CN112882482B - Fixed time trajectory tracking control method based on autonomous underwater robot with predetermined performance constraint - Google Patents

Fixed time trajectory tracking control method based on autonomous underwater robot with predetermined performance constraint Download PDF

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CN112882482B
CN112882482B CN202110110667.7A CN202110110667A CN112882482B CN 112882482 B CN112882482 B CN 112882482B CN 202110110667 A CN202110110667 A CN 202110110667A CN 112882482 B CN112882482 B CN 112882482B
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宗广灯
崔佳雯
孙海滨
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Qufu Normal University
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Abstract

A fixed time trajectory tracking control based on autonomous underwater robots with predetermined performance constraints includes establishing a kinematic model and a kinetic model of the autonomous underwater robot with model uncertainty due to hydrodynamic forces and external disturbances, giving a desired tracking trajectory, and introduces auxiliary variables to convert the auxiliary variables into a tracking error system model of the autonomous underwater robot, then introducing a predetermined performance function, converting a tracking error system into a system with predetermined performance constraint, integrating model uncertainty, external interference and non-measurable speed into interference of the autonomous underwater robot, designing a fixed time extended state observer to estimate non-measurable speed and unknown interference, designing a continuous fixed time sliding mode surface based on an observer output value, and obtaining a fixed time continuous terminal sliding mode trajectory tracking control scheme of the underwater robot; the influence of model uncertainty and external interference on the autonomous underwater robot can be effectively reduced, and accurate track tracking is realized.

Description

Fixed time trajectory tracking control method based on autonomous underwater robot with preset performance constraint
Technical Field
The invention relates to a fixed time trajectory tracking control method based on an autonomous underwater robot with preset performance constraint, which is mainly applied to the fixed time trajectory tracking control of the autonomous underwater robot and belongs to the technical field of autonomous underwater robot control.
Background
In recent years, attention has been paid to autonomous underwater robots, which are robots having intelligent behaviors and integrating control devices, navigation positioning devices, self-diagnosis and fault processing devices, measurement devices and energy devices, wherein the control devices are control centers of autonomous underwater robots for underwater operations and are core technologies of robot control. However, model uncertainty caused by hydrodynamic force and the underwater environment in which the autonomous underwater robot is located have many interference factors, which affect the control device to correctly command the robot. Therefore, it is very important how to design a control scheme of the autonomous underwater robot to reduce model uncertainty and external disturbance without affecting the system and improve control performance.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at an autonomous underwater robot system with model uncertainty and external interference and constrained by preset performance, a fixed-time trajectory tracking control method is provided, model uncertainty and external interference factors are reduced, and trajectory tracking performance is good.
The technical solution of the invention is as follows: a fixed time trajectory tracking control method based on autonomous underwater robots with predetermined performance constraints comprises establishing kinematic and dynamic models of autonomous underwater robots containing model uncertainty caused by hydrodynamic forces and external disturbances and giving a desired tracking trajectory, and introduces auxiliary variables to convert the auxiliary variables into a tracking error system model of the autonomous underwater robot, then introducing a predetermined performance function, converting the tracking error system into a system with predetermined performance constraints, totaling model uncertainty, external interference and unmeasured system variables into lumped interference of the autonomous underwater robot, then designing a fixed time extended state observer to estimate the unmeasured speed and the unknown interference, and finally, designing a continuous fixed-time sliding mode surface based on the output value of the observer, and further obtaining a fixed-time continuous terminal sliding mode trajectory tracking control scheme of the underwater robot; the method can effectively reduce model uncertainty and external environment interference caused by hydrodynamic force of the autonomous underwater robot, realizes accurate trajectory tracking, and is suitable for fixed-time trajectory tracking control of the autonomous underwater robot.
1) Establishing a kinematic model and a dynamic model of the autonomous underwater robot containing model uncertainty and external interference caused by hydrodynamic force, giving an expression of a tracked expected track, and introducing an auxiliary variable to convert the auxiliary variable into a tracking error system model of the autonomous underwater robot;
2) introducing a preset performance function, converting a tracking error system into a system with preset performance constraint, and enabling model uncertainty, external interference and unmeasured system variables to be lumped interference of the autonomous underwater robot;
3) and designing a fixed-time extended state observer to estimate the undetectable speed and unknown interference, and designing a continuous fixed-time sliding mode surface based on the output value of the observer to obtain a fixed-time continuous terminal sliding mode trajectory tracking control scheme of the underwater robot.
Firstly, establishing a kinematic model and a dynamic model of an autonomous underwater robot containing model uncertainty and external interference
Figure BDA0002918836700000021
Where eta is [ x, y, z, phi, theta, psi]TRepresenting the position, roll, pitch and yaw of the autonomous underwater robot, u, v, w, p, q, r]TIndicating unmeasurable linear and angular velocities. J (eta) is a rotational inertia matrix,
Figure BDA0002918836700000022
is a matrix of the inertia, and the inertia matrix,
Figure BDA0002918836700000023
are a coriolis and a centripetal matrix of motion,
Figure BDA0002918836700000024
in order to provide a damping matrix, the damping matrix,
Figure BDA0002918836700000025
is a matrix of the weight force,
Figure BDA0002918836700000026
and
Figure BDA0002918836700000027
for a nominal matrix, Δ M, Δ C (upsilon), Δ D (upsilon), and Δ g (η) represent model uncertainties. τ (t) is a control input, dη(t) is external interference.
Then, the system (1.1) can be converted into
Figure BDA0002918836700000031
Wherein,
Figure BDA0002918836700000032
establishing an expected tracking trajectory as etad＝[xd,yd,zd,φd,θd,ψd]T，υdBy
Figure BDA0002918836700000033
It is given.
Define σ as J (η) upsilon, σd＝J(ηd)υdThe system (1.2) is converted into the following form
Figure BDA0002918836700000034
Defining a tracking error etae＝η-ηd,σe＝σ-σdAiming at the systems (1.2) and (1.3), establishing a tracking error system model of the autonomous underwater robot:
Figure BDA0002918836700000035
wherein,
Figure BDA00029188367000000311
representing lumped disturbances including undetectable states, model uncertainty, and external disturbances.
Second, a predetermined performance function is introduced
Figure BDA0002918836700000036
Using error transformation
Figure BDA0002918836700000037
Then the system (1.4) is converted into
Figure BDA0002918836700000038
Wherein N is1＝[N11,N12,...,N16]T，Ψ＝diag{ψ1,ψ2,...,ψ6}，
Figure BDA0002918836700000039
Figure BDA00029188367000000310
To add lumped interference after a predetermined performance.
Thirdly, designing the following fixed time extended state observer:
Figure BDA0002918836700000041
Figure BDA0002918836700000042
Figure BDA0002918836700000043
wherein,
Figure BDA0002918836700000044
and
Figure BDA0002918836700000045
are respectively N1、N2And estimate of Θ, mi、ni(i-1, 2,3) and l1Is the observer gain.
Based on the output value of the observer, the following continuous fixed-time sliding mode surfaces are designed
Figure BDA0002918836700000046
Wherein,
Figure BDA0002918836700000049
the following fixed time continuous terminal sliding mode controller is further designed
τ＝-MJ-1Ξ-1Ψ-1(τeq-τn),
Figure BDA0002918836700000047
Figure BDA0002918836700000048
Wherein, c1i,c2i,i＝1,2,3，ξ1，ξ2Is the controller gain.
Compared with the prior art, the invention has the advantages that: the invention relates to a fixed time trajectory tracking control method of an autonomous underwater robot with preset performance constraint, which provides an expected tracking trajectory and introduces preset performance function constraint aiming at a type of autonomous underwater robot system containing model uncertainty and external interference caused by hydrodynamic force, designs a fixed time extended state observer aiming at the model uncertainty, the external interference and the immeasurable speed, and finally provides a continuous fixed time sliding mode control strategy based on the output value of the observer; the fixed-time trajectory tracking control method of the autonomous underwater robot with the preset performance constraint can effectively reduce model uncertainty and external interference and accurately realize trajectory tracking of the autonomous underwater robot.
Drawings
Fig. 1 is a design flowchart of a fixed time trajectory tracking control method based on an autonomous underwater robot with predetermined performance constraints according to the present invention.
Detailed Description
As shown in fig. 1, the implementation steps of the present invention are as follows (the autonomous underwater robot system is taken as an example to illustrate the implementation of the method):
1) establishing a nominal kinematics model and a nominal dynamics model of an autonomous underwater robot containing model uncertainty external interference
Figure BDA0002918836700000051
Where eta is [ x, y, z, phi, theta, psi]TRepresenting the autonomous underwater robot's position, roll, pitch and yaw, u ═ u, v, w, p, q, r]TWhich is indicative of the linear and angular velocities,
Figure BDA0002918836700000052
is a rotational inertia matrix, S*＝sin(*)，C*＝cos(*)，T*＝tan(*)。
Figure BDA0002918836700000053
Is a matrix of the inertia, and is,
Figure BDA0002918836700000054
are a coriolis and a centripetal matrix of motion,
Figure BDA0002918836700000061
in order to provide a damping matrix, the damping matrix,
Figure BDA0002918836700000062
in order to be a lumped disturbance,
Figure BDA0002918836700000063
for the gravity matrix, the initial state is selected to be eta (0) ═ 1,1, -1, pi/6, pi/18]T，υ(0)＝[0.4,0.4,0.4,0.2,0.2,0.2]T。
Expected tracking trajectory ηd＝[4(1-cos(0.15t)),4sin(0.15t),-0.2t,0,0.0]T。
Define σ ═ J (η) υ, σd＝J(ηd)υdThe system (1.1) is converted into the following form
Figure BDA0002918836700000064
Defining a tracking error etae＝η-ηd,σe＝σ-σdAiming at the systems (1.2) and (1.3), a tracking error system model of the autonomous underwater robot is established
Figure BDA0002918836700000065
Wherein,
Figure BDA0002918836700000066
to represent lumped interference, including undetectable states, model uncertainty, and external interference.
2) Introducing the following predetermined performance function
Figure BDA0002918836700000067
Wherein
Figure BDA0002918836700000068
Using error transformation
Figure BDA0002918836700000069
Then the system (1.3) is converted into
Figure BDA0002918836700000071
Wherein, N1＝[N11,N12,...,N16]T，Ψ＝diag{ψ1,ψ2,...,ψ6}，
Figure BDA0002918836700000072
Figure BDA0002918836700000073
To add lumped interference after a predetermined performance.
3) Aiming at the system (1.4), the following fixed time extended state observer is designed
Figure BDA0002918836700000074
Figure BDA0002918836700000075
Figure BDA0002918836700000076
Wherein,
Figure BDA0002918836700000077
and
Figure BDA0002918836700000078
are each N1、N2And estimate of Θ, m1＝n1＝4,m2＝n2＝8,m3＝n31 is 8 and l10.8 is the observer gain.
Based on the output value of the observer, the following continuous fixed-time sliding mode surfaces are designed
Figure BDA0002918836700000079
Wherein,
Figure BDA00029188367000000712
the following fixed time continuous terminal sliding mode controller is further designed
τ＝-MJ-1Ξ-1Ψ-1(τeq-τn),
Figure BDA00029188367000000710
Figure BDA00029188367000000711
Wherein, c1i＝c2i＝5,i＝1,2,3，κ1＝7/13,κ′1＝19/13,κ2＝7/10,κ′2＝19/16，ξ1＝0.1，ξ2The controller gain is 0.1 and α is 1.5.

Claims (3)

1. A fixed time trajectory tracking control method based on autonomous underwater robots with predetermined performance constraints, characterized by comprising the following steps:
1) establishing a kinematic model and a dynamic model of the autonomous underwater robot containing model uncertainty and external interference caused by hydrodynamic force, giving an expected tracking track, and introducing an auxiliary variable to convert the expected tracking track into a tracking error system model of the autonomous underwater robot;
2) introducing a preset performance function, converting a tracking error system into a system with preset performance constraint, and integrating model uncertainty, external interference and immeasurable speed into interference of the autonomous underwater robot;
3) designing a fixed time extended state observer to estimate the undetectable speed and unknown interference, and designing a continuous fixed time sliding mode surface based on an observer output value to obtain a fixed time continuous terminal sliding mode trajectory tracking control scheme of the underwater robot;
wherein, the following fixed time extended state observer is designed:
Figure FDA0003642923740000011
Figure FDA0003642923740000012
Figure FDA0003642923740000013
wherein,
Figure FDA0003642923740000014
and
Figure FDA0003642923740000015
are each N1、N2And estimate of Θ, mi、ni(i is 1,2,3) and l1In order to obtain the gain of the observer,
based on the observer output value, the following continuous fixed-time sliding mode surfaces are designed:
Figure FDA0003642923740000016
wherein,
Figure FDA0003642923740000017
the following fixed-time continuous terminal sliding mode controller is further designed:
τ＝-MJ-1Ξ-1Ψ-1(τeq-τn),
Figure FDA0003642923740000021
Figure FDA0003642923740000022
wherein c is1i,c2i,i＝1,2,3，ξ1，ξ2Is the controller gain.
2. The method for controlling the fixed-time trajectory tracking based on the autonomous underwater robot with the predetermined performance constraint as claimed in claim 1, wherein in the step 1, the kinematic model and the dynamic model of the autonomous underwater robot with model uncertainty and external disturbance caused by hydrodynamic force are established by:
Figure FDA0003642923740000023
where η ═ x, y, z, phi, theta, psi]TThe position, the angle, the pitch angle and the yaw angle of the autonomous underwater robot are represented;
υ＝[u,ν,w,p,q,r]Trepresenting unmeasurable linear and angular velocities;
j (eta) is a rotational inertia matrix;
Figure FDA0003642923740000024
is an inertia matrix；
Figure FDA0003642923740000025
Coriolis and centripetal matrices;
Figure FDA0003642923740000026
is a damping matrix;
Figure FDA0003642923740000027
is a gravity matrix;
Figure FDA0003642923740000028
and
Figure FDA0003642923740000029
is a nominal matrix;
Δ M, Δ C (upsilon), Δ D (upsilon), and Δ g (η) represent model uncertainty;
τ (t) is a control input;
dη(t) is external interference;
then, the system (1.1) can be converted into:
Figure FDA00036429237400000210
wherein,
Figure FDA00036429237400000211
given the desired tracking trajectory as ηd＝[xd,yd,zd,φd,θd,ψd]T，υdBy
Figure FDA00036429237400000212
Given, definition σ ═J(η)υ,σd＝J(ηd)υdThe system (1.2) is converted into the following form:
Figure FDA0003642923740000031
defining a tracking error etae＝η-ηd,σe＝σ-σdAiming at the systems (1.2) and (1.3), a tracking error system model of the autonomous underwater robot is established as follows:
Figure FDA0003642923740000032
wherein
Figure FDA0003642923740000033
To represent lumped interference, including undetectable states, model uncertainty, and external interference.
3. A method for fixed time trajectory tracking control based on autonomous underwater vehicles with predefined performance constraints according to claim 1 or 2, characterized in that in step 2, the following predefined performance functions are introduced:
Figure FDA0003642923740000034
using error transformation
Figure FDA0003642923740000035
Then the system (1.4) is converted into:
Figure FDA0003642923740000036
wherein, N1＝[N11,N12,...,N16]T，Ψ＝diag{ψ1,ψ2,...,ψ6}，
Figure FDA0003642923740000037
Figure FDA0003642923740000038
To add lumped interference after a predetermined performance.
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