CN112346461A - Automatic guided vehicle collective filtering method considering unknown noise bounded characteristic - Google Patents

Automatic guided vehicle collective filtering method considering unknown noise bounded characteristic Download PDF

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CN112346461A
CN112346461A CN202011225275.7A CN202011225275A CN112346461A CN 112346461 A CN112346461 A CN 112346461A CN 202011225275 A CN202011225275 A CN 202011225275A CN 112346461 A CN112346461 A CN 112346461A
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杨昊
张依恋
顾伟
牛王强
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Shanghai Maritime University
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Abstract

The invention provides an automated guided vehicle ensemble filtering method considering unknown bounded characteristics of noise, which comprises the following steps: establishing an AGV kinematics model and a dynamics model according to information collected by a sensor; determining an iterative formula of the ensemble membership filter and deducing necessary conditions for ensuring that the actual state is contained in the predicted state ellipse; an optimal state prediction ellipse is determined that contains true state values at time k +1, where k represents the sampling time. The automatic guided vehicle collective filtering method considering the unknown bounded characteristic of the noise, provided by the invention, considers the unknown bounded characteristic of the noise, overcomes the defects of the traditional filtering method in the aspects of precision, cost, application range and the like, improves the control precision of AGV trajectory tracking, and ensures the working efficiency and safety of the AGV. The precision requirement on the sensor is reduced, and the research and development cost is reduced. By designing the ensemble filtering algorithm, the influence of unknown bounded characteristics of noise on the track tracking process is effectively eliminated, and the predicted value of the system state is obtained.

Description

Automatic guided vehicle collective filtering method considering unknown noise bounded characteristic
Technical Field
The invention relates to the technical field of AGV filtering methods, in particular to an automatic guided vehicle collective filtering method considering unknown bounded characteristics of noise.
Background
Automated guided vehicle, AGV for short, refers to an unmanned vehicle equipped with an automated navigation device and capable of traveling along a desired path. AGVs are commonly used in the industry for the transport of goods, and their presence greatly reduces labor costs and increases production efficiency. In addition, the AGV operates by a self-contained storage battery, has excellent characteristics such as no pollution and no noise, and is a hot topic of scientific research.
One core of AGV control and application is trajectory tracking technology. The safety and effectiveness of the work can be guaranteed only when the AGV can work along the predetermined trajectory with high accuracy. Most current research on trajectory tracking does not take into account the problem of the unknown bounded nature of noise. The trajectory tracking control accuracy can be improved more effectively if the influence of the unknown bounded characteristic of the noise on the AGV control process can be eliminated. Therefore, designing a proper and high-precision filter is one of the key problems for solving the AGV trajectory tracking. Currently, the existing research on filtering methods for solving the problem of unknown bounded characteristics of noise has some drawbacks. The precision of traditional least square filtering is low excessively, can't satisfy AGV trail tracking's precision demand. The kalman filtering method is a filtering algorithm with the advantages of real-time performance, high efficiency, convenience, high precision and the like, but the application of the kalman filtering method is limited under the condition that uncertainty exists in a system model and noise statistical characteristics. When the system noise is white gaussian noise with known statistical characteristics, the kalman filter has a good filtering effect, and when the statistical characteristics of the noise are unknown, the result of the kalman filtering cannot reach the corresponding standard. Most of noises suffered by the AGV during operation are unknown bounded noises, so that the traditional Kalman filtering method cannot effectively solve the problem of trajectory tracking of the AGV.
Disclosure of Invention
The invention aims to provide an automatic guided vehicle collective filtering method considering the unknown bounded characteristic of noise, so as to solve the problem that the traditional filtering technology has high sensor precision requirement, high delay, high cost and narrow application range, so that the adverse effect of the unknown bounded noise on the AGV track tracking process cannot be well eliminated.
In order to solve the technical problems, the technical scheme of the invention is as follows: an automated guided vehicle ensemble filtering method is provided that takes into account noise-unknown bounded characteristics, comprising: establishing an AGV kinematics model and a dynamics model according to a dynamics theory and the structural characteristics of the AGV; determining an iterative formula of the ensemble membership filter and deducing necessary conditions for ensuring that the actual state is contained in the predicted state ellipse; an optimal state prediction ellipse is determined that contains true state values at time k +1, where k represents the sampling time.
Further, the AGV kinematic equation is:
Figure BDA0002763446230000021
Figure BDA0002763446230000022
Figure BDA0002763446230000023
where x denotes a horizontal direction displacement of the AGV, y denotes a displacement in a vertical direction of the AGV, v is a velocity of the AGV, ψ denotes a yaw angle, s denotes a sideslip angle, and γ denotes a yaw rate. Considering that the actual working route is mostly a small curvature route, cos (ψ + s) ≈ 1 and sin (ψ + s) ≈ ψ + s are satisfied.
Further, after discretization, the AGV dynamics model equation is as follows:
Figure BDA0002763446230000024
Figure BDA0002763446230000025
wherein the content of the first and second substances,
Figure BDA0002763446230000026
for process noise and measurement noise corresponding to each state variable and output variable, the control variable u is set to [ v, δ]Delta is the deflection angle of the front wheel of the AGV and the output variable
Figure BDA0002763446230000029
Is set as [ x, y]。
Further, designing the collector filter: assume that at time k, both process noise and measurement noise are limited to the following ellipses:
Figure BDA0002763446230000027
Figure BDA0002763446230000028
wherein
Figure BDA0002763446230000031
Figure BDA0002763446230000032
The ellipse parameters, representing the known process noise and the measurement noise, respectively, the initial state values are also limited to the following ellipses:
Figure BDA0002763446230000033
wherein
Figure BDA0002763446230000034
For the parameters of the ellipse in the known initial state,
Figure BDA0002763446230000035
the state prediction value at the zero moment;
assume system input ukFiltering with constantThe design of the device, the iterative formula of the collective filtering is:
Figure BDA0002763446230000036
at time k, the true state ellipsoid parameter
Figure BDA0002763446230000037
And the current time state prediction value
Figure BDA0002763446230000038
All known cases, from the predicted ellipsoid field
Figure BDA0002763446230000039
To obtain
Figure BDA00027634462300000310
Where xi is a constant with an absolute value less than or equal to 1, EkIs that
Figure BDA00027634462300000318
The factorization of (a) is performed,
Figure BDA00027634462300000311
by definition
Figure BDA00027634462300000312
And
Figure BDA00027634462300000313
combining with AGV dynamics model equation (6), (7), state prediction ellipse at k +1 moment,
Figure BDA00027634462300000314
is represented as:
Figure BDA00027634462300000315
considering the definition of ξ and the noise model (5), the predicted ellipse at the moment of determination of k +1 has the followingAnd (3) limiting:
Figure BDA00027634462300000316
according to S-procedure, a sufficient condition for inequalities (8) and (9) to be satisfied simultaneously is that positive scaling τ exists1，τ2，τ3Satisfy the following requirements
Figure BDA00027634462300000317
By definition
Figure BDA0002763446230000041
The inequality (10) can be simplified to
Figure BDA0002763446230000042
Finally (11) is equated according to schur compnents as:
Figure BDA0002763446230000043
at time k if there is
Figure BDA0002763446230000044
And inequality (12) is satisfied, the state prediction ellipse ensuring that the real state value at the time k +1 is included in the current time is
Figure BDA0002763446230000045
Further, by solving an optimization problem:
Figure BDA0002763446230000046
and determining the optimal state prediction ellipse containing the real state value at the moment of k + 1.
The automatic guided vehicle collective filtering method considering the unknown bounded characteristic of the noise, provided by the invention, considers the unknown bounded characteristic of the noise, overcomes the defects of the traditional filtering method in the aspects of precision, cost, application range and the like, improves the control precision of AGV trajectory tracking, and ensures the working efficiency and safety of the AGV. The precision requirement on the sensor is reduced, and the research and development cost is reduced. By designing the ensemble filtering algorithm, an effective predicted value of the system state is obtained, and the influence of unknown bounded noise on the track tracking process is eliminated.
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The invention is further described with reference to the accompanying drawings:
FIG. 1 is a flowchart illustrating steps of a automated guided vehicle ensemble filtering method considering noise-unknown bounded characteristics according to an embodiment of the present invention;
FIG. 2 is an AGV kinematics model provided by an embodiment of the present invention;
FIG. 3 is a kinetic model of an AGV according to an embodiment of the present invention.
Detailed Description
The following describes in further detail the automated guided vehicle ensemble filtering method considering the noise unknown bounded characteristic according to the present invention with reference to the accompanying drawings and specific embodiments. Advantages and features of the present invention will become apparent from the following description and from the claims. It is to be noted that the drawings are in a very simplified form and are all used in a non-precise ratio for the purpose of facilitating and distinctly aiding in the description of the embodiments of the invention.
The core idea of the invention is that the automatic guided vehicle collective member filtering method considering the unknown bounded characteristic of the noise considers the unknown bounded characteristic of the noise, overcomes the defects of the traditional filtering method in the aspects of precision, cost, application range and the like, improves the control precision of the AGV track tracking, and ensures the working efficiency and safety of the AGV. The precision requirement on the sensor is reduced, and the research and development cost is reduced. By designing the ensemble filtering algorithm, an effective predicted value of the system state is obtained, and the influence of unknown bounded noise on the track tracking process is eliminated.
The technical scheme of the invention provides an automated guided vehicle collective filtering method considering unknown bounded characteristics of noise, and fig. 1 is a flow chart of steps of the automated guided vehicle collective filtering method considering unknown bounded characteristics of noise provided by the embodiment of the invention. Referring to fig. 1, a method for automated guided vehicle ensemble filtering that accounts for the unknown bounded nature of noise includes the steps of:
s11: establishing an AGV kinematics model and a dynamics model according to a dynamics theory and the structural characteristics of the AGV;
s12: determining an iterative formula of the ensemble membership filter and deducing necessary conditions for ensuring that the actual state is contained in the predicted state ellipse;
s13: an optimal state prediction ellipse is determined that contains true state values at time k +1, where k represents the sampling time.
FIG. 2 illustrates an AGV kinematics model according to an embodiment of the present invention. Referring to fig. 2, where x denotes a horizontal direction displacement of the AGV, y denotes a displacement in a vertical direction of the AGV, v is a velocity of the AGV, ψ denotes a yaw angle, s denotes a sideslip angle, and γ denotes a yaw rate. In real world conditions, the curvature of most roads is small, so the sideslip angle of the AGV does not change significantly, and the following assumptions can be made: the kinematic model of AGV can be described as follows, combining the assumptions of cos (ψ + s) 1 and sin (ψ + s) ψ + s:
Figure BDA0002763446230000051
Figure BDA0002763446230000052
Figure BDA0002763446230000053
FIG. 3 is a kinetic model of an AGV according to an embodiment of the present invention. Referring to FIG. 3, the lateral dynamics equation for an AGV may be expressed as:
Figure BDA0002763446230000054
Figure BDA0002763446230000055
where m denotes the mass of the AGV, l1Indicates the distance from the center of gravity of the AGV to the front end,/2Indicating the distance, I, from the AGV center of gravity to the rear endzRepresenting the moment of inertia of the AGV, ω and μ are unknown bounded noise corresponding to the inside and outside of the system, and δ is the AGV front wheel deflection angle. Also due to the small curvature motion of the AGV, we can assume sin δ to be 0 and cos δ to be 1.FyfAnd FyrRespectively, the tire forces received by the tires of the front and rear wheels, respectively, can be expressed as: fyf＝Cfαf，Fyr＝CrαrCornering stiffness C of front and rear tiresf，CrCan be approximately expressed as
Figure BDA0002763446230000061
Finally, we can complete the modeling of the dynamics of the AGV by combining equations (1) and (2):
Figure BDA0002763446230000062
Figure BDA0002763446230000063
Figure BDA0002763446230000064
Figure BDA0002763446230000065
Figure BDA0002763446230000066
wherein ω isx，ωy，ωψ，ωs，ωγRespectively, corresponding to the noise of the respective state variables. The state variable is set to x,y，ψ，s，γ]with the control variable u set to [ v, δ]Output variable
Figure BDA00027634462300000611
The linear model after discretization of equation (3) can be expressed as:
Figure BDA0002763446230000067
Figure BDA0002763446230000068
where k denotes the sampling instant, ω ═ ωx，ωy，ωψ，ωs，ωγ]，μ＝[μx，μy]Process noise and measurement noise corresponding to each state variable and output variable.
After modeling of the AGV is completed, the design of the collective filter is started. First assume that at time k, both process noise and measurement noise are limited to the following ellipses:
Figure BDA0002763446230000069
Figure BDA00027634462300000610
wherein
Figure BDA0002763446230000071
Figure BDA0002763446230000072
Elliptic parameters representing known process noise and measurement noise, respectively. Likewise, the initial state values are also limited to the following ellipses:
Figure BDA0002763446230000073
wherein
Figure BDA0002763446230000074
For the parameters of the ellipse in the known initial state,
Figure BDA0002763446230000075
the state prediction value at the zero moment.
The following membership filtering iterative formula is selected to calculate the parameters of the state prediction ellipse at each time instant:
Figure BDA0002763446230000076
wherein G isk，Fk，LkAre the unknown filter parameters. Combining the discrete time model of AGV can obtain
Figure BDA0002763446230000077
In the embodiment of the invention, in order to simplify the derivation step and emphasize the filtering process, the action of the controller is not considered, and the input u of the system is assumedkFilter design with constant. When equation Fk＝(I-LkCp)BpIn the derivation process when in place
Figure BDA0002763446230000078
The method can be simplified, the whole derivation process becomes simpler, and the simplified ensemble filtering iterative formula is as follows:
Figure BDA0002763446230000079
after determining the iterative formulation of the filter, we need to derive the necessary conditions to ensure that the actual state is contained in the predicted state ellipse. At time k, the true state ellipsoid parameter
Figure BDA00027634462300000719
And the current time state prediction value
Figure BDA00027634462300000710
All known cases, from the predicted ellipsoid field
Figure BDA00027634462300000711
Can obtain
Figure BDA00027634462300000712
Where xi is a constant with an absolute value less than or equal to 1, EkIs that
Figure BDA00027634462300000713
The factorization of (a) is performed,
Figure BDA00027634462300000714
by definition
Figure BDA00027634462300000715
And
Figure BDA00027634462300000716
the state prediction ellipse at the time k +1 in combination with equations (4), (6), (7)
Figure BDA00027634462300000717
Can be expressed as:
Figure BDA00027634462300000718
in addition, considering the definition of ξ and the noise model (5), the predicted ellipse at the moment of determination of k +1 has the following constraints:
Figure BDA0002763446230000081
according to S-procedure, a sufficient condition for inequalities (8) and (9) to be satisfied simultaneously is that positive scaling τ exists1，τ2，τ3Satisfy the following requirements
Figure BDA0002763446230000082
By definition
Figure BDA0002763446230000083
The inequality (10) can be simplified to
Figure BDA00027634462300000810
Finally (11) can be equated to:
Figure BDA0002763446230000085
from the above derivation, it can be seen that at time k, if any
Figure BDA0002763446230000086
And inequality (12) is satisfied, it can be ensured that the real state value at the time k +1 is included in the state prediction ellipse at that time
Figure BDA0002763446230000087
Finally, since (12) is a parameter
Figure BDA0002763446230000088
The optimal ellipse can be determined using a convex optimization method. By solving the following optimization problem:
Figure BDA0002763446230000089
an optimal state prediction ellipse can be determined for the time k +1, containing the true state values.
It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (5)

1. An automated guided vehicle ensemble filtering method that accounts for noise unknown bounded characteristics, comprising:
establishing an AGV kinematics model and a dynamics model according to a dynamics theory and the structural characteristics of the AGV;
determining an iterative formula of the ensemble membership filter and deducing necessary conditions for ensuring that the actual state is contained in the predicted state ellipse;
an optimal state prediction ellipse is determined that contains true state values at time k +1, where k represents the sampling time.
2. The automated guided vehicle ensemble filtering method of claim 1, taking into account noise unknown bounded characteristics, wherein said AGV kinematic equation is:
Figure FDA0002763446220000011
Figure FDA0002763446220000012
Figure FDA0002763446220000013
where x denotes a horizontal direction displacement of the AGV, y denotes a displacement in a vertical direction of the AGV, v is a speed of the AGV, ψ denotes a yaw angle, s denotes a sideslip angle, γ denotes a yaw rate, and cos (ψ + s) ≈ 1, sin (ψ + s) ≈ ψ + s are satisfied.
3. The automated guided vehicle collective filtering method considering unknown bounded characteristics of noise according to claim 2, wherein after discretizing time, the AGV dynamical model equation is:
Figure FDA0002763446220000014
Figure FDA0002763446220000015
wherein the content of the first and second substances,
Figure FDA0002763446220000016
ω＝[ωx，ωy，ωψ，ωs，ωγ]，μ＝[μx，μy]for process noise and measurement noise corresponding to each state variable and output variable, the control variable u is set to [ v, δ]Delta is the deflection angle of the front wheel of the AGV and the output variable
Figure FDA0002763446220000019
Is set as [ x, y]。
4. The automated guided vehicle ensemble filtering method of claim 3, considering unknown bounded characteristics of noise, wherein the ensemble filter is designed to: assume that at time k, both process noise and measurement noise are limited to the following ellipses:
Figure FDA0002763446220000017
Figure FDA0002763446220000018
wherein
Figure FDA0002763446220000021
Ellipses representing known process and measurement noise, respectivelyThe parameters, the initial state values, are also constrained in the following ellipses:
Figure FDA0002763446220000022
wherein
Figure FDA0002763446220000023
For the parameters of the ellipse in the known initial state,
Figure FDA0002763446220000024
the state prediction value at the zero moment;
assume system input ukThe filter design is carried out under the condition of constant, and the ensemble filtering iterative formula is as follows:
Figure FDA0002763446220000025
at time k, the true state ellipsoid parameter
Figure FDA0002763446220000026
And the current time state prediction value
Figure FDA0002763446220000027
All known cases, from the predicted ellipsoid field
Figure FDA0002763446220000028
To obtain
Figure FDA0002763446220000029
Where xi is a constant with an absolute value less than or equal to 1, EkIs that
Figure FDA00027634462200000210
The factorization of (a) is performed,
Figure FDA00027634462200000211
by definition
Figure FDA00027634462200000212
And
Figure FDA00027634462200000213
combining with AGV dynamics model equation (6), (7), state prediction ellipse at k +1 moment,
Figure FDA00027634462200000214
is represented as:
Figure FDA00027634462200000215
considering the definition of ξ and the noise model (5), the prediction ellipse at the moment of determination k +1 has the following constraints:
Figure FDA00027634462200000216
according to S-procedure, a sufficient condition for inequalities (8) and (9) to be satisfied simultaneously is that positive scaling τ exists1，τ2，τ3Satisfy the following requirements
Figure FDA00027634462200000217
By definition
Figure FDA0002763446220000031
The inequality (10) can be simplified to
Figure FDA0002763446220000032
Finally (11) is equated according to schur compnents as:
Figure FDA0002763446220000033
at time k if there is
Figure FDA0002763446220000034
And inequality (12) is satisfied, the state prediction ellipse ensuring that the real state value at the time k +1 is included in the current time is
Figure FDA0002763446220000035
5. The automated guided vehicle ensemble filtering method of claim 4, considering noise unknown bounded characteristics, by solving an optimization problem:
Figure FDA0002763446220000036
Figure FDA0002763446220000037
and determining the optimal state prediction ellipse containing the real state value at the moment of k + 1.
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Application publication date: 20210209