CN112241589A - Multi-underwater unmanned ship collaborative motion formation design method based on system observability degree - Google Patents

Multi-underwater unmanned ship collaborative motion formation design method based on system observability degree Download PDF

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CN112241589A
CN112241589A CN202011060137.8A CN202011060137A CN112241589A CN 112241589 A CN112241589 A CN 112241589A CN 202011060137 A CN202011060137 A CN 202011060137A CN 112241589 A CN112241589 A CN 112241589A
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张国昌
孙骞
于飞
李一兵
叶方
田园
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Abstract

The invention discloses a multi-underwater unmanned ship collaborative motion formation design method based on system observability degree, and belongs to the technical field of multi-UUV collaborative navigation positioning. Firstly, carrying out preliminary analysis on the observability of the system by utilizing a lie derivative weak observability theory to judge whether the system is observable or not, then carrying out quantitative analysis on the observability degree of the system by utilizing a matrix condition number theory, and finally designing a formation motion scheme of the multi-UUV cooperative system according to a system observability calculation formula obtained by calculation. Therefore, the measurement accuracy of the inertial device in the system is not changed, and the overall positioning accuracy of the system is improved by improving the observable degree of the system during operation. The invention respectively designs the single-main-boat cooperative system and the double-main-boat cooperative system, so that the cooperative system can keep higher observable degree in the operation process, and the aim of improving the overall positioning precision of the system is fulfilled.

Description

Multi-underwater unmanned ship collaborative motion formation design method based on system observability degree
Technical Field
The invention relates to a multi-underwater unmanned ship collaborative motion formation design method based on system observability degree, and belongs to the technical field of multi-UUV collaborative navigation positioning.
Background
In recent years, with the continuous and deep exploration of the sea, the related technology of the underwater unmanned ship is developed vigorously. An Unmanned Underwater Vehicle (UUV) is an Unmanned Underwater Vehicle which can independently complete tasks, has the advantages of small volume, low manufacturing cost, flexibility, reliability and the like, and plays an increasingly important role in military anti-diving, sea area reconnaissance and resource exploration. Because the underwater environment of the UUV is complex, high-frequency electromagnetic wave signals can be greatly attenuated when being transmitted underwater, and therefore navigation positioning information such as a GPS (global positioning system) based on electromagnetic wave signal transmission cannot be applied to a UUV system. This makes the navigation positioning problem a significant challenge for UUV development. An inertial navigation system consisting of a gyroscope and an accelerometer is the most commonly used underwater positioning method at present. However, due to the characteristic that the inertial component of the navigation positioning system can lead to continuous accumulation of positioning errors due to the prolonged underwater working time, the navigation positioning mode is not suitable for the UUV to carry out long-time underwater operation.
In a complex marine environment, compared with an electromagnetic wave communication technology, the underwater acoustic communication has small attenuation and long transmission distance during transmission. Therefore, in recent years, a cooperative positioning technology that measures relative movement distances between UUVs by using an underwater acoustic communication technology, shares position information with each other, and corrects self position information by using a certain filtering algorithm has become a key research problem in the field of UUV positioning. Compare in single UUV during operation and need all be equipped with the navigation positioning equipment of high accuracy for each ship in order to reach the purpose of accurate operation, many UUV systems only need be in the system for 1 ~ 2 main boats are equipped with the navigation positioning equipment of high accuracy, all the other navigation positioning equipment that only need carry communication equipment and low accuracy from the ship, utilize the location technology in coordination to make the holistic location ability of system improve greatly, greatly reduced the cost. Meanwhile, the UUV system has the following outstanding advantages in cooperative work: 1) the multi-UUV system can utilize the performance of each UUV to realize collective decision and system-level stability; 2) the multi-UUV system has high expandability, and the increase and decrease of individual UUV in the system can not cause decisive influence on the system; 3) the multi-UUV system has strong stability and expandability, so the robustness of the multi-UUV system is strong; 4) and the multi-UUV system works cooperatively, so that tasks which cannot be finished by the single UUV system can be finished.
The positioning accuracy of the multi-UUV cooperative positioning system is closely related to the observability of the system. Only when the cooperative system is observable in the motion process, the state of the system can be accurately estimated according to the measurement information in the system. However, if the system is not observable, the state of the system cannot be accurately estimated by any filtering estimation method. The observability degree of the system can quantitatively describe the observability condition of the system, when the observability degree of the system is zero, the system cannot be observed, and the state of the system cannot be accurately estimated through a filtering algorithm; the greater the observability of the system, the better the observability of the system, so that the state information estimated by the system from the metrology information is more accurate. Different formation configurations of the system result in different observability, and thus the accuracy of the positioning after filtering is also different.
Aiming at the problems, the invention designs a scheme for formation of multi-underwater unmanned ship cooperative motion based on the system observability degree, and designs a single-main-ship cooperative system and a double-main-ship cooperative system respectively, so that the cooperative systems can keep higher observability degree in the operation process, and the purpose of improving the overall positioning precision of the system is realized.
Disclosure of Invention
The invention aims to provide a method for designing a multi-underwater unmanned ship collaborative motion formation based on the system observability degree, which aims to solve the problems in the prior art, and designs a single-main-ship collaborative system and a double-main-ship collaborative system respectively so that the collaborative systems can keep a higher observability degree in the operation process, thereby achieving the purpose of improving the overall positioning precision of the system.
A multi-underwater unmanned ship collaborative motion formation design method based on system observability degrees comprises the following steps:
step one, performing observability degree calculation on a cooperative system;
and step two, designing a cooperative motion formation motion scheme according to the observability degree calculation formula obtained by calculation.
Further, in step one, when the number of the main boats is a single main boat system, the calculation method of the observability degree is as follows:
establishing a system state equation and a measurement equation as follows:
Figure BDA0002712159110000021
Figure BDA0002712159110000022
in the formula, V,
Figure BDA0002712159110000023
Respectively the speed and course angle f of the slave boat in a coordinate system established by taking the center of the master boat as an origin1、f2The equation of state representing the system is in the form of a continuous component along the x, y axes in the above coordinate system, (xk,yk)、
Figure BDA0002712159110000024
Respectively are the position coordinates of the slave boat and the position coordinates of the master boat, and have
Figure BDA0002712159110000025
Calculating the system model by adopting a lie derivative weak observability theory to obtain an observability matrix of the system:
Figure BDA0002712159110000031
in the formula，Lf 0h、Lf 1h represents the zeroth order lie derivative, the first order lie derivative of the measurement equation h with respect to the state equation f,
the determinant of the observability matrix is:
Figure BDA0002712159110000032
if the system model is observable, the system is required to observe the array full rank, when the matrix Obs is full rank, according to the knowledge of mathematical theory, the determinant of the matrix is not 0,
first, the system was analyzed for the case of an unobservable state, i.e., as obtained from det (obs) ═ 0:
Figure BDA0002712159110000033
the case where the system is not observable is known from the above equation as follows:
in the first case, the master UUV and the slave UUV keep relative static motion;
in the second case, the included angle between the position of the slave UUV and the connecting line of the position of the master UUV at the current moment is equal to the heading angle of the slave UUV,
through the analysis, when the master-slave UUV in the cooperative positioning system has the two motion modes, the system can not be observed, the two motion modes are the unobservable motion modes of the master-slave UUV system in the single-master-boat mode, and in addition, the rest master-slave UUV motion modes are the observable motion modes,
the matrix condition number theory is applied to carry out quantitative analysis on the observability of the system,
calculation of Obs. ObsT：
Figure BDA0002712159110000034
In the formula, ObsTBeing a transposed matrix of the observability matrix Obs,
the singular values are:
Figure BDA0002712159110000041
the observability of the system is:
Figure BDA0002712159110000042
further, in step one, when the number of the main boats is the double-main boat system, the observability degree calculation method comprises the following steps:
establishing a system state equation and a measurement equation as follows:
Figure BDA0002712159110000043
Figure BDA0002712159110000044
in the formula (x)k,yk)、
Figure BDA0002712159110000045
Respectively represents the position coordinates of a slave boat, a No. 1 main boat and a No. 2 main boat, h1、h2The expression of the distance from the slave boat to the No. 1 master boat and the expression of the distance from the slave boat to the No. 2 master boat are respectively expressed.
The observability matrix of the system obtained by applying the weak observability theory of the lie derivative is as follows:
Figure BDA0002712159110000046
from linear algebraic knowledge, the rank for an m × n matrix a is: rank (A) min (m, n), so that the rank of the observable matrix is at most 2,
the observability matrix can be written as:
Figure BDA0002712159110000051
firstly, analyzing the situation that the system is not observable, namely the observability matrix is not full rank, namely rank (a) ═ 1, and then obtaining:
Figure BDA0002712159110000052
and calculating to obtain:
Figure BDA0002712159110000053
it is known from the above equation that the system is not observable when the master and slave UUVs move on the same straight line,
the observation can be taken as half the square of the master-slave UUV distance, expressed as:
Figure BDA0002712159110000054
calculating the singular values of the observable array as:
Figure BDA0002712159110000055
in the formula (I), the compound is shown in the specification,
Figure BDA0002712159110000056
p1、p2the distances from the boat to the two main boats are respectively; theta is the included angle between the distance directions from the boat to the two main boats,
the observability of the system is:
Figure BDA0002712159110000057
further, in the second step, specifically, the observability degree simulation analysis of the collaborative system is performed according to the observability degree calculation formula obtained in the first step, and then a corresponding collaborative motion formation scheme is designed.
Further, a formation cooperative motion scheme of the single-main-boat multi-UUV cooperative system is as follows: the main boat moves forward at a constant speed, and the auxiliary boat moves forward spirally around the main boat.
Further, a formation cooperative motion scheme of the double-main-boat multi-UUV cooperative system is as follows: and a negative feedback link is added, and in an initial state, the slave boat is placed at a position with a higher observable degree in the system, namely the distance from the slave boat to the two master boats is equal, and the included angle between the distance from the slave boat to the two master boats and the direction of the distance from the slave boat to the two master boats is 90 degrees.
The main advantages of the invention are: the method for designing the coordinated movement formation of the unmanned ships under the water based on the system observability degree can achieve the purpose that the system integrally keeps high positioning precision by improving the observability degree of the system in the operation process of the system on the premise of not improving the measurement precision of inertia components in the coordinated system.
Drawings
FIG. 1 is a contour diagram of observability of a single main boat cooperative system;
FIG. 2 is a contour diagram of observability of a twin-main boat cooperative system;
FIG. 3 is a diagram of a master-slave UUV formation motion path of a single-master boat system;
FIG. 4 is a master-slave UUV formation design diagram of a twin-master boat system;
FIG. 5 is a projection of a single master boat collaborative system motion onto a two-dimensional space;
FIG. 6 is an observable degree of a single main boat cooperative system in a motion process;
FIG. 7 shows positioning errors during movement of the single-main-boat cooperative system;
FIG. 8 illustrates master and slave boat movements in a twin master boat cooperative system;
FIG. 9 is an observable degree of a twin-hulled water craft cooperative system during movement;
fig. 10 shows positioning errors during the movement of the twin-primary boat cooperative system.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a method for designing a multi-underwater unmanned ship coordinated movement formation based on system observability degree, which comprises the following steps:
step one, performing observability degree calculation on a cooperative system;
and step two, designing a cooperative motion formation motion scheme according to the observability degree calculation formula obtained by calculation.
In step one, when the number of the main boats is a single main boat system, the calculation method of the observability degree is as follows:
establishing a system state equation and a measurement equation as follows:
Figure BDA0002712159110000071
Figure BDA0002712159110000072
in the formula, V,
Figure BDA0002712159110000073
Speed and heading angle of the slave boat in a coordinate system established with the master boat as the center, (x)k,yk)、
Figure BDA0002712159110000074
Respectively as the position coordinates of the master boat and the slave boat,
calculating the system model by adopting a lie derivative weak observability theory to obtain an observability matrix of the system:
Figure BDA0002712159110000075
the determinant of the observability matrix is:
Figure BDA0002712159110000076
if the system model is observable, the system is required to observe the array full rank, when the matrix Obs is full rank, according to the knowledge of mathematical theory, the determinant of the matrix is not 0,
if the system model is observable, the system is required to observe the array full rank. When the matrix Obs is full rank, the determinant of the matrix is not 0 as known from the knowledge of mathematical theory. First, the system was analyzed for the case of an unobservable state, i.e., as obtained from det (obs) ═ 0:
Figure BDA0002712159110000077
the case where the system is not observable is known from the above equation as follows:
in the first case, the master UUV and the slave UUV keep relative static motion;
in the second case, the included angle between the position of the slave UUV and the connecting line of the position of the master UUV at the current moment is equal to the heading angle of the slave UUV,
through the analysis, when the master-slave UUV in the cooperative positioning system has the two motion modes, the system can not be observed, the two motion modes are the unobservable motion modes of the master-slave UUV system in the single-master-boat mode, and in addition, the rest master-slave UUV motion modes are the observable motion modes,
the matrix condition number theory is applied to carry out quantitative analysis on the observability of the system,
the method qualitatively analyzes whether the system can be observed, and quantitatively analyzes the observability of the system by applying the matrix condition number theory in order to better analyze the observability of the system.
Calculation of Obs. ObsT：
Figure BDA0002712159110000081
The singular values are:
Figure BDA0002712159110000082
the observability of the system is:
Figure BDA0002712159110000083
in step one, when the number of the main boats is the double-main boat system, the calculation method of the observability degree is as follows:
establishing a system state equation and a measurement equation as follows:
Figure BDA0002712159110000084
Figure BDA0002712159110000085
the observability matrix of the system obtained by applying the weak observability theory of the lie derivative is as follows:
Figure BDA0002712159110000091
from linear algebraic knowledge, the rank for an m × n matrix a is: rank (A) min (m, n), so that the rank of the observable matrix is at most 2,
the observability matrix can be written as:
Figure BDA0002712159110000092
firstly, analyzing the situation that the system is not observable, namely the observability matrix is not full rank, namely rank (a) ═ 1, and then obtaining:
Figure BDA0002712159110000093
and calculating to obtain:
Figure BDA0002712159110000094
it is known from the above equation that the system is not observable when the master and slave UUVs move on the same straight line,
for the convenience of subsequent calculation, the observation quantity can be taken as half of the square of the distance between the master and slave UUVs, and is expressed as:
Figure BDA0002712159110000095
calculating the singular values of the observable array as:
Figure BDA0002712159110000096
in the formula (I), the compound is shown in the specification,
Figure BDA0002712159110000101
p1、p2the distances from the boat to the two main boats are respectively; theta is the included angle between the distance directions from the boat to the two main boats,
the observability of the system is:
Figure BDA0002712159110000102
in the second step, specifically, simulation analysis of the observability degree of the collaborative system is performed according to the observability degree calculation formula obtained in the first step, and then a corresponding collaborative motion formation scheme is designed.
According to the system observability degree calculation formula obtained through calculation and the simulation graph, a single-master-boat collaborative system formation motion scheme can be designed to be that the master UUV makes uniform linear motion, and the slave UUV makes spiral motion around the master UUV. The motion mode ensures that a master UUV and a slave UUV in the cooperative system have relative motion at the moment, and simultaneously, a higher observable degree can be kept in the whole motion process.
The formation movement scheme of the double-main-boat collaborative system can be designed according to the calculated system observability degree calculation formula and the simulation graph, the formation design is shown in the attached figure 4, the distance from the boat to the two main boats is equal initially, the included angle between the distance from the boat to the two main boats is 90 degrees, in order to ensure that the cooperative system can still keep higher observability degree in the operation process, a negative feedback link is added, namely the two main boats can transmit the position information of the two main boats to the auxiliary boat at any time, the auxiliary boat calculates the optimal position of the observability degree according to the position information of the main boat and the auxiliary boat, and modifies the course angle of the auxiliary boat, so that the system can always keep higher observability degree.
The present invention will be described in detail with reference to specific embodiments.
In order to verify the effectiveness of the method, software is used for simulating the multi-underwater unmanned ship coordinated movement formation design based on the system observability degree.
As shown in fig. 1, which is a contour diagram of observable degree of a single main boat cooperative system, it can be seen that the observable degree of the system spreads out in a circular ring form. Fig. 2 is a contour diagram of the observable degree of the double-main boat cooperative system, and it can be seen from the contour diagram that the observable degree of the system is the largest when the ratio of the distances from the boat to the two main boats is 1 and the included angle between the distances from the boat to the two main boats is 90 degrees. Fig. 3 is a movement path of a master-slave UUV in a single-master-boat cooperative system mode, and fig. 4 is a movement route design of the master-slave UUV in a double-master-boat cooperative system mode.
Fig. 5, 6 and 7 show the motion simulation of the single main boat cooperative system, wherein the simulation conditions are as follows: initial position of main boat (x)m,ym) (0m, -20m), speed 4m/s, course 30 °; the initial position of the slave boat is (0m,0m), the speed of the slave boat is 4m/s along the y-axis direction, and the speed of the slave boat is 5m/s along the x-axis direction. In the simulation, the velocity noise σ from the boatv＝(0.5m/s)2Acceleration ofDegree noise sigmaa＝(0.01m/s2)2Gyroscope for measuring noise
Figure BDA0002712159110000111
Distance observation noise σh＝(1m)2All are uncorrelated additive noise. And updating the estimation of the position information by using a filtering algorithm, wherein the period of each filtering estimation is 1 s. It can be seen from the figure that the system can keep a high observability degree most of the time in the operation process, and as can be seen from fig. 7, the positioning error of the ship motion trail obtained by using the EKF and UKF filtering algorithm is in a convergent form and is very small.
Fig. 8, 9 and 10 are the motion simulation of the twin-main boat cooperative system, and the simulation conditions are as follows: the initial position of the main boat 1 is (10m ), the initial speed is 3m/s, and the course is 0; the initial position of the main boat 2 is (10m,110m), the initial speed is still 4m/s, and the heading is still set to be-30 degrees; according to a calculation formula of the system observability degree, the boat position is (60m ) at the moment, and the boat speed is 4 m/s. And the velocity measurement noise sigma in the systemv＝(0.5m/s)2Gyroscopic measurement of noise
Figure BDA0002712159110000112
Distance measurement noise sigmah1＝σh2＝(1m)2. The system can automatically adjust the course of the slave boat through a negative feedback link after the motion trail of the master boat and the slave boat is interfered, and the higher observable degree is kept in the motion process. As can be seen from fig. 10, the co-location error of the system obtained by the filtering algorithm is in a converged form and is very small.
The effectiveness of the method for designing formation movement of the multi-underwater unmanned ship collaborative system based on the system observability degree is verified through the experiment, and the purpose that the system integrally keeps higher positioning precision is achieved by improving the observability degree of the system in the system operation process on the premise that the measurement precision of inertial components in the collaborative system is not improved.

Claims (6)

1. A multi-underwater unmanned ship collaborative motion formation design method based on system observability degrees is characterized by comprising the following steps:
step one, performing observability degree calculation on a cooperative system;
and step two, designing a cooperative motion formation motion scheme according to the observability degree calculation formula obtained by calculation.
2. The method for designing the formation of coordinated motions of unmanned underwater vehicles based on the system observability according to claim 1, wherein in the step one, when the number of main ships is a single main ship system, the observability calculation method comprises the following steps:
establishing a system state equation and a measurement equation as follows:
Figure FDA0002712159100000011
Figure FDA0002712159100000012
in the formula, V,
Figure FDA0002712159100000013
Respectively the speed and course angle f of the slave boat in a coordinate system established by taking the center of the master boat as an origin1、f2The equation of state representing the system is in the form of a continuous component along the x, y axes in the above coordinate system, (xk,yk)、
Figure FDA0002712159100000014
Respectively are the position coordinates of the slave boat and the position coordinates of the master boat, and have
Figure FDA0002712159100000015
Calculating the system model by adopting a lie derivative weak observability theory to obtain an observability matrix of the system:
Figure FDA0002712159100000016
in the formula, Lf 0h、Lf 1h represents the zeroth order lie derivative, the first order lie derivative of the measurement equation h with respect to the state equation f,
the determinant of the observability matrix is:
Figure FDA0002712159100000017
if the system model is observable, the system is required to observe the array full rank, when the matrix Obs is full rank, according to the knowledge of mathematical theory, the determinant of the matrix is not 0,
first, the system was analyzed for the case of an unobservable state, i.e., as obtained from det (obs) ═ 0:
Figure FDA0002712159100000021
the case where the system is not observable is known from the above equation as follows:
in the first case, the master UUV and the slave UUV keep relative static motion;
in the second case, the included angle between the position of the slave UUV and the connecting line of the position of the master UUV at the current moment is equal to the heading angle of the slave UUV,
through the analysis, when the master-slave UUV in the cooperative positioning system has the two motion modes, the system can not be observed, the two motion modes are the unobservable motion modes of the master-slave UUV system in the single-master-boat mode, and in addition, the rest master-slave UUV motion modes are the observable motion modes,
the matrix condition number theory is applied to carry out quantitative analysis on the observability of the system,
calculation of Obs. ObsT：
Figure FDA0002712159100000022
In the formula, ObsTBeing a transposed matrix of the observability matrix Obs,
the singular values are:
Figure FDA0002712159100000023
the observability of the system is:
Figure FDA0002712159100000024
3. the method for designing the formation of cooperative motion of unmanned underwater vehicles based on the system observability according to claim 1, wherein in the first step, when the number of the main ships is the double-main ship system, the observability calculation method comprises the following steps:
establishing a system state equation and a measurement equation as follows:
Figure FDA0002712159100000025
Figure FDA0002712159100000031
in the formula (x)k,yk)、
Figure FDA0002712159100000032
Respectively represents the position coordinates of a slave boat, a No. 1 main boat and a No. 2 main boat, h1、h2The expression of the distance from the slave boat to the No. 1 master boat and the expression of the distance from the slave boat to the No. 2 master boat are respectively expressed.
The observability matrix of the system obtained by applying the weak observability theory of the lie derivative is as follows:
Figure FDA0002712159100000033
from linear algebraic knowledge, the rank for an m × n matrix a is: rank (A) min (m, n), so that the rank of the observable matrix is at most 2,
the observability matrix can be written as:
Figure FDA0002712159100000034
firstly, analyzing the situation that the system is not observable, namely the observability matrix is not full rank, namely rank (a) ═ 1, and then obtaining:
Figure FDA0002712159100000035
and calculating to obtain:
Figure FDA0002712159100000036
it is known from the above equation that the system is not observable when the master and slave UUVs move on the same straight line,
the observation can be taken as half the square of the master-slave UUV distance, expressed as:
Figure FDA0002712159100000041
calculating the singular values of the observable array as:
Figure FDA0002712159100000042
in the formula (I), the compound is shown in the specification,
Figure FDA0002712159100000043
p1、p2the distances from the boat to the two main boats are respectively; theta is the included angle between the distance directions from the boat to the two main boats,
the observability of the system is:
Figure FDA0002712159100000044
4. the method for designing the coordinated movement formation of the unmanned underwater vehicles based on the system observability according to claim 1, wherein in the second step, specifically, simulation analysis of the observability of the coordinated system is performed according to the observability calculation formula obtained in the first step, and then a corresponding coordinated movement formation scheme is designed.
5. The method for designing the formation of cooperative motion of the unmanned underwater vehicles based on the system observability degree according to claim 4, wherein the formation cooperative motion scheme of the cooperative system of the multi-UUV single-main-boat is as follows: the main boat moves forward at a constant speed, and the auxiliary boat moves forward spirally around the main boat.
6. The method for designing the formation of cooperative motion of the unmanned underwater vehicles based on the system observability degree of claim 4, wherein the formation cooperative motion scheme of the multi-UUV cooperative system of the double-master-boat is as follows: and a negative feedback link is added, and in an initial state, the slave boat is placed at a position with a higher observable degree in the system, namely the distance from the slave boat to the two master boats is equal, and the included angle between the distance from the slave boat to the two master boats and the direction of the distance from the slave boat to the two master boats is 90 degrees.
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