CN115268475B - Robot fish accurate terrain tracking control method based on finite time disturbance observer - Google Patents
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Abstract
A robot fish accurate terrain tracking control method based on a finite time disturbance observer belongs to the field of underwater vehicle control. The method comprises the following steps: s1, obtaining an improved mathematical model of the robot fish; s2, establishing a robot fish terrain tracking error equation; s3, establishing a finite time convergence system; s4, designing a finite time lumped disturbance observer based on the S1 and the S3; s5, designing a limited-time terrain tracking guidance subsystem; s6, designing a limited-time sliding mode surface, and designing a limited-time precise terrain tracking controller by combining the S2, the S4 and the S5. The novel finite-time disturbance observer based on the second-order finite-time differentiator provided by the invention can rapidly and accurately estimate disturbance and inhibit buffeting caused by sign functions. The robot fish accurate terrain tracking controller designed based on the disturbance observer can ensure that the robot fish can rapidly and accurately finish the terrain tracking task, and has excellent robustness.
Description
Technical Field
The invention belongs to the field of underwater vehicle control, and particularly relates to a robot fish accurate terrain tracking control method.
Background
The robot fish is a novel bionic underwater vehicle, and has more excellent maneuverability and stealth compared with the traditional underwater vehicle, and has unique application advantages in the aspects of submarine cable detection, marine organism monitoring, marine ecological environment assessment and the like. As one of the core motion control tasks for marine applications, robot fish terrain tracking control generally requires that the robot fish cruises at a specified height based on the seabed terrain, and a fast and accurate terrain tracking controller can effectively improve the quality and economy of the robot fish to accomplish the tasks.
Accurate topography tracking control is the basis of robot fish high-efficient completion underwater operation task. However, complex marine environments and robot fish's own motion characteristics present a series of challenges for controller design, such as model and parameter uncertainty, complex time-varying unknown environmental disturbances, periodic power/torque input characteristics, input saturation, and the like. At present, the common control method for processing the total uncertainty problem of the underwater vehicle processing set mainly comprises the steps of designing a robust controller aiming at external disturbance, approaching the lumped disturbance by a neural network, constructing a lumped disturbance observer and the like. The finite-time disturbance observer can rapidly and actively estimate disturbance in finite time, and is widely focused by researchers. However, most of the finite time disturbance observers designed at present are based on sliding mode differentiators, and the application of sign functions inevitably causes buffeting of observed values, so that the conventional control method is difficult to realize high-precision terrain tracking control of the robot fish. From the practical application point of view, it is highly desirable to design a limited-time disturbance observer capable of effectively weakening the buffeting problem and a terrain tracking control scheme with higher control precision.
Disclosure of Invention
Aiming at the problems that a disturbance observer based on a sign function has buffeting and the tracking control precision of the existing controller is limited in the process of tracking and controlling the terrain of the robot fish in a complex environment, the invention provides a robot fish accurate terrain tracking and controlling method based on a novel limited-time disturbance observer.
The technical scheme adopted by the invention is as follows: the robot fish accurate terrain tracking control method based on the finite time disturbance observer is characterized by comprising the following steps of: the method comprises the following steps:
s1, improving a traditional underwater vehicle dynamics model by combining periodic power/moment input characteristics of the robot fish to obtain an improved robot fish mathematical model;
s2, establishing a robot fish terrain tracking error equation;
s3, establishing a finite time convergence system;
s4, designing a finite time lumped disturbance observer based on the S1 and the S3;
s5, designing a limited-time terrain tracking guidance subsystem;
s6, designing a limited-time sliding mode surface, and designing a limited-time precise terrain tracking controller by combining the S2, the S4 and the S5.
Compared with the prior art, the invention has the following beneficial effects:
1. the improved robot fish dynamics model provided by the invention divides robot fish generalized input power into average force and periodic force, and regards the periodic force as additional external disturbance, and can be used for solving the problem of periodic power/moment input caused by periodic motion of a propulsion system.
2. The novel finite-time disturbance observer based on the second-order finite-time differentiator provided by the invention can rapidly and accurately estimate disturbance and inhibit buffeting caused by sign functions. The robot fish accurate terrain tracking controller designed based on the disturbance observer can ensure that the robot fish can rapidly and accurately finish the terrain tracking task, and has excellent robustness.
Drawings
Fig. 1 is a conceptual diagram of a robot fish;
FIG. 2 is a schematic diagram of robotic fish terrain tracking;
FIG. 3 is a block diagram of a control system of the present invention;
FIG. 4 is a flow chart of the method of the present invention;
FIG. 5 is a diagram of a robot fish terrain tracking effect;
FIG. 6 is a diagram of robot fish x-axis direction position tracking error;
FIG. 7 is a diagram of robot fish z-axis direction position tracking error;
FIG. 8 is a diagram of robot fish pitch tracking error;
FIG. 9 is a schematic diagram of a robot fish longitudinal disturbance estimation error;
FIG. 10 is a schematic diagram of a robot fish vertical disturbance estimation error;
FIG. 11 is a schematic diagram of a disturbance estimation error in the pitch direction of a robot;
Detailed Description
For a better understanding of the objects, structures and functions of the present invention, reference should be made to the following detailed description of the invention with reference to the accompanying drawings.
Fig. 1 is a conceptual diagram of a robot fish controlled by the control method of the present invention. In order to facilitate problem elucidation, a schematic diagram of the terrain tracking of the robot fish is shown in fig. 2, and three coordinate systems are established in a vertical plane in combination with the actual situation in the terrain tracking process of the robot fish, wherein the coordinate system { n } is an inertial coordinate system and is used for describing the position and posture information of the robot fish; the coordinate system { b } is a satellite coordinate system, and the origin of the coordinate system is positioned at the gravity center position of the robot fish and is used for describing the motion state of the robot fish; the coordinate system { F } is an auxiliary coordinate system, is fixed at any position on a terrain path, is used for designing an auxiliary controller along the tangential direction of the path and the tangential direction perpendicular to the path, and can obtain the terrain tracking error and the dynamic error response in the control method by coordinate transformation among the three coordinate systems, and based on the coordinate system { F } the design of a robot fish disturbance observer, a guidance subsystem and an accurate terrain tracking controller is carried out, wherein the specific design principle is shown in figure 3.
Fig. 4 is a flowchart of a control method proposed in the present invention, and the specific process of the method is:
step one, improving a traditional underwater vehicle dynamics model by combining periodic power/moment input characteristics of the robot fish to obtain an improved robot fish mathematical model;
step two, establishing a robot fish terrain tracking error equation;
step three, establishing a finite time convergence system;
step four, designing a finite time lumped disturbance observer based on the step one and the step three;
step five, designing a limited-time terrain tracking guidance subsystem;
step six, designing a limited time sliding mode surface, and designing a limited time accurate terrain tracking controller by combining the step two, the step four and the step five.
The robot fish mathematical model comprises a kinematic model and an improved kinetic model, wherein the kinematic model is as follows:
wherein x and z respectively represent the position information of the robot fish under the geodetic coordinate system; θ is the pitch angle of the robot fish in the geodetic coordinate system; u and w respectively represent the heave and heave speeds of the robot fish under the satellite coordinate system; q is the pitch angle speed of the robot fish in the satellite coordinate system.
The improved robot fish dynamics model specifically comprises the following steps:
establishing a robot fish dynamics model taking model uncertainty, environmental disturbance, periodic power/moment and input saturation into consideration:
wherein η= [ x, z, θ ]] T Representing position coordinates and pitch angles of the robot fish under an inertial coordinate system; v= [ u, w, q] T Representing the heave speed and the pitch angle speed of the robot fish under a satellite coordinate system; m is M A Representing an inertial matrix containing additional mass; c (C) A (v) Representing the nominal values of the coriolis force and centripetal force matrices; d (D) A (v) Representing a nominal value of a damping matrix for the robotic fish; g (eta represents the nominal value of the restoring force/moment of the robot fish; tau) 0 Representing the average of the generalized input forces/moments; Δτ p A fluctuation value representing a generalized input force/moment; d represents external environmental disturbance;
representing the model and parameter uncertainty terms. Actuator input saturation may be expressed as τ 0 ＝[sat(τ u ),0,sat(τ q )] T Wherein sat (τ i ) Can be expressed as:
in the method, in the process of the invention,
and->
Representing the maximum and minimum values, respectively, of the actuator's inputtable signal.
The lumped disturbance in the robot fish terrain tracking process can be expressed as:
δ f ＝Δτ p +Δf+d
further, in the dynamic model after the improvement of the robot fish:
the matrix multiplication rule is developed and expressed as:
in the method, in the process of the invention,
is an inertia term; x is X {·} ,Z {·} And M {·} Representing the hydrodynamic coefficient; b and W represent the buoyancy and gravity of the BUV, respectively; z G And z B The gravity center and the floating center position of the robot fish in the z-axis direction under the satellite coordinate system are respectively represented.
The method for establishing the terrain tracking error equation of the robot fish comprises the following specific processes:
selecting a coordinate on a desired topographic path as (x) R ,z R ) The coordinate point of (2) is used as the origin of the coordinate system, a coordinate system is established along the tangent of the terrain path and the direction perpendicular to the terrain path, the coordinate point can be expressed as a function of a parameter s, and the following robot fish terrain tracking error equation can be obtained based on coordinate transformation:
wherein x is R 、z R Respectively the abscissa and the ordinate, theta, of a virtual coordinate point on a desired terrain path R Is the rotation angle of the path tangent coordinate system relative to the inertial coordinate system. X is x e 、z e For the actual position x, z and the virtual point position x of the robot fish R 、z R Is a function of the error of (a). The dynamic characteristics of the robot fish terrain path tracking control error equation can be expressed as:
in the middle of
For the movement attack angle of robot fish, +.>
E is the combined speed of the robot fish movement θ ＝θ-θ R U is the difference between the course angle of the robot fish and the tangent direction of the path s For the speed of a virtual point on the desired topographical path, this can be expressed as +.>
For the path update law, ++>
The partial derivatives of the virtual point location coordinates with respect to the path parameters s are respectively given.
The method for establishing the finite time convergence system comprises the following specific processes:
consider the following finite time second order differentiator:
in the method, in the process of the invention,
is a continuous second order differentiable input signal; ρ 1 And ρ 2 For a given positive real number; zeta is a positive adjustable parameter; for any time T is greater than or equal to T f There is a constant epsilon>0 and T f >0 satisfies the following:
t in f Is the convergence time of the system.
The design of the finite time lumped disturbance observer comprises the following specific processes:
defining a robot fish dynamics model comprising estimated states:
lumped disturbance sigma combined with improved dynamic model of robot fish fi (i=u, w, q) can be expressed as:
in the middle of
Is the observed error of the velocity state.
Therefore, the lumped finite time disturbance observer of the robot fish is designed to:
in the method, in the process of the invention,
is an estimate of the lumped disturbance; />
An error signal is observed for the input speed state.
According to the finite time convergence system established in the third step, the disturbance estimation error can be estimated to be more than or equal to T f When meeting
From this, it is known that the lumped disturbance can be accurately estimated in a limited time.
The design of the limited time terrain tracking and guiding subsystem comprises the following specific processes:
the topography tracking control guidance law of the robot fish with limited time is designed as follows:
wherein θ d To the desired pitch angle, k z Positive adjustable gain parameter, 0<ρ<1 is a positive constant value, and Δ is the forward looking distance.
Robot fish topography tracking virtual point speed u s Path update law
The design is as follows:
wherein k is 0 、k 1 Positive adjustable gain parameter, 0<ρ s <1 is a positive constant.
Definition of the lyapunov function:
the derivative of the Lyapunov function is obtained:
note that:
the method can obtain the following steps:
in the method, in the process of the invention,
from the above-mentioned evidence, the guidance law designed in the method can ensure the position tracking error x e And z e Is converged within a limited time.
The design of the limited time sliding mode surface and the design of the limited time accurate terrain tracking controller by combining the step two, the step four and the step five comprises the following specific processes of
A1 pitch control
The adaptive desired pitch rate is designed to be:
wherein k is θ0 Is a positive adjustable parameter that is used to adjust the parameter,
to estimate the adaptive parameters of the upper boundary information ρ 1 、ρ 2 Is a positive adjustable gain parameter.
Selecting a Lyapunov function:
and verifying the stability of the angle tracking error.
For stabilizing pitch angle rate tracking error, selecting the following integral terminal sliding mode surface:
wherein alpha is q 、β q Is a positive adjustable gain parameter that is used to adjust the gain,
is a positive constant value. q e ＝q-q d Is the pitch angle velocity tracking error.
For input saturation of the processing system, the following limited time auxiliary system is designed:
wherein χ is q As an auxiliary variable, deltaτ q ＝τ q -τ q0 K is the difference between the actual control and the nominal control χq 、k q1 Is a positive adjustable parameter.
Based on the above, the robot fish accurately tracks the control law tau in the topography q0 The design is as follows:
selecting a Lyapunov function:
and verifying the stability of the angular velocity tracking error.
A2 speed control
The desired speed is designed as:
wherein u is max To achieve the desired maximum speed, sigma 1 And u 0 Is a positive adjustable parameter.
For stabilizing the speed tracking error, selecting the following integral terminal sliding mode surface:
wherein alpha is u 、β u Positive adjustable parameter, u e ＝u-u d Is a velocity tracking error.
To handle input saturation, the following limited time auxiliary system is designed:
wherein χ is u As an auxiliary variable, deltaτ u ＝τ u -τ u0 K is the difference between the actual control and the nominal control χu 、k u1 Is a positive adjustable parameter.
Based on the above, the robot fish accurately tracks the control law tau in the topography u0 The design is as follows:
selecting a Lyapunov function:
and verifying the stability of the speed tracking error.
In order to illustrate the effectiveness of the control method according to the present invention, according to the flow shown in fig. 4, simulation verification is performed on the robot fish model shown in fig. 1, and the advantage of the control method according to the present invention is further illustrated by comparing the disturbance observer (abbreviated as IFTDO) according to the present invention with the existing disturbance observer (abbreviated as TFTDO).
Model parameters of the robot fish are as follows:
m A11 ＝9.88kg，m A22 ＝29.6kg，m A33 ＝1.25kg·m 2 ，X Au ＝0.24kg·s- 1 ，X Au|u| ＝2.26kg·m -1 ，Z Aw ＝15.78kg·s -1 ，Z Aw|w| ＝22.33kg·s -1 ，M Aq ＝10.53kg·m 2 ·s -1 ，M Aq|q| ＝0.52kg·m 2 ，z G ＝0.05m，
the model and parameter uncertainty is taken as 10% of the perturbation of the parameter, which can be expressed as:
where-represents parametric perturbation.
The external environmental disturbance is assumed as follows:
the periodic force/moment caused by the periodic oscillations of the propulsion system of the robot fish is expressed as:
in the method, in the process of the invention,
the reference terrain path is set as follows:
x R (s)＝0.85s
the initial state of the robot fish is:
η(0)＝[0,8.5,0] T ，v(0)＝[0.3,0,0] T 。
the control method comprises the following steps of:
ζ＝0.001，ρ 1 ＝0.1，ρ 2 ＝1，Δ＝6，k z ＝0.5，ρ＝0.8，k 0 ＝10，k 1 ＝0.5，ρ s ＝0.5，
α q ＝0.8，α q1 ＝0.1，α u ＝0.3，α u1 ＝0.1，k χq ＝0.2，k χu ＝0.2，u max ，σ 1 ＝2，u 0 ＝2.4，k q1 ＝1，k u1 ＝1，k q0 ＝0.2，k u0 ＝0.2，λ q ＝0.5，λ u ＝0.4，ζ q ＝0.4，ζ u ＝0.4。
fig. 5 is a graph showing the effect of the terrain tracking of the robot fish, showing that the precise terrain tracking control method of the robot fish has better terrain tracking precision based on the same finite time control method (FTC) when different disturbance observers { the disturbance observer (IFTDO) of the invention, the disturbance observer (TFTDO) based on sign functions, and the disturbance observer (NFTDO) are not present.
Fig. 6-8 are diagrams of position and posture tracking errors of the robot fish, respectively showing the tracking errors of the robot fish in the x-axis direction position, the z-axis direction position and the depression angle under the actions of the IFTDO-FTC method, the TFTDO-FTC method and the NFTDO-FTC method. As can be seen from the figure, compared with the other two control methods, under the action of the control method, the tracking error of the three pose state quantities is smaller, so that the superiority of the control method in the invention is demonstrated.
Fig. 9-11 are schematic diagrams of complex disturbance estimation errors, respectively showing disturbance estimation errors of a disturbance observer (IFTDO) and a sign function-based disturbance observer (TFTDO) in the longitudinal direction, the vertical direction and the pitching direction, and comparing the disturbance estimation errors, the disturbance observer provided by the invention has smaller estimation errors and better capability of predicting complex disturbance.
From the above description and demonstration, it can be derived that: the robot fish accurate terrain tracking control method based on the limited time disturbance observer provided by the invention has remarkable effectiveness and superiority, and can realize accurate terrain tracking control.
It will be understood that the invention has been described in terms of several embodiments, and that various changes and equivalents may be made to these features and embodiments by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (4)
1. A robot fish accurate terrain tracking control method based on a finite time disturbance observer is characterized in that: the method comprises the following steps:
s1, combining periodic power/moment input characteristics of the robot fish, improving a traditional underwater vehicle dynamics model to obtain an improved robot fish mathematical model, wherein the robot fish mathematical model comprises a kinematic model and an improved dynamics model,
the kinematic model is as follows:
wherein x and z respectively represent the position information of the robot fish under the geodetic coordinate system; θ is the pitch angle of the robot fish in the geodetic coordinate system; u and w respectively represent the heave and heave speeds of the robot fish under the satellite coordinate system; q is the pitch angle speed of the robot fish under the satellite coordinate system,
the improved robot fish dynamics model is established, and the specific process is as follows:
s11, establishing a robot fish dynamics model considering model uncertainty, environmental disturbance, periodic power/moment and input saturation:
wherein η= [ x, z, θ ]] T Representing position coordinates and pitch angles of the robot fish under an inertial coordinate system; v= [ u, w, q] T Representing the heave speed and the pitch angle speed of the robot fish under a satellite coordinate system; m is M A Representing an inertial matrix containing additional mass; c (C) A (v) Representing the nominal values of the coriolis force and centripetal force matrices; d (D) A (v) Representing a nominal value of a damping matrix for the robotic fish; g (η) represents a nominal value of the restoring force/moment of the robot fish; τ 0 Representing the average of the generalized input forces/moments; Δτ p A fluctuation value representing a generalized input force/moment; Δf represents a model and a parameter uncertainty term; d represents the disturbance of the external environment,
the lumped disturbance in the robot fish terrain tracking process can be expressed as:
δ f ＝Δτ p +Δf+d
s12, the improved dynamic model of the robot fish can be expressed as:
in the method, in the process of the invention,
is an inertia term; x is X {·} ,Z {·} And M {·} Representing the hydrodynamic coefficient; b and W respectively represent the buoyancy and gravity of the robot fish; z G And z B Respectively represents the gravity center and the floating center position of the robot fish in the z-axis direction under the satellite coordinate system,
s2, establishing a robot fish terrain tracking error equation;
selecting a coordinate on a desired topographic path as (x) R ,z R ) The coordinate point of (2) is used as the origin of the coordinate system, a coordinate system is established along the tangent of the terrain path and the direction perpendicular to the terrain path, the coordinate point can be expressed as a function of a parameter variable s, and the following robot fish terrain tracking error equation can be obtained based on coordinate transformation:
wherein x is R 、z R Respectively the abscissa and the ordinate, theta, of a virtual coordinate point on a desired terrain path R X is the rotation angle of the path tangent coordinate system relative to the inertial coordinate system e 、z e For the actual position x, z and the virtual point position x of the robot fish R 、z R The error of the robot fish terrain path tracking control error equation dynamics can be expressed as:
in the middle of
For the movement attack angle of robot fish, +.>
E is the combined speed of the robot fish movement θ ＝θ-θ R U is the difference between the course angle of the robot fish and the tangent direction of the path s The speed of a virtual point on a desired terrain path can be expressed as
For the path update law, ++>
Respectively the partial derivatives of the coordinates of the virtual point positions relative to the path parameters s;
s3, establishing a finite time convergence system,
consider the following finite time second order differentiator:
in the method, in the process of the invention,
is a continuous second order differentiable input signal; ρ 1 And ρ 2 For a given positive real number; zeta is a positive adjustable parameter; for any time T is greater than or equal to T f There is a constant epsilon>0 and T f >0 satisfies the following:
t in f Is the convergence time of the system;
s4, designing a finite time lumped disturbance observer based on S1 and S3,
defining a robot fish dynamics model comprising estimated states:
lumped disturbance sigma combined with improved dynamic model of robot fish fi (i=u, w, q) can be expressed as:
in the middle of
As an observation error of the velocity state,
therefore, the lumped finite time disturbance observer of the robot fish is designed to:
in the method, in the process of the invention,
is an estimate of the lumped disturbance; />
Observing an error signal for an input speed state;
s5, designing a limited-time terrain tracking guidance subsystem;
s6, designing a limited-time sliding mode surface, and designing a limited-time precise terrain tracking controller by combining the S2, the S4 and the S5.
2. The robot fish accurate terrain tracking control method based on the limited time disturbance observer according to claim 1, wherein the method comprises the following steps of: and S5, designing a limited time terrain tracking and guiding subsystem, wherein the specific process is as follows:
the topography tracking control guidance law of the robot fish with limited time is designed as follows:
wherein θ d To the desired pitch angle, k z Positive adjustable gain parameter, 0<ρ<1 is a positive constant value, delta is the forward looking distance,
robot fish topography tracking virtual point speed u s Path update law
The design is as follows:
wherein k is 0 、k 1 Positive adjustable gain parameter, 0<ρ s <1 is a positive constant.
3. The robot fish accurate terrain tracking control method based on the limited time disturbance observer according to claim 2, wherein the method comprises the following steps of: the S6 is provided with a limited time sliding mode surface, and is combined with the S2, the S4 and the S5 to design a limited time accurate terrain tracking controller, wherein the limited time accurate terrain tracking controller comprises pitch angle control and speed control, and the specific pitch angle control process is as follows:
s611, designing a self-adaptive expected pitch angle speed as follows:
wherein k is θ0 Is a positive adjustable parameter that is used to adjust the parameter,
to estimate the adaptive parameters of the upper boundary information ρ 1 、ρ 2 A positive adjustable gain parameter;
s612, selecting the following integral terminal sliding mode surface for stabilizing pitch angle speed tracking error:
wherein alpha is q 、β q Is a positive adjustable gain parameter that is used to adjust the gain,
is a positive constant value, q e ＝q-q d Tracking error for pitch angle rate;
s613, for input saturation of a processing system, designing a limited time auxiliary system as follows:
wherein χ is q As an auxiliary variable, deltaτ q ＝τ q -τ q0 K is the difference between the actual control and the nominal control χq 、k q1 Is a positive adjustable parameter;
s614, based on the above, the robot fish accurately tracks the control law tau in the topography q0 The design is as follows:
4. a robot fish accurate terrain tracking control method based on a finite time disturbance observer according to claim 3, characterized in that: the speed control concrete process in the S6 is as follows:
s621, designing a desired speed as follows:
wherein u is max To achieve the desired maximum speed, sigma 1 And u 0 Is a positive adjustable parameter;
s622, selecting the following integral terminal sliding mode surface for stabilizing speed tracking error:
wherein alpha is u 、β u Positive adjustable parameter, u e ＝u-u d Is a velocity tracking error;
s623, for processing input saturation, designing a limited time auxiliary system as follows:
wherein χ is u As an auxiliary variable, deltaτ u ＝τ u -τ u0 K is the difference between the actual control and the nominal control χu 、k u1 Is a positive adjustable parameter;
s624, based on the above, the robot fish accurately tracks the control law tau in the topography u0 The design is as follows:
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| CN114397899A (en) * | 2021-12-09 | 2022-04-26 | 中国科学院自动化研究所 | Bionic robot fish three-dimensional path tracking control method and device |
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