CN115718499A - Under-actuated AUV trajectory tracking control method based on extended disturbance observer - Google Patents
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Abstract
The invention relates to an under-actuated AUV (autonomous underwater vehicle) trajectory tracking control method based on an extended disturbance observer, which comprises the following steps of: step 1: establishing a kinematics and dynamics model of the horizontal plane of the under-actuated AUV; and 2, step: setting an expected track by acquiring real-time position and speed information of the AUV, and deriving a speed tracking error model by using the position tracking error model; and step 3: constructing an extended disturbance observer to estimate disturbance; and 4, step 4: according to the speed tracking error, a sliding mode function design of a nonsingular fast terminal sliding mode is carried out; and 5: and constructing a nonsingular fast terminal sliding mode controller NFTSMC according to a sliding mode function, compensating an estimated value of a disturbance observer into the output of the controller, and realizing the track tracking control of the under-actuated AUV horizontal plane under unknown time-varying disturbance. The method has good adaptability to external complex interference and high convergence speed.
Description
Technical Field
The invention belongs to the technical field of Autonomous Underwater Vehicle (AUV) trajectory tracking, and particularly relates to an under-actuated AUV trajectory tracking control method based on an extended disturbance observer.
Background
With the deep ocean exploration, mankind has put higher and higher requirements on the performance of underwater vehicles. As an underwater vehicle with small volume, good controllability, long endurance time and strong bearing capacity, the track tracking and control capacity of the underwater vehicle is an important technical guarantee for completing underwater resource exploration, environment monitoring and sea area investigation tasks. However, the marine environment is very complex, often unpredictable, with high winds and unknown currents, which also makes the associated control methods challenging. An under-actuated system can reduce manufacturing costs and energy consumption while improving propulsion efficiency compared to a fully actuated system, but also makes the design of the controller more challenging.
The traditional non-linear disturbance observer needs to meet certain assumptions during design, such as that the disturbance is slowly changed or the first derivative of the disturbance is bounded or zero, and the application range is narrow.
Due to the strong robustness of sliding mode control, a corresponding control method is provided at home and abroad aiming at the horizontal plane trajectory tracking of the under-actuated AUV. If sliding mode control is adopted to design a controller, a nonsingular terminal sliding mode control method is adopted, and the like, on one hand, the convergence speed is not high, and on the other hand, the influence of external disturbance on the system stability is not considered.
Disclosure of Invention
The invention aims to provide an under-actuated AUV trajectory tracking control method based on an extended disturbance observer, which has good adaptability to external complex interference and high convergence speed.
In order to realize the purpose, the invention adopts the technical scheme that: an under-actuated AUV trajectory tracking control method based on an extended disturbance observer comprises the following steps:
step 1: establishing a kinematics and dynamics model of the horizontal plane of the under-actuated AUV;
step 2: setting an expected track by acquiring real-time position and speed information of the AUV, and deriving a speed tracking error model by using the position tracking error model;
and step 3: constructing an extended disturbance observer to estimate disturbance;
and 4, step 4: according to the speed tracking error, a sliding mode function design of a nonsingular fast terminal sliding mode is carried out;
and 5: and constructing a nonsingular fast terminal sliding mode controller NFTSMC according to a sliding mode function, compensating an estimated value of a disturbance observer into the output of the controller, and realizing the track tracking control of the under-actuated AUV horizontal plane under unknown time-varying disturbance.
Further, in step 1, a kinematic and dynamic model of the under-actuated AUV level is established as follows:
in the formula (I), the compound is shown in the specification,
x, y denote the abscissa and ordinate of the position of the AUV in the ground fixed frame, ψ is the yaw angle,
first derivatives of x, y, ψ, respectively; u, v and r are the advancing, retreating, traversing and rotating speeds of the AUV respectively,
the first derivatives of u, v, r, respectively; m is the mass of the vehicle body, I z Is the moment of inertia, X, of the vehicle about the z-axis u 、Y v 、N r Linear hydrodynamic damping coefficients in the forward and backward, traverse and rotational directions respectively,
additional mass and additional moment of inertia, τ, in the advancing and retreating, traversing and yawing directions, respectively u For propulsion in the forward direction, τ r A yaw moment in a direction of gyration; let d = [ d ] 1 ,d 2 ,d 3 ] T Is an unknown environmental disturbance, where d 1 ,d 2 ,d 3 Disturbances in the forward and backward, lateral and yaw directions, respectively, and assuming the second derivative of the disturbance d
Is bounded, i.e.
μ is an unknown normal number.
Further, in step 2, the expected track is set to be (x) through the acquisition of the real-time position and speed information of the AUV per se d ,y d ) And deducing a speed tracking error model by using the position tracking error model:
the position tracking error is:
wherein e is x Position tracking error in x-direction, e y For position tracking error in the y-direction, its first derivative is:
wherein
Are respectively x d ,y d The first derivative of (a);
the velocity tracking error is:
wherein h is x ,g x ,h y ,g y Is a normal number, e u In the direction of travelVelocity tracking error, e v Representing a velocity tracking error in the traverse direction; according to the Lyapunov function, when e u And e v Convergence to zero, e x And e y But also converges to zero.
Further, in step 3, an extended disturbance observer is constructed as follows:
wherein, it is provided with
Is an estimate of the disturbance d (t), where
Are respectively disturbances d 1 ,d 2 ,d 3 Estimated value of, using
To represent a first derivative of the disturbance d (t)
Wherein, in
Are respectively disturbances d 1 ,d 2 ,d 3 First order of
Is estimated value of z ab (a =1,2 b =1,2,3) is an auxiliary state variable of the disturbance observer, the normal number L being positive ab (a =1,2, b =1,2,3) is the observer gain; according to the Lyapunov function, the estimation error of the disturbance observer to the unknown time-varying disturbance is globally consistent and finally bounded.
Further, in step 4, according to the speed tracking error in step 2, a sliding mode function design of the nonsingular fast terminal sliding mode is performed:
the sliding mode function is:
wherein alpha is i ,β i Are all positive and real, and have alpha i ＞0，i＝1,2,3,4，1＜β 2 ,β 4 ＜2，β 1 ＞β 2 ，β 3 ＞β 4 。
Further, in step 5, a nonsingular fast terminal sliding mode controller NFTSMC is constructed according to the sliding mode function in step 4, and an estimated value of a disturbance observer is compensated to the output of the controller, so that the trajectory tracking control of the under-actuated AUV horizontal plane under unknown time-varying disturbance is realized:
the control rate is as follows:
wherein w 1 ,w 2 Is a normal number, tau u ,τ r Thrust of the AUV advancing propeller and rotary moment required by yaw are respectively;
according to the Lyapunov function, under the action of the control rate, the speed tracking error converges to zero in a limited time, and further the position tracking error also converges to zero.
Further, in step 5, in order to reduce the chattering, a saturation function sat (S) is used instead of the sign function sign (S), that is, the saturation function sat (S) is used
Where Δ is the boundary layer.
Compared with the prior art, the invention has the following beneficial effects: the extended disturbance observer constructed by the method can better cope with the actual complex and variable disturbance, and simultaneously, a nonsingular fast terminal sliding mode method is adopted to design a controller to accelerate the convergence of a tracking error, so that the control system has good performance.
Drawings
FIG. 1 is a schematic diagram of horizontal plane motion of an under-actuated AUV in an embodiment of the present invention;
FIG. 2 is a functional block diagram of an under-actuated AUV trajectory tracking control method according to an embodiment of the present invention;
fig. 3 (a) is a diagram of the trace tracking effect of the under-actuated AUV under the first external disturbance in the embodiment of the present invention;
FIG. 3 (b) is a comparison graph of the estimated value and the actual value of the first external unknown disturbance by the disturbance observer in the embodiment of the present invention;
FIG. 3 (c) is a diagram of the convergence result of the tracking error of the horizontal plane position of the under-actuated AUV under the first interference condition in the embodiment of the present invention;
FIG. 3 (d) is a diagram of the convergence result of the horizontal plane velocity tracking error of the under-actuated AUV under the first interference condition in the embodiment of the present invention;
FIG. 3 (e) is a schematic representation of the forward thrust and yaw moment of an under-actuated AUV under the present method in a first disturbance scenario in an embodiment of the present invention;
fig. 4 (a) is a diagram of the trace tracking effect of the under-actuated AUV under the second external disturbance in the embodiment of the present invention;
FIG. 4 (b) is a comparison graph of the estimated value and the actual value of the second external unknown disturbance by the disturbance observer in the embodiment of the present invention;
FIG. 4 (c) is a diagram of the convergence result of the tracking error of the horizontal plane position of the under-actuated AUV under the second interference condition in the embodiment of the present invention;
FIG. 4 (d) is a diagram of the convergence result of the horizontal plane velocity tracking error of the under-actuated AUV under the second interference condition in the embodiment of the present invention;
FIG. 4 (e) is a schematic diagram of the forward thrust and yaw moment of an under-actuated AUV under the present method in a second disturbance situation in an embodiment of the present invention;
FIG. 5 (a) is a graph comparing the trace tracking effect of an under-actuated AUV under several methods in the first interference situation according to the embodiment of the present invention;
FIG. 5 (b) is a comparison graph of the horizontal plane position tracking error convergence results of the under-actuated AUV under several methods in the first interference situation in the embodiment of the present invention;
FIG. 6 (a) is a graph comparing the trace tracking effect of under-actuated AUV under several methods in the second interference situation according to the embodiment of the present invention;
fig. 6 (b) is a comparison diagram of the horizontal plane position tracking error convergence results of the under-actuated AUV under several methods in the second interference situation in the embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure herein. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an", and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The embodiment provides an under-actuated AUV trajectory tracking control method based on an extended disturbance observer, and the implementation principle of the under-actuated AUV trajectory tracking control method is shown in FIG. 2. The method provides an extended disturbance observer to estimate unknown external interference, compared with the complexity of the design requirement of the traditional disturbance observer, the extended disturbance observer constructed by the invention is simpler in design and can estimate the first derivative of the interference, and the estimated value is compensated in the non-singular rapid terminal sliding mode controller to solve the problem, so that the accuracy of tracking control of the under-actuated AUV horizontal plane track is improved.
In this embodiment, the horizontal plane motion of the under-actuated AUV is shown in fig. 1. The under-actuated AUV only has independent actuators in the surge direction and the yaw direction, and has no control input in the transverse moving direction, so that the kinematic and dynamic models of the horizontal plane of the under-actuated AUV are established as follows:
in the formula (I), the compound is shown in the specification,
x, y denote the abscissa and ordinate of the position of the AUV in the ground fixed frame, ψ is the yaw angle,
first derivatives of x, y, ψ, respectively; u, v and r are respectively the advancing, retreating, transverse moving and rotating speeds of the AUV,
first derivatives of u, v, r, respectively; m is the mass of the vehicle body, I z Is the moment of inertia, X, of the vehicle about the z-axis u 、Y v 、N r Linear hydrodynamic damping coefficients in the advancing and retreating, transverse moving and rotating directions respectively,
respectively advance and retreat and traverseAdditional mass and additional moment of inertia, τ, in the yaw direction u For propulsion in the forward direction, τ r A yaw moment in the direction of rotation; let d = [ d = 1 ,d 2 ,d 3 ] T Is an unknown environmental disturbance, where d 1 ,d 2 ,d 3 Disturbances in the forward and backward, lateral and yaw directions, respectively, and assuming the second derivative of the disturbance d
Is bounded, i.e.
μ is an unknown normal number.
Acquiring self real-time position and speed information through the AUV, and simultaneously setting an expected track as (x) d ,y d ) And deriving a speed tracking error model from the position tracking error model as follows:
the position tracking error is:
wherein e is x Position tracking error in the x-direction, e y For position tracking error in the y-direction, its first derivative is:
thus, the desired speed can be designed to be:
in the formula h x ,g x ,h y ,g y Is a normal number.
The velocity tracking error is:
wherein e is u Representing the velocity tracking error in the forward direction, e v Indicating the velocity tracking error in the traverse direction.
Because of the matrix
Is non-singular, so when e u And e v When converging to 0, there is
The Lyapunov function was chosen as:
according to formula (6), for V 1 Derivation can be obtained:
it is obvious that
Is negative, whereby it can be demonstrated when e u And e v Convergence to zero, e x And e y Will also converge to zero.
Due to the fact that the external environment is complex, in order to guarantee that the aircraft can better cope with the external environment changes when in work, the disturbance observer is designed to estimate the disturbance. The assumption conditions of the common non-linear disturbance observer are too strict, and it is generally assumed that the external disturbance is a constant disturbance or the disturbance is a slow change, that is, the disturbance is a constant disturbance
However, for practical purposes, the external disturbance changes are time-varying and complexUnfortunately, the adaptation range of such a disturbance observer is too small. An extended disturbance observer is therefore designed to improve that not only does it not require severe assumptions, but can also estimate the first derivative of the disturbance.
The extended disturbance observer was constructed as follows:
wherein is provided with
Is an estimate of the disturbance d (t), where
Are respectively disturbances d 1 ,d 2 ,d 3 Estimated value of, using
To represent a first derivative of the disturbance d (t)
Wherein, in
Are disturbances d respectively 1 ,d 2 ,d 3 First conductance of
Estimate of z ab (a =1,2 b =1,2,3) is an auxiliary state variable of the disturbance observer, the normal number L being positive ab (a =1,2, b =1,2,3) is an observationAnd (4) gain of the device. According to the Lyapunov function, the estimation error of the disturbance observer to the unknown time-varying disturbance is globally consistent and finally bounded.
The extended disturbance observer stability proves that:
the extended disturbance observer constructed by the invention can be written as follows:
in the formula, D d ＝[d 1 ,d 2 ,d 3 ] T ，V＝[u,v,r] T ，
Z 1 ＝[z 11 ,z 12 ,z 13 ] T ，Z 2 ＝[z 21 ,z 22 ,z 23 ] T According to the above formula:
wherein
From equation (13), it follows:
wherein
The derivation of equation (14) can be:
order to
Then there are:
wherein
Then there are:
λ 2 +L 1 λ+L 2 ＝0 (17)
thus can be selected by selecting L 1 And L 2 So that the matrix L d All lie in LHP (left half plane), then the positive definite matrix P can always be found d Such that:
wherein Q d Is a positive definite matrix with a minimum eigenvalue of λ m . Selecting a Lyapunov function:
then V d The first derivative of (d) is:
then when
When it is satisfied
Thus, it is possible to provide
Convergence to tight-set:
design NFTSMC sliding mode function:
wherein alpha is i ,β i Are all positive and real, and have alpha i ＞0(i＝1,2,3,4)，1＜β 2 ,β 4 ＜2，β 1 ＞β 2 ，β 3 ＞β 4 。
From this, it can be obtained that the NFTSMC control rate is:
wherein w 1 ,w 2 Is a normal number, tau u ,τ r Respectively the thrust of the AUV advancing propeller and the yaw moment required by the yaw,
choosing a Lyapunov function as:
to V 2 Derivation is obtained and obtained from equations (22) and (23):
it is obvious from the formula (21) that λ can be adjusted m So that
Is negative. Thus, two slip form surfaces S can be ensured 1 ,S 2 The finite time converges to zero.That is, the velocity tracking error converges to zero within a finite time, and it is guaranteed that the position tracking error converges to zero.
Because of the sign function sign(s) in the sliding mode control law, there is a large chattering. To reduce chatter, we use the saturation function sat(s) instead for the sign function. Namely that
Where Δ is the boundary layer.
In this embodiment, the first disturbance is a slightly varying continuous time-varying disturbance, and fig. 3 (a) to 3 (e) are graphs of simulation results of trajectory tracking control under the first disturbance. From fig. 3 (a), it can be seen that the control method adopted by the present invention has good robustness to the slightly varying continuous time-varying disturbance, and fig. 3 (b) shows that the designed extended disturbance observer has good performance; fig. 3 (c) and fig. 3 (d) show that the position tracking error and the velocity tracking error under such interference, respectively, can be well converged to zero under the control method adopted by the present invention; fig. 3 (e) is the control input for this disturbance and it can be seen that the chattering is well suppressed by the saturation function.
In this embodiment, the second type of disturbance is a disturbance with a large mutation at a certain time, which takes into account the winding of a large ocean current or underwater plants that actually attack suddenly. Fig. 4 (a) to 4 (e) are graphs showing simulation results of trajectory tracking control under the second disturbance. Fig. 4 (a) shows that the control method adopted in the present invention still has good tracking performance under the interference of large mutation at this certain time; from fig. 4 (b), it can be found that the extended disturbance observer designed by the present invention also has good performance for such abrupt disturbance; FIGS. 4 (c) and 4 (d) are position tracking error and velocity tracking error, respectively, under such interference; fig. 4 (e) is the control input under such a disturbance.
Fig. 5 (a) and 5 (b) are a trajectory tracking effect simulation comparison diagram and a tracking error simulation comparison diagram respectively under several different control methods under the first slightly-changed continuous time-varying disturbance condition, which are a nonsingular fast terminal sliding mode control method with an extended disturbance observer, a nonsingular terminal sliding mode control method with an extended disturbance observer and a nonsingular fast terminal sliding mode control method without the effect of the extended disturbance observer in the present invention. It can be seen that the nonsingular fast terminal sliding mode control method has good tracking performance even without the action of an extended disturbance observer when facing the slightly-changed continuous time-varying interference, and shows good robustness.
Fig. 6 (a) and fig. 6 (b) are a trajectory tracking effect simulation comparison diagram and a tracking error simulation comparison diagram respectively under several different control methods under the second interference condition with a large mutation at a certain time, which are a nonsingular fast terminal sliding mode control method with an extended disturbance observer, a nonsingular terminal sliding mode control method with an extended disturbance observer and a nonsingular fast terminal sliding mode control method without the function of the extended disturbance observer in the invention. It can be seen that the nonsingular fast terminal sliding mode control method based on the extended disturbance observer still has good tracking performance when facing the interference of large mutation at a certain moment, but the position tracking error of the system cannot be converged to zero without the action of the extended disturbance observer.
It can be seen from fig. 5 (b) and fig. 6 (b) that the nonsingular fast terminal sliding mode control method based on the extended disturbance observer provided by the present invention has a faster convergence speed than the general nonsingular terminal sliding mode control method.
Simulation results show that the designed controller can well realize the track tracking control of the under-actuated AUV on the horizontal plane.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (7)
1. An under-actuated AUV trajectory tracking control method based on an extended disturbance observer is characterized by comprising the following steps:
step 1: establishing a kinematics and dynamics model of the horizontal plane of the under-actuated AUV;
step 2: setting an expected track by acquiring real-time position and speed information of the AUV, and deducing a speed tracking error model by using a position tracking error model;
and step 3: constructing an extended disturbance observer to estimate disturbance;
and 4, step 4: according to the speed tracking error, a sliding mode function design of a nonsingular fast terminal sliding mode is carried out;
and 5: and constructing a nonsingular fast terminal sliding mode controller NFTSMC according to a sliding mode function, compensating an estimated value of a disturbance observer into the output of the controller, and realizing the track tracking control of the under-actuated AUV horizontal plane under unknown time-varying disturbance.
2. The under-actuated AUV trajectory tracking control method based on the extended disturbance observer according to claim 1, wherein in step 1, a kinematic and dynamic model of an under-actuated AUV horizontal plane is established as follows:
in the formula (I), the compound is shown in the specification,
x, y denote the abscissa and ordinate of the position of the AUV in the ground fixed frame, ψ is the yaw angle,
first derivatives of x, y, ψ, respectively; u, v and r are the advancing, retreating, traversing and rotating speeds of the AUV respectively,
the first derivatives of u, v, r, respectively; m is the mass of the vehicle body, I z Is the moment of inertia, X, of the vehicle about the z-axis u 、Y v 、N r Linear hydrodynamic damping coefficients in the advancing and retreating, transverse moving and rotating directions respectively,
additional mass and additional moment of inertia, τ, in the advancing and retreating, traversing and yawing directions, respectively u For propulsion in the forward direction, τ r A yaw moment in a direction of gyration; let d = [ d = 1 ,d 2 ,d 3 ] T Is an unknown environmental disturbance, where d 1 ,d 2 ,d 3 Disturbances in the forward and backward, lateral and yaw directions, respectively, and assuming the second derivative of the disturbance d
Is bounded, i.e.
μ is an unknown normal number.
3. The under-actuated AUV (autonomous Underwater vehicle) trajectory tracking control method based on the extended disturbance observer as claimed in claim 2, wherein in the step 2, the expected trajectory is set to (x) through the acquisition of the real-time position and speed information of the AUV per se d ,y d ) And deducing a speed tracking error model by using the position tracking error model:
the position tracking error is:
wherein e is x Position tracking error in the x-direction, e y For position tracking error in the y-direction, its first derivative is:
wherein
Are each x d ,y d The first derivative of (a);
the velocity tracking error is:
wherein h is x ,g x ,h y ,g y Is a normal number, e u Representing the velocity tracking error in the forward direction, e v Representing a velocity tracking error in the traverse direction; according to the Lyapunov function, when e u And e v Convergence to zero, e x And e y Also converging to zero.
4. The under-actuated AUV trajectory tracking control method based on the extended disturbance observer as claimed in claim 3, wherein in step 3, the extended disturbance observer is constructed as follows:
wherein is provided with
Is an estimate of the disturbance d (t), where
Are disturbances d respectively 1 ,d 2 ,d 3 Estimated value of, using
To represent a first derivative of the disturbance d (t)
Wherein, in
Are disturbances d respectively 1 ,d 2 ,d 3 First conductance of
Estimate of z ab (a =1,2, b =1,2, 3) is an auxiliary state variable of the disturbance observer, the normal number L being a positive number ab (a =1,2, b =1,2,3) is the observer gain; according to the Lyapunov function, the estimation error of the disturbance observer to the unknown time-varying disturbance is globally consistent and finally bounded.
5. The under-actuated AUV trajectory tracking control method based on the extended disturbance observer according to claim 4, characterized in that in step 4, according to the speed tracking error in step 2, a sliding mode function design of a nonsingular fast terminal sliding mode is performed:
the sliding mode function is:
wherein alpha is i ,β i Are all positive and real, and have alpha i ＞0，i＝1,2,3,4，1＜β 2 ,β 4 ＜2，β 1 ＞β 2 ，β 3 ＞β 4 。
6. The under-actuated AUV trajectory tracking control method based on the extended disturbance observer as claimed in claim 5, wherein in step 5, a nonsingular fast terminal sliding mode controller NFTSMC is constructed according to the sliding mode function in step 4, and an estimated value of the disturbance observer is compensated to the controller output, so as to realize trajectory tracking control of the under-actuated AUV horizontal plane under unknown time-varying disturbance:
the control rate is as follows:
wherein w 1 ,w 2 Is a normal number, tau u ,τ r Thrust of the AUV advancing propeller and rotary moment required by yaw are respectively;
according to the Lyapunov function, under the action of the control rate, the speed tracking error converges to zero in a limited time, and further the position tracking error also converges to zero.
7. The extended disturbance observer based under-actuated AUV trajectory tracking control method according to claim 6, wherein in step 5, in order to reduce buffeting, a saturation function sat (S) is adopted to replace a sign function sign (S), that is, the sign function sat (S) is adopted to reduce buffeting in the step
Where Δ is the boundary layer.
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