CN111781938A - Under-actuated underwater vehicle and stabilizing method and device thereof - Google Patents

Under-actuated underwater vehicle and stabilizing method and device thereof Download PDF

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CN111781938A
CN111781938A CN202010580862.1A CN202010580862A CN111781938A CN 111781938 A CN111781938 A CN 111781938A CN 202010580862 A CN202010580862 A CN 202010580862A CN 111781938 A CN111781938 A CN 111781938A
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target
data
control data
threshold
control
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CN111781938B (en
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王锐
司昌龙
马慧
郝程鹏
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Institute of Acoustics CAS
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Institute of Acoustics CAS
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/04—Control of altitude or depth
    • G05D1/06—Rate of change of altitude or depth
    • G05D1/0692—Rate of change of altitude or depth specially adapted for under-water vehicles

Abstract

The application relates to an under-actuated underwater vehicle and a stabilizing method and a stabilizing device thereof, wherein the method comprises the following steps: acquiring first target navigation data of the aircraft, wherein the first target navigation data comprises ideal position coordinates and ideal course angles; determining target control data of the aircraft at the next moment according to the first target navigation data, wherein the target control data comprise target control thrust and target control torque; and determining that an updating condition is met according to the target control data and first control data of the aircraft at the current moment, and updating the first control data, wherein the first control data comprises first control thrust and first control torque. The method realizes stabilization of the under-actuated underwater vehicle.

Description

Under-actuated underwater vehicle and stabilizing method and device thereof
Technical Field
The application relates to the technical field of control, in particular to an under-actuated underwater vehicle and a stabilizing method and device thereof.
Background
The under-actuated underwater vehicle has no lateral control force, and the system has the under-actuated characteristic, so that the vehicle must meet the Brockett condition when being stabilized, namely, the under-actuated underwater vehicle can be stabilized only by designing a time-varying or unsmooth control law. In the stabilizing process of the underwater vehicle, the requirement on maneuverability is not high, but the requirements on control precision and resource saving are high. At present, the traditional continuous state feedback can not realize the stabilization control target.
Disclosure of Invention
The application aims to provide an under-actuated underwater vehicle and a stabilizing method and device thereof, and solves the problem that a stabilizing control target cannot be realized at present.
To achieve the above object, a first aspect of the present application provides a stabilizing method for an under-actuated underwater vehicle, the method comprising:
acquiring first target navigation data of the aircraft, wherein the first target navigation data comprises ideal position coordinates and ideal course angles;
determining target control data of the aircraft at the next moment according to the first target navigation data, wherein the target control data comprise target control thrust and target control torque;
and determining that an updating condition is met according to the target control data and first control data of the aircraft at the current moment, and updating the first control data, wherein the first control data comprises first control thrust and first control torque.
Optionally or preferably, said determining target control data for said aircraft at a next time instant from said first target voyage data comprises:
determining navigation error data of the aircraft at the current moment according to the first target navigation data, wherein the navigation error data comprises: a position error and a course error;
determining second target navigation data of the aircraft at the next moment according to the navigation error data, wherein the second target navigation data comprises an ideal linear velocity and an ideal angular velocity;
and determining the target control data according to the second target navigation data.
Optionally or preferably, the specific formula for determining the second target voyage data of the aircraft at the next time according to the voyage error data is as follows:
Figure BDA0002553126710000021
in the formula udIs an ideal linear velocity, rdIs the ideal angular velocity, k1、k2、ξ、
Figure BDA0002553126710000022
Being constant and/or variable, z1X-axis coordinate value phi (V) of the navigator in the body coordinate system1) To relate to V1H (t) is a smooth function with respect to t,
Figure BDA0002553126710000023
is the derivative of h (t), t is the current moment, v is the lateral linear velocity of the aircraft under the body coordinate system,
Figure BDA0002553126710000024
r is the yaw rate and the yaw rate,
Figure BDA0002553126710000025
alternatively or preferably, ξ ═ z3+Φ(V1)h(t)，
Figure BDA0002553126710000026
Wherein z is3C is the ratio of the first system inertia to the second system inertia.
Optionally or preferably, the specific formula for determining the target control data according to the second target navigation data is as follows:
Figure BDA0002553126710000027
wherein i is 1 or 2,
Figure RE-GDA0002645095030000029
the thrust force is controlled for the purpose of the target,
Figure RE-GDA00026450950300000210
in order to control the torque for the target,i∈(0,1)，αiis a variable or constant, e1As linear velocity tracking error, e2For tracking error of angular velocity,/i w＞0，p3xi＝p3As aircraft quality parameter, p3xi＝p6The moment of inertia of the aircraft is taken as a parameter, and t is the current moment;i(t) is a function of t, satisfiesi(t) > 0, and ρi> 0, so that
Figure RE-GDA0002645095030000028
CiIs the trigger threshold.
Optionally or preferably, the determining that an update condition is satisfied and updating the first control data based on the target control data and the first control data of the aircraft at the first time comprises:
selecting a trigger threshold based on the magnitude relation between the target control data and a switching threshold, wherein the trigger threshold is a first threshold or a second threshold, the first threshold is a fixed threshold, and the second threshold is a relative threshold;
obtaining a difference value between the target control data and the first control data to obtain a control error;
and determining that the control error is higher than the trigger threshold, and updating the first control data into the target control data.
Optionally or preferably, the selecting a trigger threshold based on a magnitude relationship between the target control data and a handover threshold includes:
if the target control data is greater than or equal to the switching threshold, determining that the triggering threshold is the first threshold;
and if the target control data is smaller than the switching threshold, determining that the triggering threshold is the second threshold.
Optionally or preferably, the specific formula of the second threshold is:
Ei＝i|τi(t)|+Di
in the formula, EiIs the second threshold value, and is,i∈(0,1)，τ1for the first control of thrust, τ2Is a first control torque, DiBe a constant or variable.
A second aspect of the application provides a stabilizing device for an under-actuated underwater vehicle, the device comprising:
the system comprises an acquisition module, a navigation module and a navigation module, wherein the acquisition module is used for acquiring first target navigation data of the aircraft, and the first target navigation data comprises ideal position coordinates and ideal course angles;
the determining module is used for determining target control data of the aircraft at the next moment according to the first target navigation data, wherein the target control data comprise target control thrust and target control torque;
and the updating module is used for determining that an updating condition is met according to the target control data and first control data of the aircraft at the current moment, and updating the first control data, wherein the first control data comprises first control thrust and first control torque.
A third aspect of the application provides an under-actuated underwater vehicle comprising a ballast device of the under-actuated underwater vehicle as described in the second aspect.
Compared with the prior art, the under-actuated underwater vehicle and the stabilizing method and device thereof in the embodiment of the application determine target control data of the vehicle at the next moment based on the target navigation data of the vehicle; and then, determining that the updating condition is met based on the target control data and the control data of the aircraft at the current moment, and updating the control data of the aircraft at the current moment, so that the driving parameters of the aircraft, such as linear speed, angular speed and the like, can accurately track the ideal driving parameters of the aircraft, and the stabilization of the whole system is realized.
Drawings
Fig. 1 is a schematic flow chart of a stabilizing method of an under-actuated underwater vehicle according to an embodiment of the present application;
fig. 2 is a schematic diagram illustrating a step of determining target control data of an under-actuated underwater vehicle at a next time in a stabilizing method of the under-actuated underwater vehicle according to an embodiment of the present application;
fig. 3 is a schematic diagram illustrating a step of updating first control data in a stabilizing method of an under-actuated underwater vehicle according to an embodiment of the present application;
fig. 4 is a schematic diagram of coordinate track change of an under-actuated underwater vehicle simulated by using a stabilizing method of the under-actuated underwater vehicle provided in the embodiment of the present application;
fig. 5 is a schematic view of tracking error of position coordinates and course angle of an under-actuated underwater vehicle simulated by using a stabilizing method of the under-actuated underwater vehicle provided in the embodiment of the present application;
fig. 6 is a schematic view of velocity, angular velocity, error tracking of an under-actuated underwater vehicle simulated by using a stabilizing method of the under-actuated underwater vehicle provided in an embodiment of the present application;
fig. 7 is a schematic diagram of a control thrust variation curve of an under-actuated underwater vehicle simulated by using a stabilizing method of the under-actuated underwater vehicle provided in the embodiment of the present application;
fig. 8 is a schematic diagram of a control moment variation curve of an under-actuated underwater vehicle simulated by using a stabilizing method of the under-actuated underwater vehicle provided in the embodiment of the present application;
fig. 9 is a schematic diagram of a control thrust trigger interval of an under-actuated underwater vehicle simulated by using a stabilizing method of the under-actuated underwater vehicle provided in the embodiment of the present application;
fig. 10 is a schematic diagram of an under-actuated underwater vehicle control moment trigger interval simulated by using a stabilizing method of the under-actuated underwater vehicle provided in the embodiment of the present application;
fig. 11 is a schematic diagram showing the comparison between the communication times of a controller and the communication times of a conventional controller simulated by using a stabilizing method of an under-actuated underwater vehicle provided by an embodiment of the application;
fig. 12 is a schematic structural diagram of a stabilizing device of an under-actuated underwater vehicle according to an embodiment of the present application;
fig. 13 is a schematic structural diagram of an under-actuated underwater vehicle according to an embodiment of the present application.
Detailed Description
The technical solution of the present application is further described in detail by the accompanying drawings and examples.
In the description of the present application, it should be understood that the terms "first," "second," "third," and the like are used for limiting the components, and are used only for the convenience of distinguishing the components from one another, and if not otherwise stated, the terms have no special meaning, and thus, should not be construed as limiting the scope of the present application. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
Fig. 1 is a schematic flow chart of a stabilizing method of an under-actuated underwater vehicle according to an embodiment of the present application. As shown in fig. 1, the stabilizing method of the under-actuated underwater vehicle includes:
s101, acquiring first target navigation data of the aircraft, wherein the first target navigation data comprises ideal position coordinates and ideal heading angles.
Specifically, the first target navigation data may be pre-stored in a memory in the aircraft, and when the first target navigation data is needed, the first target navigation data may be directly called from the memory. Wherein the first target voyage data includes ideal position coordinates and an ideal heading angle.
And S102, determining target control data of the aircraft at the next moment according to the first target navigation data, wherein the target control data comprise target control thrust and target control torque.
Specifically, determining the first target navigation data can determine target control data of the aircraft at the next time according to the first target navigation data. The target control data comprises target control thrust and target control torque.
As a possible implementation, as shown in fig. 2, the method includes the following steps:
s201, determining navigation error data of the aircraft at the current moment according to the first target navigation data, wherein the navigation error data comprises: position error and heading error.
Specifically, the driving data of the aircraft at the current moment, such as the current position coordinate, the current heading angle and the like, are acquired by using sensors such as a position sensor, an accelerometer, a gyroscope, a magnetic navigator and the like in the aircraft. And then, calculating a difference value between the first target navigation data and the current-time traveling data, so as to determine navigation error data of the aircraft at the first time. Wherein the navigation error data includes a position error and a heading error.
And S202, determining second target navigation data of the aircraft at the next moment according to the navigation error data, wherein the second target navigation data comprises an ideal linear velocity and an ideal angular velocity.
Specifically, determining the flight error data can determine second target flight data of the aircraft at the next time based on the flight error data, for example, determining based on a mapping relationship between the flight error data and the second target flight data. Wherein the second target voyage data includes an ideal linear velocity and an ideal angular velocity.
Optionally, according to the flight error data, a specific formula for determining second target flight data of the aircraft at the next time is as follows:
Figure BDA0002553126710000051
in the formula udIs an ideal linear velocity, rdIs the ideal angular velocity, k1、k2、ξ、
Figure BDA0002553126710000052
Being constant and/or variable, z1X-axis coordinate value phi (V) of the navigator in the body coordinate system1) To relate to V1H (t) is a smooth function with respect to t,
Figure BDA0002553126710000061
is the derivative of h (t), t is the current time, v is the coordinates of the aircraft on the bodyThe lateral linear velocity of the tie-down,
Figure BDA0002553126710000062
r is the yaw rate and the yaw rate,
Figure BDA0002553126710000063
wherein, ξ ═ z3+Φ(V1)h(t)，
Figure BDA0002553126710000064
Wherein z is3The value of the heading angle of the aircraft at the current moment, c is the ratio between the inertia of the first system and the inertia of the second system, and d is the ratio between the hydrodynamic damping of the first system and the inertia of the second system. In this embodiment, the first system inertia includes a mass and an additional mass, and the second system inertia includes a rotational inertia and an additional rotational inertia.
And S203, determining target control data according to the second target navigation data.
Specifically, when the second target navigation data is determined, the target control data can be determined based on the second target navigation data.
Optionally, according to the second target navigation data, a specific formula for determining the target control data is as follows:
Figure BDA0002553126710000065
wherein i is 1 or 2,
Figure RE-GDA0002645095030000065
the thrust force is controlled for the purpose of the target,
Figure RE-GDA0002645095030000066
in order to control the torque for the target,i∈(0,1)，αiis a variable or constant, e1As linear velocity tracking error, e2For tracking error of angular velocity,/i w＞0，p3xi＝p3As aircraft quality parameter, p3xi＝p6The moment of inertia of the aircraft is taken as a parameter, and t is the current moment;i(t) is a function of t, satisfiesi(t) > 0, and ρi> 0, so that
Figure RE-GDA0002645095030000067
CiIs the trigger threshold.
S103, determining that an updating condition is met according to the target control data and first control data of the aircraft at the current moment, and updating the first control data, wherein the first control data comprise first control thrust and first control torque.
Specifically, after the target control data is determined, it can be determined that the updating condition is met according to the target control data and first control data of the aircraft at the current moment, and the first control data is updated, so that stabilization of the aircraft is achieved. Wherein the first control data includes a first control thrust and a first control torque.
As a possible implementation, as shown in fig. 3, the method includes the following steps:
s301, selecting a trigger threshold based on the size relation between target control data and a switching threshold, wherein the trigger threshold is a first threshold or a second threshold, the first threshold is a fixed threshold, and the second threshold is a relative threshold.
Specifically, if the target control data is greater than or equal to the switching threshold, determining that the triggering threshold is a first threshold; and if the target control data is small in switching threshold, determining that the triggering threshold is a second threshold. Wherein, the first threshold is a fixed threshold, and the second threshold is a relative threshold. It will be appreciated that the first threshold is a fixed amount and the second threshold is a variable.
Optionally, the specific formula of the second threshold is:
Ei＝i|τi(t)|+Di
in the formula, EiIs the second threshold value, and is,i∈(0,1)，τ1for the first control of thrust, τ2Is a first control torque, DiBe a constant or variable.
S302, obtaining a difference value between the target control data and the first control data to obtain a control error.
Specifically, the control error can be obtained by performing difference calculation on the target control data and the first control data.
And S303, determining that the control error is higher than the trigger threshold, and updating the first control data into target control data.
Specifically, if the control error is higher than the trigger threshold, the update condition is satisfied, that is, the aircraft needs to be stabilized, and at this time, the first control data is updated to the target control data. For example, the first control thrust is updated to the target control thrust, and the first control torque is updated to the target control torque.
The stabilizing method of the under-actuated underwater vehicle in the embodiment of the application is characterized in that target control data of the vehicle at the next moment are determined based on target navigation data of the vehicle; and then, determining that the updating condition is met based on the target control data and the control data of the aircraft at the current moment, and updating the control data of the aircraft at the current moment, so that the driving parameters of the aircraft, such as linear speed, angular speed and the like, can accurately track the ideal driving parameters of the aircraft, and the stabilization of the whole system is realized.
For ease of understanding, a detailed flow for implementing the stabilizing method of the under-actuated underwater vehicle in the present embodiment is described below.
Step 1: under-actuated underwater vehicle model establishment and decomposition
Definition η ═ x, y, ψ]TThe coordinate of an x axis, the coordinate of a y axis and a heading angle psi under an inertial coordinate system of the aircraft; v ═ u, v, r]TThe linear velocity u, the lateral linear velocity v and the yaw angular velocity r under the coordinate system of the vehicle body.
The under-actuated underwater vehicle model is
Figure BDA0002553126710000071
Figure BDA0002553126710000072
Wherein
Figure BDA0002553126710000081
Figure BDA0002553126710000082
m11、m22、m33As a parameter of system inertia, m11Containing mass and additional mass, m22、m33The device comprises a rotational inertia and an additional rotational inertia; d11、d22、d33For the hydrodynamic damping parameter of the system, τ1For system control of force, τ2The torque is controlled for the system. Aircraft calm control objective is to design a control input τ1And τ2Enabling the aircraft to navigate from an initial state to a target point η in inertial spaced＝[xd,yd,ψd]T，
Figure BDA0002553126710000083
Definitions ηe＝η-ηd＝[xe,ye,ψe]TFor the aircraft position error in the inertial frame, z is [ z ]1,z2,z3]TThe position error of the aircraft under the body coordinate system is satisfied
Figure BDA0002553126710000084
The above formula is derived by combining formula (1)
Figure BDA0002553126710000085
To eliminate
Figure BDA00025531267100000811
V in (3), introducing state transitions
Figure BDA0002553126710000086
Derived by derivation
Figure BDA0002553126710000087
In combination with formulas (4) to (5), system models (1) to (2) can be rewritten as
Figure BDA0002553126710000088
Figure BDA0002553126710000089
As can be seen from the equations (3) and (5), the above state transition process is reversible and there are no singularities, so the stabilization problem of the system models (1) - (2)
Figure BDA00025531267100000810
The equivalence is as follows: designing control thrust and control moment tau (·)1(·),τ2(·)]TThe systems (6) to (7) are converged to 0.
As can be seen from the second line of equation (2), the equation has no control input, resulting in the under-actuated characteristic of the system. It can be understood from equations (6) to (7) after the state change that the thrust τ is controlled1And control of the moment τ2The linear velocity variable u and the angular velocity variable r can be directly controlled, so that the system model can be decomposed into an outer ring subsystem (6) and an inner ring subsystem (7), and the ideal linear velocity u is utilizeddAnd ideal angular velocity rdDesign u as an intermediate control quantitydAnd rdSo that the outer ring subsystem (6) is gradually stabilized, and finally tau is designed by utilizing an event trigger mechanism1And τ2Tracking u of the subsystem (7) in the systemdAnd rdAnd the asymptotic stability of a closed-loop system is realized.
Step 2: intermediate control quantity u of outer ring subsystemd、rdDesign of
In order to design the time-varying control law to satisfy the Brockett requirement, an auxiliary variable is defined that exhibits a time variable t:
ξ＝z3+Φ(V1)h(t) (8)
wherein the content of the first and second substances,
Figure BDA0002553126710000091
phi (-) is a smooth kappa-like saturation function for variables whose derivatives satisfy
Figure BDA0002553126710000092
h (t) is a smooth function with respect to the time variable t, the derivatives of which satisfy
Figure BDA0002553126710000093
And is
Figure BDA0002553126710000094
Design the velocity control law as
Figure BDA0002553126710000095
Wherein k is2＞0，
Figure BDA0002553126710000096
Defining the linear velocity tracking error as e1＝u-udThe tracking error of angular velocity is e2＝r-rd. The stability analysis of the outer ring system is given by lemma 1.
Introduction 1
When the outer ring subsystem speed tracking error e i0, (i-1, 2), i.e., u-udAnd r ═ rdThe speed control law (9) can enable the outer ring subsystem (6) to be asymptotically stable when the speed control law is used as the control input of the outer ring (6) of the system.
And (3) proving that: by substituting formula (9) for formula (6)
Figure BDA0002553126710000097
Defining a lyapunov function
Figure BDA0002553126710000098
The derivation of equation (11) along equation (10) and substitution of equation (9) can yield:
Figure BDA0002553126710000101
Figure BDA0002553126710000102
can know that V1,V2∈L∞Thus, therefore, it is
Figure BDA0002553126710000103
v,ξ∈L∞. Due to the fact that
Figure BDA0002553126710000104
Z is shown by the formula (8)3∈L∞The above results are combined with formula (9) to find ud,rd∈L∞Therefore, according to the formula (10), it is found that
Figure BDA0002553126710000105
By combining formula (9) and (10) by deriving formula (8)
Figure BDA0002553126710000106
By deriving from formula (12)
Figure BDA0002553126710000107
Thus it can be seen that
Figure BDA0002553126710000108
Consistently continuous, again because of V2Not less than 0, according to the Barbalt theorem,
Figure BDA0002553126710000109
namely, it is
Figure BDA00025531267100001010
Due to the fact that
Figure BDA00025531267100001011
Thus, it is possible to provide
Figure BDA00025531267100001012
Thereby to obtain
Figure BDA00025531267100001013
Thus, it is possible to provide
Figure BDA00025531267100001014
Are consistent and continuous. Due to the fact that
Figure BDA00025531267100001015
The Barbalat is used again to obtain
Figure BDA00025531267100001016
According to the formula (10), the
Figure BDA00025531267100001017
By using the above results, the
Figure BDA00025531267100001018
And substituting the formulas (9) and (11)
Figure BDA00025531267100001019
Can be unfolded in a combined manner (16)
Figure BDA00025531267100001020
Due to the fact that
Figure BDA00025531267100001021
Thus, it is possible to obtain
Figure BDA00025531267100001022
The combined type (8), (11) and (16) can be obtained
Figure BDA00025531267100001023
So that the outer ring system (6) is asymptotically stable,
Figure BDA00025531267100001024
and step 3: inner loop subsystem event triggered controller design
Design of actual control thrust τ based on switching threshold event trigger mechanism1And control of the moment τ3To realize the ideal linear velocity udAnd ideal angular velocity rdThe tracking of (2).
Design event triggering mechanism
Figure BDA0002553126710000111
Figure BDA0002553126710000112
Wherein
Figure BDA0002553126710000113
Subscript, t, indicating the trigger time of the recording controller i,00 is the initial time. Deltai＝wi(ti,k+1)-τi(t) is the control error between the current time and the trigger time, Ci,Di,i＞0，0＜iAnd < 1 is a trigger mechanism design parameter.
When the value of the control signal is larger than the set switching thresholdiI.e. | τi(t)|≥iThe trigger threshold of the controller is a fixed value CiI.e. when the controller error | Δi|≥CiThe system is triggered, and the controller is updated by adopting a fixed threshold triggering strategy, so that sudden change of a control signal can be avoided, and system oscillation is prevented; when the value of the control signal is small, i.e. | τi(t)|＜iThe controller error is linear with the value of the control signal, i.e. | Δi|≥i|τi(t)|+DiAt this time, the controller is updated by switching to a relative threshold triggering strategy, so that accurate control can be realized, and the control precision of the system is improved. As long as the system satisfies the trigger condition of equation (20), the trigger time is recorded as ti,k+1The control signal is updated according to equation (19)
Figure BDA0002553126710000114
And applying control thrust and control torque to the under-actuated underwater vehicle through an actuating mechanism. The advantage of the above-described method is that,
Figure BDA0002553126710000115
the output value of the controller is constant
Figure BDA0002553126710000116
Therefore, communication with the outside is not needed in the time period, the operation times of the executing mechanism are reduced, and system resources are saved.
Through the analysis, the event-driven stabilization control problem of the under-actuated underwater vehicle is converted into a pair control signal
Figure BDA0002553126710000117
After design, the actual control force and control torque can be calculated by using the equations (19) and (20).
Define control quantity αiIs composed of
Figure BDA0002553126710000118
Wherein
Figure BDA0002553126710000119
Figure BDA00025531267100001110
As defined in the formula (47),
Figure BDA00025531267100001111
designing control signals
Figure BDA00025531267100001112
Is composed of
Figure BDA0002553126710000121
Wherein the control parameters satisfy:
Figure BDA0002553126710000122
i(t) is a function of a time variable t, satisfyingi(t) > 0, and a constant ρi> 0, so that
Figure BDA0002553126710000123
When the speed error e of the ring system in the aircraftiWhen larger, the first term and the third term in equation (23) play a main control role, so that eiAnd rapidly decreases. When e isiWhen the error is close to 0, the first term and the second term in the equation (23) play a main control role, and can compensate the controller error deltaiThe influence on the system improves the control precision.
And 4, step 4: closed loop stability analysis
The analysis of the stability of the closed loop system of the under-actuated underwater vehicle is given by the above lemma 1.
Lemma 1 for an under-actuated underwater vehicle as described in equations (1) - (2), the control thrust τ based on the switching event trigger strategy as designed by equations (19) - (23) is utilized1And controlling the control moment tau2The overall consistency of the closed loop system of the under-actuated underwater vehicle can be gradually stabilized, the stabilization control is realized, and simultaneously the lower bound of the trigger interval can be proved to be positive, namely
Figure BDA0002553126710000124
The designed trigger strategy may be implemented.
And (3) proving that:
make the outer ring at the desired speedSubstituting the speed command (9) into the speed command (6) can obtain the existence of the speed error eiThe outer ring subsystem equation of time is
Figure BDA0002553126710000125
The inner loop tracking error equation is
Figure BDA0002553126710000126
Defining a lyapunov function
Figure BDA0002553126710000127
The formula (26) can be derived from the following formulae (24) to (25)
Figure BDA0002553126710000131
Figure BDA0002553126710000132
Figure BDA0002553126710000133
By combining formula (29) with formula (21)
Figure BDA0002553126710000134
As can be seen from equation (20), the event trigger strategy is based oniIs switched, thus according to | τi(t) | andithe relationship of (2) is discussed in the case of equation (30).
a. Fixing a threshold: when | τi(t)|≥iAs can be seen from the first line of equation (20),
Figure BDA0002553126710000135
Figure BDA0002553126710000136
there is thus a function λ1i(t) satisfies lambda1i(tk)＝0，λ1i(tk+1)＝±1，|λ1i(t) is less than or equal to 1, so that
Figure BDA0002553126710000137
Namely, it is
Figure BDA0002553126710000138
By substituting formula (31) for formula (30)
Figure BDA0002553126710000139
By substituting formula (23) for formula (32)
Figure BDA00025531267100001310
Wherein
Figure BDA00025531267100001311
Also because of- αiei≤(1+i)|αiei|，|λ1i(t)|≤1，
Figure BDA00025531267100001312
It can be known that
Figure BDA00025531267100001313
Thus, formula (33) can be rewritten as
Figure BDA0002553126710000141
According to the inequality
Figure BDA0002553126710000142
Can be obtained by combining formula (34)
Figure BDA0002553126710000143
b. And (3) proportional threshold: when | τi(t)|＜iThen, the second line of the formula (20) shows
Figure BDA0002553126710000144
Figure BDA0002553126710000145
There is thus a function λ2i(t) and lambda3i(t) satisfies | λ2i(t)|,|λ3i(t) is less than or equal to 1 so that
Figure BDA0002553126710000146
Namely, it is
Figure BDA0002553126710000147
By substituting formula (36) for formula (30)
Figure BDA0002553126710000148
Due to | λ2i(t)|,|λ3i(t)|≤1，0＜i< 1, it is known that 0 < 1-i＜1+λ2i(t)i＜1+i. According to the formula (23)
Figure BDA0002553126710000149
Thus is easy to obtain
Figure BDA00025531267100001410
By combining formula (38) with formula (37)
Figure BDA00025531267100001411
By substituting formula (23) for formula (39)
Figure BDA0002553126710000151
According to the inequality
Figure BDA0002553126710000152
The combined type (40) can be obtained
Figure BDA0002553126710000153
Based on the easy availability of equations (35) and (41), using the event triggering mechanism described above,
Figure BDA0002553126710000154
must satisfy
Figure BDA0002553126710000155
Wherein
Figure BDA0002553126710000156
Due to the fact that
Figure BDA0002553126710000157
Integrating the two sides of equation (42) with respect to time
Figure BDA0002553126710000158
Wherein
Figure BDA0002553126710000159
By combining formula (26) with formula (43)
Figure BDA00025531267100001510
Thus V3(t) is globally bounded,
Figure BDA00025531267100001511
combining the above results with the formulas (21), (22), (23)) By substituting the formula (31) and (36), it is found thati(t)∈L∞. By combining formula (9) and (24) by deriving formula (8)
Figure BDA00025531267100001512
The results are combined with the formulas (24) and (25), and it is found that
Figure BDA00025531267100001513
Further, according to the formula (44), it is possible to obtain
Figure BDA00025531267100001514
Figure BDA00025531267100001515
Thus, z is known1,v,ξ,ei∈L2. Obtained by utilizing the Barbalt theorem
Figure BDA00025531267100001516
Due to the fact that
Figure BDA0002553126710000161
Thus, it is possible to provide
Figure BDA0002553126710000162
Thereby to obtain
Figure BDA0002553126710000163
Thus, it is possible to provide
Figure BDA0002553126710000164
Are consistent and continuous. Due to the fact that
Figure BDA0002553126710000165
The Barbalat is used again to obtain
Figure BDA0002553126710000166
According to the formula (24)
Figure BDA0002553126710000167
By using the above results, the
Figure BDA0002553126710000168
And substituting the formulas (9) and (26)
Figure BDA00025531267100001619
Can be unfolded in a combined manner (46)
Figure BDA0002553126710000169
Due to the fact that
Figure BDA00025531267100001610
Thus, it is possible to obtain
Figure BDA00025531267100001611
The combined type (8), (26) and (46) can be obtained
Figure BDA00025531267100001612
So that the closed loop system of the under-actuated underwater vehicle is asymptotically stable,
Figure BDA00025531267100001613
all signals have been demonstrated above to be globally bounded, due to Ci，Di，iAre both normal numbers, and a constant must exist in combination with the formulas (20) and (23)
Figure BDA00025531267100001614
Satisfy the requirement of
Figure BDA00025531267100001615
Further, the following formula (20) shows
Figure BDA00025531267100001616
Therefore, in the combination of equations (49) and (50), the lower bound of the trigger interval must satisfy:
Figure BDA00025531267100001617
namely, it is
Figure BDA00025531267100001618
Thus proving that the minimum trigger interval for the event-triggered controller is positive and the controller can implement it.
And 5: simulation verification
This section verifies the algorithm validity through digital simulation.
The model parameter of the under-actuated underwater vehicle is m11＝155kg，m22＝105kg，m33＝20kg·m2， d11＝70kg/s，d22＝100kg/s，d33＝50kg·m2S; the initial state of the aircraft is x (0) — 15m, y (0) — 30m, ψ (0) — 1rad, u (0) — 0m/s, v (0) — 0m/s, r (0) — 0 rad/s; ideal position and heading xd＝0m，yd＝0m，ψ d0 rad; the control parameter is k1＝0.09，k2＝0.7，l1＝0.5， l2＝0.6，1＝100，2＝50，C1＝40，C2＝2，D1＝1，D2＝0.1，1＝0.1，2＝0.05，
Figure BDA0002553126710000171
The controller function is defined as Φ (V)1)＝2.4tanh(V1)， h(t)＝sin(0.1t)，i(t)＝0.3e-0.01t. As shown in fig. 4 to 11, it can be seen from the graphs that the stabilizing method of the under-actuated underwater vehicle provided in the embodiment of the present application decomposes a system into an under-actuated outer ring system and a fully-actuated inner ring system by using an event trigger mechanism and an inner-outer ring method, where the outer ring system stabilizes a position angle by using an ideal linear velocity and an angular velocity, and the inner ring system designs an actual control by using a switching threshold trigger mechanismThe system input enables the linear velocity and the angular velocity to track the ideal linear velocity and angular velocity, finally realizes the high-precision state stabilization of a closed-loop system, reduces the communication of an underwater vehicle and the operation times of an actuating mechanism, and achieves the purpose of saving system resources.
Fig. 9 is a schematic structural diagram of a stabilizing device of an under-actuated underwater vehicle according to an embodiment of the present application. As shown in fig. 9, the stabilizing device 100 for an underactuated underwater vehicle includes:
the acquisition module 11 is configured to acquire first target navigation data of the aircraft, where the first target navigation data includes an ideal position coordinate and an ideal course angle;
the determining module 12 is configured to determine target control data of the aircraft at the next moment according to the first target navigation data, where the target control data includes a target control thrust and a target control torque;
and the updating module 13 is configured to determine that an updating condition is met according to the target control data and first control data of the aircraft at the current time, and update the first control data, where the first control data includes a first control thrust and a first control torque.
Further, the determining module 12 is further configured to:
determining navigation error data of the aircraft at the current moment according to the first target navigation data, wherein the navigation error data comprises: a position error and a course error;
determining second target navigation data of the aircraft at the next moment according to the navigation error data, wherein the second target navigation data comprises an ideal linear velocity and an ideal angular velocity;
and determining target control data according to the second target navigation data.
Further, the determining module 12 determines, according to the flight error data, a specific formula of second target flight data of the aircraft at the next time as follows:
Figure BDA0002553126710000172
in the formula udIs an ideal linear velocity, rdIs the ideal angular velocity, k1、k2、ξ、
Figure BDA0002553126710000173
Being constant and/or variable, z1X-axis coordinate value phi (V) of the navigator in the body coordinate system1) To relate to V1H (t) is a smooth function with respect to t,
Figure BDA0002553126710000181
is the derivative of h (t), t is the current moment, v is the lateral linear velocity of the aircraft under the body coordinate system,
Figure BDA0002553126710000182
r is the yaw rate and the yaw rate,
Figure BDA0002553126710000183
further, ξ ═ z3+Φ(V1)h(t)，
Figure BDA0002553126710000184
Wherein z is3C is the ratio of the first system inertia to the second system inertia.
Further, the determining module 12 determines, according to the second target navigation data, a specific formula of the target control data as follows:
Figure BDA0002553126710000185
wherein i is 1 or 2, w1Controlling thrust for the purpose, w2In order to control the torque for the target,i∈(0,1)，αiis a variable or constant, e1As linear velocity tracking error, e2In order to be an angular velocity tracking error,
Figure BDA0002553126710000186
p3xi＝p3as aircraft quality parameter, p3xi＝p6The moment of inertia of the aircraft is taken as a parameter, and t is the current moment; i (t) is a function of t, satisfiesi(t) > 0, and ρi> 0, so that
Figure BDA0002553126710000187
Figure BDA0002553126710000188
CiIs the trigger threshold.
Further, the updating module 13 is further configured to:
selecting a trigger threshold based on the size relation between target control data and a switching threshold, wherein the trigger threshold is a first threshold or a second threshold, the first threshold is a fixed threshold, and the second threshold is a relative threshold;
acquiring a difference value between the target control data and the first control data to obtain a control error;
and determining that the control error is higher than the trigger threshold, and updating the first control data into target control data.
Further, the updating module 13 is further configured to:
if the target control data is greater than or equal to the switching threshold, determining that the triggering threshold is a first threshold;
and if the target control data is small in switching threshold, determining that the triggering threshold is a second threshold.
Further, the specific formula of the second threshold is as follows:
Ei＝i|τi(t)|+Di
in the formula, EiIs the second threshold value, and is,i∈(0,1)，τ1for the first control of thrust, τ2Is a first control torque, DiBe a constant or variable.
It should be understood that the above-mentioned apparatus is used for executing the method in the above-mentioned embodiments, and the implementation principle and technical effect of the apparatus are similar to those described in the above-mentioned method, and the working process of the apparatus may refer to the corresponding process in the above-mentioned method, and is not described herein again.
In summary, the stabilizing device of the under-actuated underwater vehicle provided by the embodiment of the application determines target control data of the vehicle at the next moment based on the target navigation data of the vehicle at the current moment; and then, determining that the updating condition is met based on the target control data and the control data of the aircraft at the current moment, and updating the control data of the aircraft at the current moment, so that the driving parameters of the aircraft, such as linear speed, angular speed and the like, can accurately track the ideal driving parameters of the aircraft, and the stabilization of the whole system is realized.
In order to implement the above embodiments, the present application further provides an under-actuated underwater vehicle, as shown in fig. 10, including the stabilizing device 100 of the under-actuated underwater vehicle in the above embodiments.
The above-mentioned embodiments, objects, technical solutions and advantages of the present application are described in further detail, it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present application, and are not intended to limit the scope of the present application, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present application should be included in the scope of the present application.

Claims (10)

1. A method of calming an under-actuated underwater vehicle, the method comprising:
acquiring first target navigation data of the aircraft, wherein the first target navigation data comprises ideal position coordinates and ideal course angles;
determining target control data of the aircraft at the next moment according to the first target navigation data, wherein the target control data comprise target control thrust and target control torque;
and determining that an updating condition is met according to the target control data and first control data of the aircraft at the current moment, and updating the first control data, wherein the first control data comprises first control thrust and first control torque.
2. The method of claim 1, wherein determining target control data for the aircraft at a next time based on the first target voyage data comprises:
determining navigation error data of the aircraft at the current moment according to the first target navigation data, wherein the navigation error data comprises: a position error and a course error;
determining second target navigation data of the aircraft at the next moment according to the navigation error data, wherein the second target navigation data comprises an ideal linear velocity and an ideal angular velocity;
and determining the target control data according to the second target navigation data.
3. A method as set forth in claim 2 wherein the specific formula for determining second target voyage data for the aircraft at a next time based on the voyage error data is:
Figure RE-FDA0002645095020000011
in the formula udIs an ideal linear velocity, rdIs the ideal angular velocity, k1、k2、ξ、
Figure RE-FDA0002645095020000012
Being constant and/or variable, z1X-axis coordinate value phi (V) of the navigator in the body coordinate system1) To relate to V1H (t) is a smooth function with respect to t,
Figure RE-FDA0002645095020000013
is the derivative of h (t), t is the current moment, v is the lateral linear velocity of the aircraft under the body coordinate system,
Figure RE-FDA0002645095020000014
r is the yaw rate and the yaw rate,
Figure RE-FDA0002645095020000015
4. a method as claimed in claim 3, wherein ξ ═ z3+Φ(V1)h(t)，
Figure RE-FDA0002645095020000016
Figure RE-FDA0002645095020000017
Wherein z is3C is the ratio of the first system inertia to the second system inertia.
5. The method of claim 2, wherein the specific formula for determining the target control data based on the second target voyage data is:
Figure RE-FDA0002645095020000021
wherein i is 1 or 2,
Figure RE-FDA0002645095020000022
the thrust force is controlled for the purpose of the target,
Figure RE-FDA0002645095020000023
in order to control the torque for the target,i∈(0,1)，αiis a variable or constant, e1As linear velocity tracking error, e2In order to be an angular velocity tracking error,
Figure RE-FDA0002645095020000024
p3xi＝p3as aircraft quality parameter, p3xi＝p6The moment of inertia of the aircraft is taken as a parameter, and t is the current moment;i(t) is a function of t, satisfiesi(t) > 0, and ρi> 0, so that
Figure RE-FDA0002645095020000025
Figure RE-FDA0002645095020000026
CiIs the trigger threshold.
6. A method as set forth in any one of claims 1-5 wherein determining that an update condition is satisfied based on the target control data and first control data of the aircraft at a first time, and updating the first control data comprises:
selecting a trigger threshold based on the magnitude relation between the target control data and a switching threshold, wherein the trigger threshold is a first threshold or a second threshold, the first threshold is a fixed threshold, and the second threshold is a relative threshold;
obtaining a difference value between the target control data and the first control data to obtain a control error;
and determining that the control error is higher than the trigger threshold, and updating the first control data into the target control data.
7. The method of claim 6, wherein selecting a trigger threshold based on a magnitude relationship between the target control data and a handover threshold comprises:
if the target control data is greater than or equal to the switching threshold, determining that the triggering threshold is the first threshold;
and if the target control data is smaller than the switching threshold, determining that the triggering threshold is the second threshold.
8. The method of claim 7, wherein the second threshold is specifically expressed by:
Ei＝i|τi(t)|+Di
in the formula, EiIs the second threshold value, and is,i∈(0,1)，τ1for the first control of thrust, τ2Is a first control torque, DiBe a constant or variable.
9. A stabilizing device for an under-actuated underwater vehicle, the device comprising:
the system comprises an acquisition module, a navigation module and a navigation module, wherein the acquisition module is used for acquiring first target navigation data of the aircraft, and the first target navigation data comprises ideal position coordinates and ideal course angles;
the determining module is used for determining target control data of the aircraft at the next moment according to the first target navigation data, wherein the target control data comprise target control thrust and target control torque;
and the updating module is used for determining that an updating condition is met according to the target control data and first control data of the aircraft at the current moment, and updating the first control data, wherein the first control data comprises first control thrust and first control torque.
10. An under-actuated underwater vehicle comprising a ballast device of the under-actuated underwater vehicle as claimed in claim 9.
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