CN107816994B - Underwater positioning method for indoor limited structured water area - Google Patents

Underwater positioning method for indoor limited structured water area Download PDF

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CN107816994B
CN107816994B CN201710978261.4A CN201710978261A CN107816994B CN 107816994 B CN107816994 B CN 107816994B CN 201710978261 A CN201710978261 A CN 201710978261A CN 107816994 B CN107816994 B CN 107816994B
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underwater robot
wall surface
altimeter
pool
coordinates
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CN107816994A (en
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陶建国
罗阳
李战东
邓立平
李�浩
那强
丁亮
邓宗全
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Harbin Institute of Technology
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G01C21/206—Instruments for performing navigational calculations specially adapted for indoor navigation

Abstract

The invention relates to an underwater positioning method for an indoor limited structured water area, in particular to an underwater positioning method, aiming at solving the problem that the existing positioning method cannot realize high-precision positioning of an indoor narrow poolRBMaking a straight line l with a slope tan α0(ii) a Then passing through point CBLMake a straight line l0Perpendicular line l1；l0And l1Dividing the plane x 'Oy' into four regions; thirdly, determining which area of the four areas the underwater robot belongs to according to the position of the underwater robot at the time t-1, the attitude and heading reference system at the time t and data returned by the front altimeter and the side altimeter; and fourthly, calculating the position of the underwater robot at the time t by adopting a multi-zone division positioning algorithm according to the area to which the underwater robot belongs. The invention is used for the field of underwater positioning of robots.

Description

Underwater positioning method for indoor limited structured water area
Technical Field
The invention relates to an underwater positioning method.
Background
The spent fuel pool is mainly used for storing and cooling reactor core fuel of the reactor. Due to the strong radiation, the underwater robot is used for replacing manpower to complete daily maintenance and overhaul work of the water pool. Because the spent fuel pool is an indoor limited structured water area, the positioning of the underwater robot becomes a difficult problem. The current mature underwater positioning method mainly comprises the following steps: 1) the dead reckoning is realized by using an inertial navigation system, but the dead reckoning has low positioning precision and large error accumulation and cannot perform high-precision positioning for a long time. 2) Underwater acoustic positioning, including long baseline positioning, short baseline positioning, ultra-short baseline positioning, etc., is only applicable to open water areas such as ocean rivers. 3) Global navigation satellite system positioning, such as GPS positioning, beidou satellite positioning, etc., cannot be applied to indoor environments. 4) The acousto-optic imaging positioning is realized by utilizing images of sensors such as sonar, Doppler and a camera, but is seriously interfered in narrow water areas. Because the underwater environment of the spent fuel pool is special, the positioning method can not realize underwater high-precision positioning of the spent fuel pool.
Disclosure of Invention
The invention aims to solve the problem that the existing positioning method cannot realize high-precision positioning of an indoor narrow pool, and provides an underwater positioning method for an indoor limited structured water area.
The underwater positioning method for the indoor limited structured water area comprises the following specific processes:
step one, rotating a geodetic coordinate system O-xyz by an angle beta according to a yaw angle of the underwater robot to obtain a new coordinate system O-x ' y ' z ';
step two, according to the new coordinate system O-x ' y ' z ' obtained in the step one, the pool wall surfaces are sequentially represented as R, B, L and U in the O-x ' y ' z ', wherein the positive direction of the x ' axis corresponds to the pool wall surface R, the positive direction of the y ' axis corresponds to the pool wall surface B, and the negative direction of the x ' axis corresponds to the pool wall surface L; the negative direction of the y' axis corresponds to the wall surface U of the pool;
passing point CRBMaking a straight line l with a slope tan α0(ii) a Then passing through point CBLMake a straight line l0Perpendicular line l1Slope of-1/tan α; /)0And l1Dividing the pool plane x 'Oy' into four regions;
point CRBIs an intersection point formed by the pool wall surface R and the pool wall surface B on a plane x 'Oy';
point CBLIs an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy';
thirdly, determining which of the four areas the underwater robot belongs to according to the position of the underwater robot at the time t-1, the attitude and heading reference system at the time t and data returned by the front altimeter and the side altimeter;
and step four, calculating the position of the underwater robot at the time t by adopting a multi-zone division positioning algorithm according to the area to which the underwater robot belongs.
The invention has the beneficial effects that:
the invention adopts an attitude heading reference sensor and 2 underwater height sensors to realize the underwater positioning of the indoor limited structured water area. The data of the sensor are fused by using the multi-zone division positioning algorithm (MRDL algorithm), so that the high-precision underwater positioning effect is obtained. Experiments show that in a water pool with 8m by 4m, the average positioning error is controlled within 90mm, and the authenticity of the invention is proved. The problem that the high-precision positioning of an indoor narrow pool cannot be achieved by an existing positioning method is solved.
In the embodiment of the invention, three groups of experiments are carried out in the water pool, namely rectangular motion, oblique line motion and circular arc motion, in the rectangular motion, the algorithm positioning result is almost coincident with the real motion track, and the maximum error is not more than 6 mm. In oblique line movement, the positioning effect is also ideal, and the maximum error does not exceed 7 mm. Because the position and the angle of the circular arc motion are changed simultaneously, the circular arc motion is the motion which is most difficult to position in the positioning method, so that the positioning error is the largest, the maximum error is 40mm, and the positioning requirement can still be met. As shown in fig. 13a, 13b, 14a, 14b, 15a, 15 b.
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FIG. 1 is a schematic view of a sensor installation according to the present invention;
FIG. 2 is a schematic diagram of a pool coordinate system of the present invention, with side I being pool wall 1, side II being pool wall 2, side III being pool wall 3, and side IV being pool wall 4;
fig. 3 is a schematic diagram of l0 and l1 dividing a plane x 'Oy' into four regions, UWV being an underwater robot;
FIG. 4 is a schematic diagram of a robot located in area 1;
FIG. 5 is a schematic diagram of the robot located in area 2;
FIG. 6 is a schematic view of dead reckoning;
FIG. 7 is a schematic view of the transmission angle of the altimeter;
FIG. 8 is a schematic view of the distance of the underwater robot from the boundary;
FIG. 9 is a graph showing the relationship between p and d at different λ;
FIG. 10 is a diagram of an underwater robot;
FIG. 11a is a schematic view of an attitude and heading reference system model Mti-G-700;
FIG. 11b is a schematic view of an underwater altimeter model ISA-500L;
FIG. 12 is an experimental environment;
FIG. 13a is a diagram of a positioning result of rectangular motion, where Real track is the Real coordinates of the underwater robot, and Estimated track is the coordinates of the underwater robot obtained by the underwater positioning method of the present invention;
FIG. 13b is a plot of positioning error for the rectangular motion of FIG. 13a, with localization error being the positioning error and the slope of the line;
FIG. 14a is a diagram of the positioning result of the diagonal movement;
FIG. 14b is a plot of positioning error for the diagonal motion of FIG. 14 a;
FIG. 15a is a diagram of the positioning result of the circular motion;
fig. 15b is a plot of positioning error for the circular arc motion of fig. 15 a.
Detailed Description
The first embodiment is as follows: the underwater positioning method for the indoor limited structured water area of the embodiment comprises the following specific processes:
step one, rotating a geodetic coordinate system O-xyz by an angle beta according to a yaw angle of the underwater robot to obtain a new coordinate system O-x ' y ' z ';
step two, according to the new coordinate system O-x ' y ' z ' obtained in the step one, the pool wall surfaces are sequentially represented as R, B, L and U in the O-x ' y ' z ', wherein the positive direction of the x ' axis corresponds to the pool wall surface R, the positive direction of the y ' axis corresponds to the pool wall surface B, and the negative direction of the x ' axis corresponds to the pool wall surface L; the negative direction of the y' axis corresponds to the wall surface U of the pool;
passing point CRBMaking a straight line l with a slope tan α0(ii) a Then passing through point CBLMake a straight line l0Perpendicular line l1Slope of-1/tan α; /)0And l1Dividing a pool plane x 'Oy' (a plane formed by the walls R, B, U and L of the pool) into four areas; (line l0、l1The area enclosed by the pool wall surface U and the pool wall surface R is an area 1 and a straight line l0、l1The area enclosed by the pool wall surface U and the pool wall surface L is an area 2 and a straight line L0、l1The area enclosed by the wall surface L of the water pool is an area 3, a straight line L0、l1The area surrounded by the pool wall B is an area 4, areas 1 and 3 are opposite vertex angles, and areas 2 and 4 are opposite vertex angles);
point CRBIs an intersection point formed by the pool wall surface R and the pool wall surface B on a plane x 'Oy';
point CBLIs an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy';
thirdly, determining which area of the four areas the underwater robot belongs to according to the position of the underwater robot at the t-1 moment, an Attitude and Heading Reference System (AHRS) at the t moment and data returned by the front altimeter and the side altimeter;
and fourthly, calculating the position of the underwater robot at the t moment by adopting a multi-zone division positioning algorithm (MRDL algorithm) according to the area to which the underwater robot belongs.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the first step, a geodetic coordinate system O-xyz is rotated by an angle beta according to the yaw angle of the underwater robot to obtain a new coordinate system O-x ' y ' z '; the specific process is as follows:
aiming at the problem that an indoor limited water area in a spent fuel pool is difficult to accurately position, a novel underwater positioning method combining an attitude heading reference system and an altimeter is provided. As shown in figure 1, two height gauges are respectively arranged on the front and the side of the machine body and form an included angle of 90 degrees. An Attitude Heading Reference System (AHRS) is mounted within the nacelle for detecting the attitude of the body.
The attitude of the underwater robot is represented as [ phi, theta, psi ═ phi]TWherein phi is a roll angle, theta is a pitch angle, and psi is a yaw angle; the distance data measured by the two altimeters are dfAnd ds(ii) a The two altimeters are respectively arranged in front of and at the side of the underwater robot and form an included angle of 90 degrees, and an Attitude Heading Reference System (AHRS) is arranged in a cabin of the underwater robot;
dfdata returned for the front altimeter (distance of the front altimeter to the wall surface in the emission direction), dsData returned for the side altimeter (distance of the front altimeter to the wall surface in the emission direction);
for ease of calculation, the following assumptions are made:
1) the underwater robot always keeps horizontal in the attitude in water, so phi is 0;
2) the transmission angle of the altimeter is small enough, and the ultrasonic wave transmitted by the altimeter can be approximately regarded as a ray;
the spent fuel pool is a standard rectangular pool, such as [ D, W, H ]]TThe length, width and height of the pool are shown, and T is a transposition; the pool coordinate system is shown in figure 2.
Let l be D/2 and W be W/2, so the equation for the four walls of the pool is:
wall surface I: x-l ═ 0
Wall surface II: y-w is 0
Wall surface III: x + l is 0
Wall surface IV: y + w is 0
For simple calculation, the four equations are combined into a standard plane equation form
Figure BDA0001437581060000041
Wherein Θ is [ x, y, z ═ z]T，NiIs the normal vector of pool wall i, hence N1＝[1,0,0]T，N2＝[0,1,0]T，N3＝[-1,0,0]TN4＝[0,-1,0]T；piIs the intersection point of the pool coordinate axis and the pool wall i under the geodetic coordinate system O-xyz, so p1＝[l,0,0]T，p2＝[0,w,0]T，p3＝[-l,0,0]T，p4＝[0,-w,0]T(ii) a x is an x-axis coordinate in a pool coordinate system, y is a y-axis coordinate in the pool coordinate system, z is a z-axis coordinate in the pool coordinate system, l is a half of the length of the pool, and w is a half of the width of the pool;
the yaw angle of the underwater robot satisfies psi ∈ [ -pi, pi), and the yaw angle of the underwater robot is divided into four regions [ -pi, -pi/2), [ -pi/2, 0), [0, pi/2), [ pi/2, pi) according to the value of psi;
counterclockwise rotating the geodetic coordinate system O-xyz by an angle beta to generate a new coordinate system O-x ' y ' z ', wherein the angle beta belongs to { -pi, -pi/2, 0, pi/2 }; the wall surfaces of the pool are sequentially represented as R, B, L and U in O-x 'y' z ', wherein the positive direction of the x' axis corresponds to the wall surface R of the pool, the positive direction of the y 'axis corresponds to the wall surface B of the pool, and the negative direction of the x' axis corresponds to the wall surface L of the pool; the negative direction of the y' axis corresponds to the wall surface U of the pool;
o-x 'y' z 'can ensure that the included angle alpha between the underwater robot and Ox' is psi-beta epsilon [0, pi/2);
let thetat＝[xt,yt,zt]TIs the coordinate theta of the underwater robot in a geodetic coordinate system O-xyz't＝[x′t,y′t,z′t]TCoordinates of the underwater robot in O-x ' y ' z '; t is time;
then
Θ′＝Cz(β)·Θ
Wherein
Figure BDA0001437581060000051
Cz(β) is an intermediate variable;
the z coordinate of the underwater robot is directly measured by using the pressure sensor, so that the theta can be simplified to be [ x, y ]]T；
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: in the second step, according to the new coordinate system O-x ' y ' z ' obtained in the first step, the wall surfaces of the pool are sequentially represented as R, B, L and U in the O-x ' y ' z ', wherein the positive direction of the x ' axis corresponds to the wall surface R of the pool, the positive direction of the y ' axis corresponds to the wall surface B of the pool, and the negative direction of the x ' axis corresponds to the wall surface L of the pool; the negative direction of the y' axis corresponds to the wall surface U of the pool; passing point CRBMaking a straight line l with a slope tan α0(ii) a Then passing through point CBLMake a straight line l0Perpendicular line l1Slope of-1/tan α; /)0And l1Dividing a pool plane x 'Oy' (a plane formed by the walls R, B, U and L of the pool) into four areas; the specific process is as follows:
in O-x ' y ' z ', as shown in FIG. 3, the point C is crossedRBMaking a straight line l with a slope tan α0Then passing through point CBLMake a straight line l0Perpendicular line l1The slope is-1/tan α, l0And l1The plane x 'Oy' is divided into four regions,
point CRBIs an intersection point formed by the pool wall surface R and the pool wall surface B on a plane x 'Oy';
point CBLIs an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy';
the size of the pool is defined in O-x ' y ' z ' as:
Figure BDA0001437581060000061
wherein, p'RIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface R of the sink'RIs origin O to p'RDistance of p'LIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface L of the sink'LIs origin O to p'LDistance of p'BIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface B of the sink'BIs origin O to p'BDistance of p'UIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface U of the sink'UIs origin O to p'UThe distance of (a) is l or w, and b is l or w.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: determining which area of the four areas the underwater robot belongs to according to the position of the underwater robot at the time t-1, an Attitude and Heading Reference System (AHRS) at the time t and data returned by the front altimeter and the side altimeter in the third step; the specific process is as follows:
altimeter data correction
As shown in FIG. 7, let the transmission angle of the altimeter be half, the transmission vector of the front-end altimeter is in the robot body coordinate system O-xbybzbThe following (robot body coordinate system is fixed to the robot body and moves with the robot) is expressed as:
Figure BDA0001437581060000062
whereinfIs half of the emission angle of the front altimeter, kfIs [0,2 π ]]Any value within the interval of time is,
Figure BDA0001437581060000063
is the transmission vector of the front altimeter,
Figure BDA0001437581060000064
emission vector of side altimeter is in robot body coordinate system O-xbybzbThe following is expressed as:
Figure BDA0001437581060000065
whereinsIs half of the emission angle, k, of the lateral altimetersIs [0,2 π ]]Any value within the interval of time is,
Figure BDA0001437581060000066
is the transmission vector of the front altimeter,
Figure BDA0001437581060000067
the emission vectors of the two altimeters are obtained by transformation under a geodetic coordinate system O-xyz:
V＝J()·Vr
wherein
Figure BDA0001437581060000071
VrComprises that
Figure BDA0001437581060000072
And
Figure BDA0001437581060000073
j () is a rotation transformation matrix;
in a multi-zone division positioning algorithm (MRDL algorithm), the attitude of the robot and the coordinate theta at the time t-1t-1The wall surface that the altimeter contacts is determined. The vertical distance between the underwater robot and the wall surface is dvThus altimeter measurement data
Figure BDA0001437581060000074
The shortest distance between the ultrasonic wave emitted by the altimeter and the wall surface i:
Figure BDA0001437581060000075
wherein <, > is the cosine of the included angle of the two vectors; comprises thatfAnds(ii) a Kappa includes kappafAnd kappas；
Figure BDA0001437581060000076
Comprises that
Figure BDA0001437581060000077
And
Figure BDA0001437581060000078
is the measurement data of the front altimeter,
Figure BDA0001437581060000079
measurement data for a lateral altimeter;
Figure BDA00014375810600000710
and
Figure BDA00014375810600000711
is of the above formula
Figure BDA00014375810600000712
The solution of (a) is:
Figure BDA00014375810600000713
the direction vector of the altimeter actual measurement is therefore:
Figure BDA00014375810600000714
the value d used in the multi-region partition algorithm is then:
Figure BDA00014375810600000715
d is a corrected value of the measurement data of the altimeter, d includes dfAnd ds，dfCorrected value for the measurement data of the front altimeter, dsCorrected values for the measurement data of the side altimeter;
case 1: as shown in fig. 4, if the underwater robot coordinates at time t-1 satisfy the following condition, the underwater robot is located in the area 1,
Θ′t-1∈{Θ|y/x(Θ,CRB)≥tanα∪y/x(Θ,CBL)≥-tan-1α}
in the formula (I), the compound is shown in the specification,y/x(Θ,CRB) Is a straight line l0The slope of (a) of (b) is,y/x(Θ,CBL) Is a straight line l1The slope of (a);
wherein
Figure BDA0001437581060000081
Figure BDA0001437581060000082
A y-axis coordinate value of an intersection point formed by the pool wall surface R and the pool wall surface B on the plane x 'Oy';
Figure BDA0001437581060000083
an x-axis coordinate value of an intersection point formed by the pool wall surface R and the pool wall surface B on the plane x 'Oy';
Figure BDA0001437581060000084
a y-axis coordinate value of an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy';
Figure BDA0001437581060000085
an x-axis coordinate value of an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy'; thetayIs a y-axis coordinate value theta of the underwater robot in a geodetic coordinate system O-xyzxAn x-axis coordinate value of the underwater robot in a geodetic coordinate system O-xyz;
case 2: as shown in fig. 5, if the underwater robot coordinates at time t-1 satisfy the following condition, the underwater robot is located in the area 2,
Θ′t-1∈{Θ|y/x(Θ,CRB)≥tanα∪y/x(Θ,CBL)＜-tan-1α}
case 3: in a similar situation to the area 1, if the underwater robot coordinates at the time t-1 satisfy the following condition, the underwater robot is located in the area 3,
Θ′t-1∈{Θ|y/x(Θ,CRB)＜tanα∪y/x(Θ,CBL)＜-tan-1α}
case 4: the situation is similar to that of the area 2, the two altimeters are in contact with the wall surface B at the same time, and if the coordinates of the underwater robot at the moment t-1 meet the following conditions, the underwater robot is located in the area 4;
Θ′t-1∈{Θ|y/x(Θ,CRB)＜tanα∪y/x(Θ,CBL)≥-tan-1α}。
other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: in the fourth step, the position of the underwater robot at the t moment is calculated by adopting a multi-zone division positioning algorithm (MRDL algorithm) according to the area to which the underwater robot belongs; the specific process is as follows:
case 1: when the underwater robot is located in the area 1, the ultrasonic waves emitted by the front altimeter and the side altimeter respectively contact the wall surface R and the wall surface B, so that the coordinates of the underwater robot at the time t in O-x ' y ' z ' are:
Figure BDA0001437581060000086
x 'in the formula'tIs the x-axis t time coordinate, y 'of the underwater robot in O-x' y 'z'tIs the y-axis t time coordinate, d, of the underwater robot in O-x 'y' zRThe vertical distance between the underwater robot and the wall surface R is equal to dfcosαt；dBThe vertical distance between the underwater robot and the wall surface B is equal to dscosαt；αtIs the included angle between the underwater robot and the Ox' at the moment t; dfCorrected value for the measurement data of the front altimeter, dsCorrected values for the measurement data of the side altimeter;
when the underwater robot is located in the area 1, the coordinates of the underwater robot can be directly obtained through altimeter data and can also be obtained through dead reckoning:
Figure BDA0001437581060000091
in formula (c)'trknIs a coordinate of the underwater robot at the time t, delta y ', obtained by dead reckoning'tIs y't-y′t-1，Δx′tIs x't-x′t-1；
And obtaining the coordinates of the underwater robot by variable confidence coefficient data fusion as follows:
Θ′＝PTΘ′t+(1-PT)Θ′rkn
wherein
Figure BDA0001437581060000092
pj∈{g(dj)|dj∈{dl0,dl1}}
In the formula pxConfidence of front altimeter, pyConfidence of the lateral altimeter, pjAs confidence, g (d)j) As confidence, dl0Is the vertical distance of the underwater robot from the line l 0; dl1Is the vertical distance of the underwater robot from the line l 1; p is a radical ofjIs pxOr py；
Case 2: when the underwater robot is located in the area 2, ultrasonic waves emitted by the front altimeter and the side altimeter respectively contact the wall surface R and the wall surface L, and the x' coordinate of the underwater robot at the moment t is as follows:
x′t＝|Op′R|-dR＝a-dfcosαt
＝-|Op′L|+dL＝-a+dssinαt
since the wall surface R and the wall surface L are parallel to each other, the y' coordinate of the underwater robot at time t cannot be obtained. The position and attitude of the underwater robot at time t-1 can be used to estimate its coordinates at time t. As shown in FIG. 6, the coordinate of the underwater robot at the time t-1 in O-x 'y' z 'is theta'tThe geometrical relationship is expressed as:
Figure BDA0001437581060000093
wherein
Figure BDA0001437581060000094
Gamma is the angle change of the underwater robot in delta t time; Δ t is t- (t-1);
therefore, the y' coordinate of the underwater robot at the time t is as follows:
Figure BDA0001437581060000101
when the underwater robot is located in the area 2, the coordinates of the underwater robot are obtained by variable confidence coefficient data fusion:
Figure BDA0001437581060000102
wherein p isj∈{g(dj)|dj∈{dl0,dl1}}，pjIs pfOr ps；pfConfidence of front altimeter data, psIs confidence of the side altimeter data, Θ'fIs a coordinate, Θ ', obtained by a front altimeter'sCoordinates obtained by using a lateral altimeter; (Θ't＝[x′t,y′t,z′t]TCoordinates of the underwater robot in O-x ' y ' z '; theta'fTo obtain the coordinates theta ' of the underwater robot in O-x ' y ' z ' by using a front altimeter 'sCoordinates of the underwater robot in O-x ' y ' z ' obtained by using a lateral altimeter; to illustrate the formula
Figure BDA0001437581060000103
Are respectively connected with
Figure BDA0001437581060000104
And
Figure BDA0001437581060000105
the relationship of (c).
Case 3: when the underwater robot is located in the area 3, the ultrasonic waves emitted by the front altimeter and the side altimeter respectively contact the wall surface B and the wall surface L, so that the coordinates of the underwater robot at the time t in O-x ' y ' z ' are:
Figure BDA0001437581060000106
dLd is the vertical distance between the underwater robot and the wall surface Lssinαt；
When the underwater robot is located in the area 3, the coordinates of the underwater robot can be directly obtained through altimeter data and can also be obtained through dead reckoning:
Figure BDA0001437581060000107
in formula (c)'trknIs a coordinate of the underwater robot at the time t, delta y ', obtained by dead reckoning'tIs y't-y′t-1，Δx′tIs x't-x′t-1；
And obtaining the coordinates of the underwater robot by variable confidence coefficient data fusion as follows:
Θ′＝PTΘ′+(1-PT)Θ′rkn
wherein
Figure BDA0001437581060000111
pj∈{g(dj)|dj∈{dl0,dl1}}，pjIs pxOr py；pxConfidence of the lateral altimeter, pyConfidence of front altimeter, pjAs confidence, g (d)j) As confidence, dl0Is the vertical distance of the underwater robot from the line l 0; dl1Is the vertical distance of the underwater robot from the line l 0;
case 4: when the underwater robot is located in the area 4, the coordinates of the underwater robot in O-x ' y ' z ' at the time t are:
Figure BDA0001437581060000112
when the underwater robot is positioned in the area 4, the coordinates of the underwater robot are obtained by variable confidence coefficient data fusion:
Figure BDA0001437581060000113
wherein p isj∈{g(dj)|dj∈{dl0,dl1}}，pjIs pfOr ps；pfConfidence of front altimeter data, psIs confidence of the side altimeter data, Θ'fIs a coordinate, Θ ', obtained by a front altimeter'sCoordinates obtained by using a lateral altimeter; (Θ't＝[x′t,y′t,z′t]TCoordinates of the underwater robot in O-x ' y ' z '; theta'fTo obtain the coordinates theta ' of the underwater robot in O-x ' y ' z ' by using a front altimeter 'sCoordinates of the underwater robot in O-x ' y ' z ' obtained by using a lateral altimeter; to illustrate the formula
Figure BDA0001437581060000114
And
Figure BDA0001437581060000115
the relationship of (c).
Finally, the coordinates of the underwater robot in O-xyz are obtained by the inverse matrix of C (β):
Θ＝Cz -1(β)·Θ′。
the following two assumptions were made before for ease of calculation: 1) the underwater robot maintains a horizontal attitude in water, and therefore, θ is 0. 2) The transmission angle of the altimeter is small enough that the ultrasonic wave transmitted by the altimeter can be approximately seen as a ray. However, in actual use, the attitude of the underwater robot changes from time to time, and the ultrasonic waves emitted by the altimeter have an emission angle of 6 °, which affect the accuracy of the positioning algorithm. To make matters worse, when the robot moves to the boundary defined by the multi-region division algorithm, the positioning result is greatly interfered due to the errors of the emission angle of the altimeter and the AHRS yaw angle, which is called as the boundary effect. Therefore, the multi-area partition positioning algorithm is optimized accordingly to achieve the best positioning effect.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: said Θ' ═ PTΘ′+(1-PT)Θ′rknAnd
Figure BDA0001437581060000121
the specific solving process is as follows:
in the multi-zone division positioning algorithm, the pool is divided into four zones according to the size of the alpha angle. However, when the underwater robot coordinates approach the boundary between the areas, the data returned by the altimeter may not be the distance from the wall surface predicted by the algorithm, but the data of its adjacent wall surface, causing an error. Therefore, we propose a variable confidence filtering to perform data fusion to reduce errors.
Setting the current coordinates of the underwater robot under O-x 'y' z 'as theta' and l0And l1Are respectively Vl0＝[cosα,sinα]TAnd Vl1＝[-sinα,cosα]T；
As shown in FIG. 8, an underwater robot and0the vertical distance between them is:
Figure BDA0001437581060000122
likewise, underwater robots and1the vertical distance between them is:
Figure BDA0001437581060000123
the altimeter data becomes less reliable as the underwater robot gets closer to the boundary, and therefore, the reliability of the altimeter data is measured by a confidence coefficient p:
Figure BDA0001437581060000124
wherein λ is a convergence rate factor and σ is an offset; the relationship between p and d is shown in FIG. 9.
When the underwater robot is located in the area 1 and the area 3, the coordinates of the underwater robot are not only directly obtained through altimeter data, but also can be obtained through dead reckoning:
Figure BDA0001437581060000125
and obtaining the coordinates of the underwater robot by variable confidence coefficient data fusion as follows:
Θ′＝PTΘ′+(1-PT)Θ′rkn
wherein
Figure BDA0001437581060000131
pj∈{g(dj)|dj∈{dl0,dl1}}
When the underwater robot is positioned in the area 2 and the area 4, the coordinates of the underwater robot are obtained by variable confidence coefficient data fusion:
Figure BDA0001437581060000132
wherein p isj∈{g(dj)|dj∈{dl0,dl1}}。
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the preparation method comprises the following steps:
the experimental environment is as follows: the size of the pool is a square pool with the length of 8 meters, the width of 4 meters and the depth of 2.5 meters.
Experimental equipment:
1. the underwater robot is a cabled open-frame type underwater welding robot developed by Harmony, is powered by 300V direct current, weighs 100kg, and has the three-dimensional size of 1.06m in length, 0.68m in width and 0.61m in height.
2. The sensors used were: the attitude heading reference system is MTi-G-700 model, and the precision is 0.3 degrees. The underwater height meter is ISA500-L, the precision is 1mm, and the measuring range is 0.1 m-120 m. As shown in fig. 10, 11a, 11b, 12;
in the water pool, three groups of experiments are carried out, namely rectangular motion, oblique line motion and circular arc motion, in the rectangular motion, the algorithm positioning result is almost coincident with the real motion track, and the maximum error is not more than 6 mm. In oblique line movement, the positioning effect is also ideal, and the maximum error does not exceed 7 mm. Because the position and the angle of the circular arc motion are changed simultaneously, the circular arc motion is the motion which is most difficult to position in the positioning method, so that the positioning error is the largest, the maximum error is 40mm, and the positioning requirement can still be met. As shown in fig. 13a, 13b, 14a, 14b, 15a, 15 b.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (5)

1. An underwater positioning method for an indoor confined structured water area, characterized by: the method comprises the following specific processes:
step one, rotating a geodetic coordinate system O-xyz by an angle beta according to a yaw angle of the underwater robot to obtain a new coordinate system O-x ' y ' z ';
step two, according to the new coordinate system O-x ' y ' z ' obtained in the step one, the pool wall surfaces are sequentially represented as R, B, L and U in the O-x ' y ' z ', wherein the positive direction of the x ' axis corresponds to the pool wall surface R, the positive direction of the y ' axis corresponds to the pool wall surface B, and the negative direction of the x ' axis corresponds to the pool wall surface L; the negative direction of the y' axis corresponds to the wall surface U of the pool;
passing point CRBMaking a straight line l with a slope tan α0(ii) a Then passing through point CBLMake a straight line l0Perpendicular line l1Slope of-1/tan α; /)0And l1Dividing the pool plane x 'Oy' into four regions;
point CRBIs an intersection point formed by the pool wall surface R and the pool wall surface B on a plane x 'Oy';
point CBLIs an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy';
thirdly, determining which of the four areas the underwater robot belongs to according to the position of the underwater robot at the time t-1, the attitude and heading reference system at the time t and data returned by the front altimeter and the side altimeter;
step four, calculating the position of the underwater robot at the time t by adopting a multi-zone division positioning algorithm according to the area to which the underwater robot belongs; the specific process is as follows:
case 1: when the underwater robot is located in the area 1, the ultrasonic waves emitted by the front altimeter and the side altimeter respectively contact the wall surface R and the wall surface B, so that the coordinates of the underwater robot at the time t in O-x ' y ' z ' are:
Figure FDA0002575477620000011
in the formula xt' is the x-axis t time coordinate of the underwater robot in O-x ' y ' zt'is the y-axis t time coordinate of the underwater robot in O-x' y 'z', dRThe vertical distance between the underwater robot and the wall surface R is equal to dfcosαt；dBThe vertical distance between the underwater robot and the wall surface B is equal to dscosαt；αtIs the included angle between the underwater robot and the Ox' at the moment t; dfCorrected value for the measurement data of the front altimeter, dsCorrected values for the measurement data of the side altimeter;
when the underwater robot is located in the area 1, the coordinates of the underwater robot can be obtained by dead reckoning:
Figure FDA0002575477620000012
in formula (c)'trkn△ y 'as coordinates of the underwater robot at time t estimated from the track'tIs y't-y′t-1，△x′tIs x't-x′t-1；
And obtaining the coordinates of the underwater robot by variable confidence coefficient data fusion as follows:
Θ′＝PTΘ′t+(1-PT)Θ′rkn
wherein
Figure FDA0002575477620000021
pj∈{g(dj)|dj∈{dl0,dl1}}
In the formula pxConfidence of front altimeter, pyConfidence of the lateral altimeter, pjAs confidence, g (d)j) As confidence, dl0Is the vertical distance of the underwater robot from the line l 0; dl1Is the vertical distance of the underwater robot from the line l 1; p is a radical ofjIs pxOr py；
Case 2: when the underwater robot is located in the area 2, ultrasonic waves emitted by the front altimeter and the side altimeter respectively contact the wall surface R and the wall surface L, and the x' coordinate of the underwater robot at the moment t is as follows:
x′t＝|Op′R|-dR＝a-dfcosαt
＝-|Op′L|+dL＝-a+dssinαt
the coordinate of the underwater robot at the t-1 moment in O-x 'y' z 'is theta'tThe geometrical relationship is expressed as:
Figure FDA0002575477620000022
wherein
Figure FDA0002575477620000023
Gamma is the angle change of the underwater robot in △ t time, △ t is t- (t-1);
therefore, the y' coordinate of the underwater robot at the time t is as follows:
Figure FDA0002575477620000024
when the underwater robot is located in the area 2, the coordinates of the underwater robot are obtained by variable confidence coefficient data fusion:
Figure FDA0002575477620000025
wherein p isj∈{g(dj)|dj∈{dl0,dl1}}，pjIs pfOr ps；pfConfidence of front altimeter data, psIs confidence of the side altimeter data, Θ'fIs a coordinate, Θ ', obtained by a front altimeter'sCoordinates obtained by using a lateral altimeter;
case 3: when the underwater robot is located in the area 3, the ultrasonic waves emitted by the front altimeter and the side altimeter respectively contact the wall surface B and the wall surface L, so that the coordinates of the underwater robot at the time t in O-x ' y ' z ' are:
Figure FDA0002575477620000031
dLd is the vertical distance between the underwater robot and the wall surface Lssinαt；
When the underwater robot is located in the area 3, the coordinates of the underwater robot can be obtained by dead reckoning:
Figure FDA0002575477620000032
in formula (c)'trknTo derive from dead reckoning△ y 'of underwater robot t'tIs y't-y′t-1，△x′tIs x't-x′t-1；
And obtaining the coordinates of the underwater robot by variable confidence coefficient data fusion as follows:
Θ′＝PTΘ′+(1-PT)Θ′rkn
wherein
Figure FDA0002575477620000033
pj∈{g(dj)|dj∈{dl0,dl1}}，pjIs pxOr py；pxConfidence of the lateral altimeter, pyConfidence of front altimeter, pjAs confidence, g (d)j) As confidence, dl0Is the vertical distance of the underwater robot from the line l 0; dl1Is the vertical distance of the underwater robot from the line l 0;
case 4: when the underwater robot is located in the area 4, the coordinates of the underwater robot in O-x ' y ' z ' at the time t are:
Figure FDA0002575477620000034
when the underwater robot is positioned in the area 4, the coordinates of the underwater robot are obtained by variable confidence coefficient data fusion:
Figure FDA0002575477620000035
wherein p isj∈{g(dj)|dj∈{dl0,dl1}}，pjIs pfOr ps；pfConfidence of front altimeter data, psIs confidence of the side altimeter data, Θ'fIs a coordinate, Θ ', obtained by a front altimeter'sCoordinates obtained by using a lateral altimeter;
finally, the coordinates of the underwater robot in O-xyz are obtained by the inverse matrix of C (β):
Θ＝Cz -1(β)·Θ′。
2. an underwater positioning method for indoor confined structured waters as claimed in claim 1 wherein: in the first step, a geodetic coordinate system O-xyz is rotated by an angle beta according to the yaw angle of the underwater robot to obtain a new coordinate system O-x ' y ' z '; the specific process is as follows:
the attitude of the underwater robot is represented as [ phi, theta, psi ═ phi]TWherein phi is a roll angle, theta is a pitch angle, and psi is a yaw angle; the distance data measured by the two altimeters are dfAnd ds(ii) a The two altimeters are respectively arranged in front of and at the side of the underwater robot and form an included angle of 90 degrees, and the attitude heading reference system is arranged in the underwater robot cabin;
dfdata returned for the front altimeter, dsData returned for the side altimeter;
the following assumptions are made:
1) keeping the attitude of the underwater robot in water horizontal, wherein phi is 0;
2) the ultrasonic wave emitted by the altimeter is regarded as a ray;
let [ D, W, H]TThe length, width and height of the pool are shown, and T is a transposition;
let l be D/2 and W be W/2, so the equation for the four walls of the pool is:
wall surface I: x-l ═ 0
Wall surface II: y-w is 0
Wall surface III: x + l is 0
Wall surface IV: y + w is 0
The four equations are combined into a standard plane equation form
Figure FDA0002575477620000041
Wherein Θ is [ x, y, z ═ z]T，NiIs the normal vector of pool wall i, N1＝[1,0,0]T，N2＝[0,1,0]T，N3＝[-1,0,0]TN4＝[0,-1,0]T；piIs the intersection point of the pool coordinate axis and the pool wall i under the geodetic coordinate system O-xyz, so p1＝[l,0,0]T，p2＝[0,w,0]T，p3＝[-l,0,0]T，p4＝[0,-w,0]T(ii) a x is an x-axis coordinate in a pool coordinate system, y is a y-axis coordinate in the pool coordinate system, z is a z-axis coordinate in the pool coordinate system, l is a half of the length of the pool, and w is a half of the width of the pool;
the yaw angle of the underwater robot satisfies psi ∈ [ -pi, pi), and the yaw angle of the underwater robot is divided into four regions [ -pi, -pi/2), [ -pi/2, 0), [0, pi/2), [ pi/2, pi) according to the value of psi;
counterclockwise rotating the geodetic coordinate system O-xyz by an angle beta to generate a new coordinate system O-x ' y ' z ', wherein the angle beta belongs to { -pi, -pi/2, 0, pi/2 }; the wall surfaces of the pool are sequentially represented as R, B, L and U in O-x 'y' z ', wherein the positive direction of the x' axis corresponds to the wall surface R of the pool, the positive direction of the y 'axis corresponds to the wall surface B of the pool, and the negative direction of the x' axis corresponds to the wall surface L of the pool; the negative direction of the y' axis corresponds to the wall surface U of the pool;
o-x 'y' z 'ensures that the included angle alpha between the underwater robot and the Ox' is psi-beta epsilon [0, pi/2);
let thetat＝[xt,yt,zt]TIs the coordinate theta of the underwater robot in a geodetic coordinate system O-xyz't＝[x′t,y′t,z′t]TCoordinates of the underwater robot in O-x ' y ' z '; t is time;
then
Θ′＝Cz(β)·Θ
Wherein
Figure FDA0002575477620000051
Cz(β) is an intermediate variable;
the z coordinate of the underwater robot is directly measured by using the pressure sensor, so that the theta is simplified to be [ x, y ]]T。
3. Use according to claim 2An underwater positioning method for an indoor limited structured water area, characterized in that: in the second step, according to the new coordinate system O-x ' y ' z ' obtained in the first step, the wall surfaces of the pool are sequentially represented as R, B, L and U in the O-x ' y ' z ', wherein the positive direction of the x ' axis corresponds to the wall surface R of the pool, the positive direction of the y ' axis corresponds to the wall surface B of the pool, and the negative direction of the x ' axis corresponds to the wall surface L of the pool; the negative direction of the y' axis corresponds to the wall surface U of the pool; passing point CRBMaking a straight line l with a slope tan α0(ii) a Then passing through point CBLMake a straight line l0Perpendicular line l1Slope of-1/tan α; /)0And l1Dividing the pool plane x 'Oy' into four regions; the specific process is as follows:
in O-x ' y ' z ', a point C is crossedRBMaking a straight line l with a slope tan α0Then passing through point CBLMake a straight line l0Perpendicular line l1The slope is-1/tan α, l0And l1The plane x 'Oy' is divided into four regions,
point CRBIs an intersection point formed by the pool wall surface R and the pool wall surface B on a plane x 'Oy';
point CBLIs an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy';
the size of the pool is defined in O-x ' y ' z ' as:
Figure FDA0002575477620000061
wherein, p'RIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface R of the sink'RIs origin O to p'RDistance of p'LIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface L of the sink'LIs origin O to p'LDistance of p'BIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface B of the sink'BIs origin O to p'BDistance of p'UIs the intersection point, Op ', of the coordinate axis of the sink under the geodetic coordinate system O-xyz and the wall surface U of the sink'UIs origin O to p'UA is taken as l or w, b is taken asl or w.
4. An underwater positioning method for indoor confined structured waters as claimed in claim 3 wherein: determining which area of the four areas the underwater robot belongs to according to the position of the underwater robot at the time t-1, the attitude and heading reference system at the time t and data returned by the front altimeter and the side altimeter in the third step; the specific process is as follows:
if the emitting angle of the altimeter is half of the emitting angle of the altimeter, the emitting vector of the front-end altimeter is in a robot body coordinate system O-xbybzbThe following is expressed as:
Figure FDA0002575477620000062
whereinfIs half of the emission angle of the front altimeter, kfIs [0,2 π ]]Any value within the interval of time is,
Figure FDA0002575477620000063
is the transmission vector of the front altimeter,
Figure FDA0002575477620000064
emission vector of side altimeter is in robot body coordinate system O-xbybzbThe following is expressed as:
Figure FDA0002575477620000065
whereinsIs half of the emission angle, k, of the lateral altimetersIs [0,2 π ]]Any value within the interval of time is,
Figure FDA0002575477620000066
is the transmission vector of the front altimeter,
Figure FDA0002575477620000067
the emission vectors of the two altimeters are obtained by transformation under a geodetic coordinate system O-xyz:
V＝J()·Vr
wherein
Figure FDA0002575477620000068
VrComprises that
Figure FDA0002575477620000069
And
Figure FDA00025754776200000610
j () is a rotation transformation matrix;
the vertical distance between the underwater robot and the wall surface is dvThus altimeter measurement data
Figure FDA00025754776200000611
The shortest distance between the ultrasonic wave emitted by the altimeter and the wall surface i:
Figure FDA0002575477620000071
wherein<·,·>Is the cosine of the included angle of the two vectors; comprises thatfAnds(ii) a Kappa includes kappafAnd kappas；
Figure FDA0002575477620000072
Comprises that
Figure FDA0002575477620000073
And
Figure FDA0002575477620000074
Figure FDA0002575477620000075
is the measurement data of the front altimeter,
Figure FDA0002575477620000076
measurement data for a lateral altimeter;
Figure FDA0002575477620000077
and
Figure FDA0002575477620000078
is of the above formula
Figure FDA0002575477620000079
The solution of (a) is:
Figure FDA00025754776200000710
the direction vector of the altimeter actual measurement is therefore:
Figure FDA00025754776200000711
then d is:
Figure FDA00025754776200000712
d is a corrected value of the measurement data of the altimeter, d includes dfAnd ds，dfCorrected value for the measurement data of the front altimeter, dsCorrected values for the measurement data of the side altimeter;
case 1: if the coordinates of the underwater robot at the time t-1 meet the following conditions, the underwater robot is positioned in the area 1,
Θ′t-1∈{Θ|y/x(Θ,CRB)≥tanα∪y/x(Θ,CBL)≥-tan-1α}
in the formula (I), the compound is shown in the specification,y/x(Θ,CRB) Is a straight line l0The slope of (a) of (b) is,y/x(Θ,CBL) Is a straight line l1The slope of (a);
wherein
Figure FDA00025754776200000713
Figure FDA00025754776200000714
A y-axis coordinate value of an intersection point formed by the pool wall surface R and the pool wall surface B on the plane x 'Oy';
Figure FDA00025754776200000715
an x-axis coordinate value of an intersection point formed by the pool wall surface R and the pool wall surface B on the plane x 'Oy';
Figure FDA00025754776200000716
a y-axis coordinate value of an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy';
Figure FDA00025754776200000717
an x-axis coordinate value of an intersection point formed by the pool wall surface B and the pool wall surface L on the plane x 'Oy'; thetayIs a y-axis coordinate value theta of the underwater robot in a geodetic coordinate system O-xyzxAn x-axis coordinate value of the underwater robot in a geodetic coordinate system O-xyz;
case 2: if the coordinates of the underwater robot at the time t-1 meet the following conditions, the underwater robot is located in the area 2,
Θ′t-1∈{Θ|y/x(Θ,CRB)≥tanα∪y/x(Θ,CBL)＜-tan-1α}
case 3: if the coordinates of the underwater robot at the time t-1 meet the following conditions, the underwater robot is located in the area 3,
Θ′t-1∈{Θ|y/x(Θ,CRB)＜tanα∪y/x(Θ,CBL)＜-tan-1α}
case 4: if the coordinates of the underwater robot at the time t-1 meet the following conditions, the underwater robot is located in the area 4;
Θ′t-1∈{Θ|y/x(Θ,CRB)＜tanα∪y/x(Θ,CBL)≥-tan-1α}。
5. an underwater positioning method for indoor confined structured waters as claimed in claim 4 wherein: said Θ' ═ PTΘ′+(1-PT)Θ′rknAnd
Figure FDA0002575477620000081
the specific solving process is as follows:
setting the current coordinates of the underwater robot under O-x 'y' z 'as theta' and l0And l1Are respectively Vl0＝[cosα,sinα]TAnd Vl1＝[-sinα,cosα]T；
Underwater robot and0the vertical distance between them is:
Figure FDA0002575477620000082
likewise, underwater robots and1the vertical distance between them is:
Figure FDA0002575477620000083
the reliability of the altimeter data is measured by a confidence coefficient p:
Figure FDA0002575477620000084
wherein λ is a convergence rate factor and σ is an offset;
when the underwater robot is located in the area 1 and the area 3, the coordinates of the underwater robot are obtained by dead reckoning:
Figure FDA0002575477620000085
and obtaining the coordinates of the underwater robot by variable confidence coefficient data fusion as follows:
Θ′＝PTΘ′+(1-PT)Θ′rkn
wherein
Figure FDA0002575477620000091
pj∈{g(dj)|dj∈{dl0,dl1}}
When the underwater robot is positioned in the area 2 and the area 4, the coordinates of the underwater robot are obtained by variable confidence coefficient data fusion:
Figure FDA0002575477620000092
wherein p isj∈{g(dj)|dj∈{dl0,dl1}}。
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