law for processing the comprehensive interference item F;
Figure BDA0003056457250000061
Figure BDA0003056457250000062
Figure BDA0003056457250000063
in the formula, a0，a1，a2In order for the positive number to be known,
Figure BDA0003056457250000064
are respectively as
Figure BDA0003056457250000065
The first derivatives are intermediate sign variables which are convenient to understand and deduce, and have the same sign meaning as the sign in the step two; l and p are positive odd numbers and satisfy 0 < l/p < 1,
Figure BDA0003056457250000066
α2in order for the diagonal matrix to be known,
Figure BDA0003056457250000067
s is a sliding mode variable.
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The specific implementation method nine: this embodiment is different from the first to eighth embodiments in that the auxiliary variable ζ is structured as follows:
Figure BDA0003056457250000068
where μ is a known positive number, h (s, Δ τ, ζ) is a smoothing function, and ζ is an auxiliary variable; λ is a known constant; and delta tau is the difference between the actual AUV control input and the control law obtained by the control algorithm.
Other steps and parameters are the same as those in one to eight of the embodiments.
The detailed implementation mode is ten: this embodiment differs from one of the first to ninth embodiments in that the smoothing function h (s, Δ τ, ζ) has the following form
Figure BDA0003056457250000069
In the formula, deltawIs a known positive number and satisfies δw＞max{kζ1,kζ2,kζ3,kζ4,kζ5,kζ6}，εζIn order for the positive number to be known,γmax(kζ) Is the maximum sign.
Other steps and parameters are the same as those in one of the first to ninth embodiments.
Theoretical basis
Problem description and design goals
The motion of the benthonic AUV needs to be processed by considering model parameter uncertainty and input saturation factors. First, the AUV mathematical model given by equations (1), (2) can be converted into the following form:
Figure BDA0003056457250000071
Figure BDA0003056457250000072
model uncertainty and external interference analysis
(1) Model uncertainty analysis
The parameters of the benthic AUV model are difficult to accurately measure, and the two main reasons are as follows:
it is not realistic for most underwater vehicles to measure their hydrodynamic coefficients experimentally, but the results must be inaccurate if the hydrodynamic coefficients are derived by only theoretical analysis. For the analysis object, the structure of the analysis object is different from the appearance of the traditional fish type AUV, the AUV is in a semi-open frame structure and is a strong nonlinear system, and the hydrodynamic coefficient of the analysis object is more difficult to accurately measure;
in a complex and variable marine environment, various factors such as temperature, salinity and depth also change correspondingly with the change of the water area and the depth, which inevitably causes perturbation of hydrodynamic parameters of the AUV;
these factors cause uncertainty of the parameters of the benthic AUV model, which requires a designed control system to have strong robustness, which is one of the difficulties in control algorithm design.
The uncertainty of the AUV motion mathematical model is represented in the uncertainty of inertia, the uncertainty of hydrodynamic coefficients and the uncertainty of gravity and buoyancy, namely the values of M, C (upsilon), D (upsilon) and g (eta) matrixes are not completely accurate. Model uncertainty is typically expressed in the form:
Figure BDA0003056457250000073
in the formula, C (ν), D (ν), and g (η) represent actual values of model parameters.
Figure BDA0003056457250000074
The nominal values (estimated values) of the model parameters are represented.
Figure BDA0003056457250000075
Perturbation values representing model parameters.
Suppose 1[1]: uncertainty of model parameter expressed by equation (16)
Figure BDA0003056457250000076
And
Figure BDA0003056457250000077
boundaries exist but are unknown, and according to the boundedness of perturbation of model parameters, the following results are obtained:
Figure BDA0003056457250000078
in the formula, DPRepresenting an upper interference bound for the perturbation of the model parameters.
(2) External interference analysis
External interference tau considered in patent track tracking algorithm of the inventiondThere is an unknown boundary. Thus, it is possible to provide，RM-1τdThere are also unknown boundaries, i.e. satisfying:
||RM-1τd||≤D (18)
wherein D is an unknown positive number.
For external interference and model uncertainty in AUV trajectory tracking control, the adaptive method is adopted in this chapter to perform boundary approximation on the AUV trajectory tracking control. The adaptive control has the advantages that adaptive parameters can be updated on line, the stability and the accuracy of control precision can be ensured after the controller reaches convergence, and the defect that the stability is difficult to maintain at the initial stage of the operation of the controller is overcome. Adaptive control methods can generally be divided into two categories — direct adaptive control and indirect adaptive control. The working principle of direct adaptive control is that the tracking error tends to zero by the controller through parameter online adjustment, and the input of the controller is derived through the Lyapunov stability theory. The working principle of indirect self-adaptive control is to estimate model parameters on line[2]And estimates the parameter values, and then brings the latest estimated values of the parameters into the controller gain and updates. In consideration of strong nonlinearity and interference characteristics of the AUV model, an indirect self-adaptive method is adopted in the chapter to solve the influence of model parameter uncertainty and external interference.
Actuator input saturation characteristic analysis
The actuator structure (propeller) of the AUV is physically constrained in actual operation, i.e. the active control force (torque) applied to the system is always bounded. When the output of the actuator fails to reach the control input calculated by the controller, an imbalance phenomenon occurs between the command output and the actual output of the actuator, which is called actuator saturation.
In order to avoid the influence of hysteresis, flutter, control performance reduction and even instability caused by the saturation of the input of the controller on the system, the factor needs to be taken into account in the design of the controller, and an appropriate control strategy is designed to eliminate the adverse effect caused by the saturation error on the system performance. Control input term τ ═ τ1,τ2,τ3,τ4,τ5,τ6]TThe following conditions are satisfied:
Figure BDA0003056457250000081
in accordance with the above definition, the control input may be represented in the form of:
τ＝τc+Δτ (19)
in the formula, Δ τ is the difference between the actual control input of the AUV and the control law obtained by the control algorithm.
Suppose 2[3]Δ τ is bounded, i.e., satisfies
Figure BDA0003056457250000082
Thus, MR-1τΔIs also bounded, i.e. satisfies | | MR-1τΔAnd | is less than delta, and delta is a known positive number.
Basic theory and definition
Introduction 1[4]Suppose xi(i ═ 1.., n) and b (0 < b < 1), the following inequality holds:
(|x1|+...+|xn|)b≤|x1|b+...+|xb|b
the controller design goal of this chapter is: the design method has the advantages that the reasonable trajectory tracking controller is designed under the conditions of considering external time-varying interference, model parameter uncertainty and input saturation, the controller design is more in line with the benthonic AUV characteristic and the working environment, the problem of three-dimensional curve trajectory tracking of the benthonic AUV is solved, the controller design can achieve limited time convergence of control variables, and the controller has high control precision and good robustness and stability.
Controller design
In order to achieve the patent control target of the invention, the section firstly processes the AUV model to obtain an AUV three-dimensional trajectory tracking error model, and then designs a trajectory tracking control law based on a nonsingular fast terminal sliding mode control method. For external interference and model parameter uncertainty of the AUV, performing upper bound approximation on the AUV by adopting a self-adaptive control method so as to reduce the influence on a control system; meanwhile, the influence of AUV input saturation on a control system is solved by adopting the ADS, and a smooth function is introduced into the ADS to enable the input of the controller to be more stable and gentle. The designed controller proves the limited time convergence of the control system through the Lyapunov stability theory.
In the design process of the controller, an AUV (autonomous Underwater vehicle) trajectory tracking error model is established firstly, and then a control law is designed based on the AUV error model and a nonsingular fast terminal sliding mode function. The control block diagram of the patent design controller of the invention is shown in FIG. 19:
trajectory tracking error model
And substituting the model parameter uncertainty model (16) into the AUV motion mathematical model to obtain:
Figure BDA0003056457250000091
Figure BDA0003056457250000092
in the formula (I), the compound is shown in the specification,
Figure BDA0003056457250000093
defining pose error model variables as:
ηe＝η-ηd (21)
in the formula, eta represents the practical pose of AUV,
Figure BDA0003056457250000094
representing the desired pose in tracking control.
According to equations (20), (21), an AUV error model of the form:
Figure BDA0003056457250000101
Figure BDA0003056457250000102
in the formula (I), the compound is shown in the specification,
Figure BDA0003056457250000103
and representing a comprehensive interference item superimposed by external time-varying interference and perturbation of model parameters in the error model. As can be seen from the assumptions 1 and 2, the combined interference F in the equation (22) also has a boundary condition, and the boundary condition is unknown.
Suppose 3[5]: when dealing with a control problem with external interference and uncertainty of model parameters, the external interference and uncertainty of model parameters may be generally superimposed to be handled as a synthetic interference, which is assumed to be denoted by Δ d (t), and when a boundary exists in Δ d (t), the synthetic interference satisfies the following boundary conditions:
Figure BDA0003056457250000104
in the formula, gammaiIs an unknown positive number and x is a control state variable.
In equation (23), the order of r is determined by the complexity of the controller and the overall interference characteristics. When a traditional sliding mode controller is designed, if r is 0, the comprehensive interference is a constant value; if r is 1, the integrated interference is time-varying. For the AUV trajectory control problem, considering the nature of its combined disturbances, the value of r will typically be set to 2[6]。
The unknown boundary of the synthetic interference term F in equation (22) can be expressed in the form of
Figure BDA0003056457250000105
In the formula, gammai(i ═ 1,2,3) is an unknown normal number.
Figure BDA0003056457250000106
Is gammai1.., 3. Defining a deviation variable of the form:
Figure BDA0003056457250000107
in the following subsections, reasonable adaptation laws were designed
Figure BDA0003056457250000108
The method can realize accurate estimation of the comprehensive interference item boundary, and the self-adaptive control method based on the boundary condition assumption of the formula (24) does not need to know the upper bound of the external interference, thereby relaxing the limitation on the prior knowledge of the interference.
Control law design
The invention adopts the following nonsingular fast terminal sliding mode control switching function:
Figure BDA0003056457250000109
in the formula, s is a sliding mode variable and belongs to Rn×1。
Figure BDA00030564572500001010
Is a positive integer, l and p are positive odd numbers, and satisfy 0 < l/p < 1,
Figure BDA00030564572500001011
α1、α2in order for the diagonal matrix to be known,
Figure BDA00030564572500001012
defining pose error model variables as:
ηe＝η-ηd (27)
in the formula, eta represents the practical pose of AUV,
Figure BDA0003056457250000111
representing the desired pose in tracking control.
Bringing equation (27) into a sliding mode function of the form of equation (26) yields the following form:
Figure BDA0003056457250000112
the sliding mode function is derived to obtain the following form
Figure BDA0003056457250000113
The control law is designed based on the AUV error model of the formula (22) and the sliding mode function of the formula (28) as follows:
τ＝τc+Δτ (30a)
τc＝τ0+τ1+τ2 (30b)
Figure BDA0003056457250000114
Figure 2
Figure BDA0003056457250000116
Figure BDA0003056457250000117
in the formula, k1Is a known normal number; k is a radical ofζ＝diag[kζ1kζ2kζ3kζ4kζ5kζ6],kζi(i 1.., 6) is a known constant; k is a radical ofλ＝diag[kλ1kλ2kλ3kλ4kλ5kλ6],kζi(i 1.., 6) is a known positive number; gamma raymin(kλ)＝min{kλ1,kλ2,kλ3,kλ4,kλ5,kλ6}; zeta isAn auxiliary variable.
In the equations (30a, 30b, 30c, 30d, 30e), τ is the actual controller input, τ iscThe control law is the expected control law obtained after the operation of the controller. At taucIn, tau1The method does not consider interference, model uncertainty and conventional input items under input saturation, and the items can ensure that the input amplitude of a controller is larger when the AUV pose error is larger, so that the AUV pose error can be ensured to be converged in a rapid and stable trend; tau is1In order to process the self-adaptive item of the comprehensive interference, the self-adaptive part in the item can be updated in real time according to pose and speed information, so that the online approximation of the upper interference bound is achieved, and the controller is ensured to have better robustness; tau is2To handle the adaptive term of input saturation, the term can input the influence of saturation on the stability of the controller and make the input of the controller more stable and smooth.
Adaptive law design
In order to process the comprehensive interference item, the self-adaptive part designs a self-adaptive law with the following form:
Figure BDA0003056457250000121
Figure BDA0003056457250000122
Figure BDA0003056457250000123
in the formula, a0，a1，a2Is a known positive number.
ADS auxiliary variable design
In the literature[7]In the method, an ADS control method is adopted to solve the influence of input saturation on a control system, and the control performance of the method is verified through a simulation test. Literature reference[8]The proposed improved ADS control strategy solves the jitter phenomenon caused by the discontinuity of auxiliary variables in the conventional ADS control method,and a good simulation effect is obtained. The ADS control method has good effect on solving input saturation, but most of controllers designed based on the ADS control method are in fixed time convergence or consistent asymptotic convergence[9]-[11]Finite time convergence cannot be achieved. The convergence performance is an important performance index for normal work of the control system, the closed-loop control system with limited time convergence can not only realize the limited time convergence, but also has better robustness due to the fractional order characteristic of the limited time controller. Based on the above analysis, this section designs a new ADS control method to ensure the finite time convergence of the whole control system.
In (30a, 30b, 30c, 30d, 30e), the auxiliary variable ζ is constructed as follows:
Figure BDA0003056457250000124
in the formula, μ is a known positive number. h (s, τ)Δζ) is a smooth function of the form
Figure BDA0003056457250000125
In the formula, deltawIs a known positive number and satisfies δw＞max{kζ1,kζ2,kζ3,kζ4,kζ5,kζ6}，εζIs a known positive number.
Demonstration of stability
The stability of the control system is demonstrated using a lyapunov function of the form:
Figure BDA0003056457250000131
taking the derivative with respect to time for (34):
Figure BDA0003056457250000132
in the formula (I), the compound is shown in the specification,
Figure BDA0003056457250000133
(36) carry in (35) to get:
Figure BDA0003056457250000134
bringing formula (29) into (37) yields:
Figure BDA0003056457250000135
bringing (30a, 30b, 30c, 30d, 30e) into (38) results in:
Figure BDA0003056457250000136
to prove the conciseness and clarity of the process, the upper formula is classified into γ1，Υ1Two parts are used for derivation proof.
Figure BDA0003056457250000137
(1) Pair upsilon1The derivation proves that:
Figure BDA0003056457250000138
bringing formula (31) into (40a) yields:
Figure BDA0003056457250000141
bringing (25) into (40c)
Figure BDA0003056457250000151
The following equation is defined:
Figure BDA0003056457250000152
Figure BDA0003056457250000153
Figure BDA0003056457250000154
Figure BDA0003056457250000155
bringing formula (40e) into (40d) yields:
Figure BDA0003056457250000156
(2) pair upsilon2The derivation proves that:
Figure BDA0003056457250000157
bringing (32) into (41a) to:
Figure BDA0003056457250000158
Figure BDA0003056457250000161
bringing (33) into (41b) results in:
Figure BDA0003056457250000162
the following equation is defined:
Figure BDA0003056457250000163
bringing (41d) into (41c) to obtain:
Figure BDA0003056457250000164
bringing (40f), (41e) into (39) to obtain:
Figure BDA0003056457250000165
introduction 2[12]If the differentiable function f (t) has a finite boundary at t → + ∞ and
Figure BDA0003056457250000166
to maintain consistent continuity, then when t → + ∞,
Figure BDA0003056457250000171
according to lemma 2, the nonlinear sliding mode variables and error variables and the adaptive error are asymptotically stable. On the basis of the above, the finite time convergence of the system can be proved, and the proving process is divided into the following two cases.
(1) The first condition is as follows:
Figure BDA0003056457250000172
and | si|≠0(i＝1,2,3,4,5,6)
According to the lemma 1, the formula (41f) can be deformed into the following form:
Figure BDA0003056457250000173
in the formula, ρv＝min{ρs,ρ0,ρ1,ρ2,ρζ}。
According to the introduction 2, the controller of the present patent design is able to achieve convergence in a limited time. A finite convergence time of
Figure BDA0003056457250000174
(2) Case two:
Figure BDA0003056457250000175
will be provided with
Figure BDA0003056457250000176
And substitution (22) of the control law (32) to obtain
Figure BDA0003056457250000177
This means that
Figure BDA0003056457250000178
The system is not an attractor during its arrival, and the system does not remain there
Figure BDA0003056457250000179
According to the two conditions, under the condition of considering external interference, model parameter perturbation and input saturation, the three-dimensional trajectory tracking error can be converged to zero in a limited time.
In conclusion, the controller designed by the invention can ensure the benthonic AUV curve trajectory tracking control task under the condition of considering external interference, model parameter uncertainty and input saturation, ensure that the benthonic AUV autonomously completes the underwater navigation task, and lay the foundation for the successful and accurate bottom-setting of the benthonic AUV.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
by simulation of reasonable designExperiments are conducted to verify the performance of the curve trajectory tracking controller under the conditions of considering external time-varying interference, perturbation of model parameters and input saturation. The controller designed by the invention is marked as ADS-ANFTMC controller. The test adopts AUV six-degree-of-freedom model, and the model parameters are shown in table 1. First of all, it is disclosed in the literature[13]The nonsingular fast fuzzy terminal sliding mode controller based on the disturbance observer is used for test comparison, and external disturbance, model parameter uncertainty and input saturation are considered by the controller at the same time. The proposed ADS-ANFTMC controller is then compared to the ANFTMC controller without regard for input saturation.
According to the invention, simulation parameters in the ADS-ANFTMC controller are set as follows:
TABLE 1 ADS-ANFTMC controller parameter settings
Figure BDA00030564572500001710
Figure BDA0003056457250000181
In the simulation test, the initial value of the AUV pose η is set to be [ [9,7,21,0.5,0.5,0.5 ] η (0) ]]T(ii) a Initial value setting of variables in the adaptation law
Figure BDA0003056457250000182
The initial value of the ADS auxiliary variable is set to ζ (0) ═ 0.1,0.1,0.1,0.1,0.1,0.1]T. External time-varying interference is set as
τd1＝4+3sin(0.3t)N
τd2＝5+3sin(0.3t)N
τd3＝2+4sin(0.1t)N
τd4＝0Nm
τd5＝4+3sin(0.3t)Nm
τd6＝4+sin(0.3t)Nm (42)
The expected trajectory selected by the simulation test is
Figure BDA0003056457250000183
Is arranged as
Figure BDA0003056457250000184
In order to reflect the parameter uncertainty in the benthic AUV mathematical model, the proportion uncertainty [14] is adopted in the simulation to reduce C (v), D (v) and g (eta) in the AUV dynamic model by 20%, namely the values of the model parameters are considered to have a perturbation range of 20%, the maximum thrust output of the longitudinal thruster, the maximum thrust output of the transverse thruster and the maximum thrust output of the vertical thruster are all set to be 150N, and the maximum yaw moment and the maximum pitch moment are set to be 100 Nm/s.
Test one: comparing the patent controller (ADS-ANFTMC) with the Nonsingular Fast Fuzzy Terminal Sliding Mode Controller (NFFTSMC), simulating and comparing the pose convergence response curve and the speed response curve of the two controllers, and performing independent analysis on the sliding mode variable response curve of the controller designed by the invention, wherein the test results are shown in FIGS. 2 to 13.
As can be seen from fig. 2, both controllers achieve the purpose of trajectory tracking control with good effect, and both controllers can reach a stable state within a limited time after the initial state, but the convergence speed of the ADS-ANFTMC controller is faster and the time to reach the stable state is shorter.
Fig. 3 to 7 are three-dimensional trajectory tracking pose error response curves. In the error response curves of fig. 3 and fig. 4, the tracking error of the ADS-ANFTMC controller converges to zero, and a smaller oscillation occurs because the controller approaches the synthetic interference through the adaptive law, and the ADS-ANFTMC controller reacts more sensitively than the NFFTSMC controller and is more stable after convergence; in the vertical tracking error response curve shown in fig. 5, no overshoot occurs in the ADS-ANFTMC controller, a small overshoot occurs in the NFFTSMC controller, and no jitter occurs after the error of the ADS-ANFTMC controller converges to zero; in the angle tracking error response curves shown in fig. 6 and fig. 7, the ADS-ANFTMC controller converges more rapidly, and neither overshoot occurs, and the NFFTSMC controller overshoots and has less jitter during convergence. From the above analysis, the ADS-ANFTMC controller has a faster convergence speed than the NFFTSMC controller, and has smoother convergence, shorter time to reach a stable state, less oscillation in convergence, and better robustness.
Fig. 8-12 are AUV speed response curves. As can be seen from fig. 8 to fig. 12, the speeds of both the NFFTSMC controller and the ADS-ANFTMC controller can converge from the initial position to the desired speed, but the convergence of the ADS-ANFTMC controller is quicker, the time for reaching the steady state is shorter, both controllers will have the jitter phenomenon after the speed reaches the steady state, but the amplitude of the jitter of the ADS-ANFTMC controller is smaller, and the jitter time is shorter, which indicates that the ADS-ANFTMC controller has better control response and better robustness.
Fig. 13 is a response curve of sliding mode variable s in the controller of the present invention. From the joint analysis of the pose change curves of the ADS-ANFTMC controller in FIG. 13 and FIGS. 3 to 12, s in FIG. 13i(1,2,3,5 and 6) when convergence is not reached, the controller drives the control system to approach the sliding mode switching surface from the initial position, and the pose errors shown in the steps of fig. 3 to fig. 12 converge quickly at the stage; when s isiAfter converging to zero, the controller drives the controlled variable to converge towards the origin, at which time the convergence of the pose errors of fig. 3-12 becomes relatively flat. The pose error of the patent controller reaches convergence within a limited time, and can keep a stable state under the conditions of interference and perturbation of model parameters, so that the superior performance of the controller is reflected.
And (2) test II: in order to verify the solving effect of the ADS control method adopted by the invention on input saturation, the controller disclosed by the invention is compared with an ANFTMC controller which does not consider input saturation in a simulation mode. The two controllers are marked as an ADS-ANFTMC controller and an ANFTMC controller, the same external interference and the same perturbation of model parameters are considered in the simulation of the two controllers, and the test results are shown in fig. 14 to 18.
Fig. 14-18 are AUV actuator output response curves. As can be seen from fig. 14 to 16, in the starting stage, the actuator output response amplitude of the ADS-ANFTMC controller is significantly reduced and changes more smoothly compared to the ANFTMC controller, after the actuator output is stable, intermittent jitter occurs in both the ANFTMC controller and the ADS-ANFTMC controller, but the jitter amplitude of the ADS-ANFTMC controller is smaller and the transition is more gradual; as can be seen from fig. 17 and 18, in the outputs of the actuators of the yaw moment and the pitch moment, the amplitudes of the two controllers are basically the same in the initial stage, but after the outputs of the actuators are stable, the ANFTMC controller shakes more frequently, and the shaking amplitude is larger than that of the ADS-ANFTMC controller.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Reference to the literature
[1]W.M.Bessa,M.S.Dutra,and E.Kreuzer.An adaptive fuzzy sliding mode controller for remotely operated underwater vehicles[J].Robtics&Autonomous Systems.2010,58(1): 16-26.
[2]Shinskey F G,Schnelle P D,Liptk B G.Nonlinear and Adaptive Control[J].Process Control(ThirdEdition).1995,5(2):77-82.
[3]Raúl Rascón,Moreno-Valenzuela J.Output feedback controller for trajectory tracking of robot manipulators without velocity measurements nor observers[J].IET Control Theory& Applications.2020,14(14):1819-1827.
[4]Hardy G H,Littlewood J E,Polya G.Inequalities[M].Cambridge:Cambridge University Press,1952.
[5]Mondal S,Mahanta C.Adaptive second order terminal sliding mode controller for robotic manipulators[J].Journal ofthe Franklin Institute.2014,351(4):2356–2377.
[6]Patre B M,Londhe P S,Waghmare L M,et al.Disturbance estimator based non-singular fast fuzzy terminal sliding mode control of an autonomous underwater vehicle[J].Ocean Engineering.2018,159(JUL.1):372-387.
[7]Zheng,L.Sun,Adaptive sliding mode trajectory tracking control ofrobotic airships with parametric uncertaintyandwinddisturbance[J].J.Franklin Inst.2018,355(1):106-122.
[8]Zhu G,Du J.Robust adaptive neural practical fixed-time tracking control for uncertain Euler-Lagrange systems underinput saturations[J].Neurocomputing,2020,25(1):221-235.
[9]S.S.Ge,C.C.Hang,L.C.Woon,Adaptive neural network control ofrobotmanipulators in task space[J].IEEE Trans.Ind.Electron.1997,44(6):746-752.
[10]Zheng Z,M.Feroskhan.Path following ofa surface vessel with prescribedperformance in the presence of input saturation and external disturbances[J].IEEE/ASME Trans. Mechatron.2017,22(6):2564-2575.
[11]Zhang M,Liu,X,Yin,B,et al.Adaptive terminal sliding mode basedthruster fault tolerant control for underwater vehicle in time-varying ocean currents[J].J.Franklin Inst.,2015, 352(11):4935–4961.
[12]J.J.E.Slotine,W.Li.Applied Nonlinear Control,PrenticeHall[M],NewJersey,1991.
[13]Patre B M,Londhe P S,Waghmare L M,et al.Disturbance estimator based non-singular fast fuzzy terminal sliding mode control of an autonomous underwater vehicle[J].Ocean Engineering.2018,159(JUL.1):372-387.
[14]Qiao L,Zhang W.Adaptive non-singular integral terminal sliding mode tracking control for autonomous underwater vehicles[J].IET Control Theory&Applications.2017, 11(8):1293-1306。

Claims (10)

1. The benthonic AUV self-adaptive terminal sliding mode trajectory tracking control method based on the auxiliary dynamic system is characterized by comprising the following steps: the method comprises the following specific processes:
step one, establishing an AUV kinematic equation;
secondly, defining a pose error model variable based on the AUV kinematic equation established in the first step;
step three, establishing an AUV error model based on the AUV kinematic equation established in the step one and the pose error model variable defined in the step two;
and step four, designing the AUV error model established in the control law control step three.
2. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 1, characterized in that: establishing an AUV kinematic equation in the first step; the specific process is as follows:
the AUV kinematic equation expression is:
Figure FDA0003056457240000011
in the formula, R (eta) is a transformation matrix between a carrier coordinate system and an inertia coordinate system, eta represents the AUV actual pose,
Figure FDA0003056457240000012
is the first derivative of η, and upsilon is the velocity and angular velocity of AUV;
the six-degree-of-freedom kinetic equation of the AUV under the carrier coordinate system is in the form as follows:
Mυ+C(υ)υ+D(υ)υ+g(η)＝τ+τd (2)
wherein M represents an inertia matrix; c (upsilon) represents a Coriolis centripetal force matrix; d (upsilon) represents a fluid damping moment; g (η) represents a restoring force vector generated by gravity and buoyancy; τ represents a force or moment vector generated by the control law; tau isdRepresenting the external disturbance force vector.
3. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 2, characterized in that: in the second step, a pose error model variable is defined based on the AUV kinematic equation established in the first step; the expression is as follows:
ηe＝η-ηd (3)
in the formula, eta represents AUV actual pose, etadRepresenting a desired pose in tracking control; etaeAnd (4) representing AUV pose errors.
4. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 3, characterized in that: in the third step, an AUV error model is established based on the AUV kinematic equation established in the first step and the pose error model variable defined in the second step; the specific process is as follows:
according to the formulas (1), (2) and (3), an AUV error model with the following form is established:
Figure FDA0003056457240000021
in the formula, F represents a comprehensive interference item superimposed by external time-varying interference and perturbation of model parameters in the AUV error model;
Figure FDA0003056457240000022
expression ηeThe first derivative of (a) is,
Figure FDA0003056457240000023
the first derivative of η is represented as,
Figure FDA0003056457240000024
expression ηdThe first derivative of (a) is,
Figure FDA0003056457240000025
expression ηeThe second derivative of (a) is,
Figure FDA0003056457240000026
the second derivative of η is represented as,
Figure FDA0003056457240000027
expression ηdThe second derivative of (a) is,
Figure FDA0003056457240000028
the first derivative of R is indicated and τ is the control law.
5. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 4, characterized in that: designing an AUV error model established in the control law control step I in the step four; the specific process is as follows:
the nonsingular fast terminal sliding mode control switching function is as follows:
Figure FDA0003056457240000029
in the formula, s is a sliding mode variable;
Figure FDA00030564572400000210
is a positive integer, l and p are positive odd numbers, and satisfy 0 < l/p < 1,
Figure FDA00030564572400000211
α1、α2known diagonal matrix;
the control law is designed based on the AUV error model of the formula (4) and the sliding mode control switching function of the formula (5) as follows:
τ＝τc+Δτ (6)
in the formula, tau represents a force or moment vector generated by a control law; tau iscThe expected control law is obtained after the controller is operated; and delta tau is the difference between the actual AUV control input and the control law obtained by the control algorithm.
6. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 5, characterized in that: expected control law tau obtained by the controller after operationcExpression (2)Comprises the following steps:
τc＝τ0+τ1+τ2 (7)
Figure FDA00030564572400000212
Figure 1
Figure FDA0003056457240000031
in the formula, τ0To disregard the control law under various disturbances, τ1For handling the adaptation term of the integrated interference, tau2To handle the adaptive term of input saturation, Θ is the intermediate symbolic variable, k1Is a known normal number; k is a radical ofζIs a known constant, kζ＝diag[kζ1 kζ2 kζ3kζ4 kζ5 kζ6]，kζiIs a known constant, i ═ 1.., 6; k is a radical ofλIs a known constant, kλ＝diag[kλ1 kλ2 kλ3 kλ4 kλ5kλ6]，kλiIs a known positive number, i ═ 1.., 6; gamma raymin(kλ) Is the sign of the minimum value, γmin(kλ)＝min{kλ1,kλ2,kλ3,kλ4,kλ5,kλ6}; ζ is the auxiliary variable, T is the transpose, and λ is a known constant.
7. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 6, characterized in that: the expression of the intermediate symbolic variable Θ is:
Figure FDA0003056457240000032
in the formula (I), the compound is shown in the specification,
Figure FDA0003056457240000033
are all intermediate symbol variables.
8. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 7, characterized in that: the intermediate symbol variable
Figure FDA0003056457240000034
The expression of (a) is:
Figure FDA0003056457240000035
in the formula, a0，a1，a2In order for the positive number to be known,
Figure FDA0003056457240000036
are respectively as
Figure FDA0003056457240000037
The first derivative of (a); l and p are positive odd numbers and satisfy 0 < l/p < 1,
Figure FDA0003056457240000038
α2known diagonal matrix; s is a sliding mode variable.
9. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 8, characterized in that: the auxiliary variable ζ is constructed as follows:
Figure FDA0003056457240000039
where μ is a known positive number, h (s, Δ τ, ζ) is a smoothing function, and ζ is an auxiliary variable; λ is a known constant; and delta tau is the difference between the actual AUV control input and the control law obtained by the control algorithm.
10. The auxiliary dynamic system-based bentable AUV adaptive terminal sliding mode trajectory tracking control method according to claim 9, characterized in that: the smoothing function h (s, Δ τ, ζ) is of the form
Figure FDA0003056457240000041
In the formula, deltawIs a known positive number and satisfies δw＞max{kζ1,kζ2,kζ3,kζ4,kζ5,kζ6}，εζIs a known positive number, gammamax(kζ) Is the maximum sign.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107247411A (en) * 2017-06-15 2017-10-13 大连海事大学 Non-singular terminal sliding formwork Track In Track control method based on disturbance observer
WO2018023201A1 (en) * 2016-08-03 2018-02-08 孟强 Adaptive terminal sliding mode control method
CN109283941A (en) * 2018-11-15 2019-01-29 哈尔滨工程大学 Default capabilities seabed flight node-locus tracking and controlling method based on disturbance observer
CN110262255A (en) * 2019-07-16 2019-09-20 东南大学 A kind of mechanical arm Trajectory Tracking Control method based on adaptive terminal sliding mode controller
CN111650948A (en) * 2020-06-10 2020-09-11 哈尔滨工程大学 Quick tracking control method for horizontal plane track of benthonic AUV
AU2021100238A4 (en) * 2021-01-14 2021-04-15 Girish Vithalrao Lakhekar Adaptive spatial trajectory tracking control for autonomous underwater vehicle

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018023201A1 (en) * 2016-08-03 2018-02-08 孟强 Adaptive terminal sliding mode control method
CN107247411A (en) * 2017-06-15 2017-10-13 大连海事大学 Non-singular terminal sliding formwork Track In Track control method based on disturbance observer
CN109283941A (en) * 2018-11-15 2019-01-29 哈尔滨工程大学 Default capabilities seabed flight node-locus tracking and controlling method based on disturbance observer
CN110262255A (en) * 2019-07-16 2019-09-20 东南大学 A kind of mechanical arm Trajectory Tracking Control method based on adaptive terminal sliding mode controller
CN111650948A (en) * 2020-06-10 2020-09-11 哈尔滨工程大学 Quick tracking control method for horizontal plane track of benthonic AUV
AU2021100238A4 (en) * 2021-01-14 2021-04-15 Girish Vithalrao Lakhekar Adaptive spatial trajectory tracking control for autonomous underwater vehicle

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
LEI QIAO，等: "Trajectory Tracking Control of AUVs via Adaptive Fast Nonsingular Integral Terminal Sliding Mode Control", 《IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS》 *
李明等: "基于非奇异终端滑模的欠驱动UUV航迹跟踪控制", 《应用科技》 *
杨超,等: "基于RBF神经网络的作业型AUV自适应终端滑模控制方法", 《机器人》 *

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