CN112077836A - Overhead suspender error correction method based on four-flexible-cable traction parallel actuator - Google Patents

Overhead suspender error correction method based on four-flexible-cable traction parallel actuator Download PDF

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CN112077836A
CN112077836A CN202010937266.4A CN202010937266A CN112077836A CN 112077836 A CN112077836 A CN 112077836A CN 202010937266 A CN202010937266 A CN 202010937266A CN 112077836 A CN112077836 A CN 112077836A
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point
coordinate
value
actuator
rope
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CN112077836B (en
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周姣
刘基顺
车行
刘庆龙
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Beijing Bette Shengdi Technology Development Co ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/10—Programme-controlled manipulators characterised by positioning means for manipulator elements
    • B25J9/104—Programme-controlled manipulators characterised by positioning means for manipulator elements with cables, chains or ribbons
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1692—Calibration of manipulator

Abstract

The invention provides an overhead suspender error correction method based on a four-flexible-cable traction parallel actuator, which comprises the following steps: establishing a three-dimensional space coordinate system x-y-z; determining coordinate measurement calibration values of all hoisting points; dragging the actuator E to different space target position points according to a set dragging rule, and recording length values of all ropes; solving an equation set to obtain a coordinate calculation value of each lifting point; comparing the coordinate calculation value of each lifting point with the corresponding coordinate measurement calibration value to obtain a lifting point calibration error value; and superposing half of the calibration error value of each lifting point to the corresponding coordinate measurement calibration value to obtain the coordinate value of each lifting point after final correction. The method can reduce the length error of the rope caused by the position of the lifting point of the overhead suspender, and improve the control precision of the overhead suspender. In addition, in the whole implementation process, the algorithm is simple, and the method is very suitable for being applied to various stage spaces.

Description

Overhead suspender error correction method based on four-flexible-cable traction parallel actuator
Technical Field
The invention belongs to the technical field of research and development of stage performance innovation technologies, and particularly relates to an overhead suspender error correction method based on a four-flexible-cable traction parallel actuator.
Background
The stage four-wire traction parallel actuator performance system has the structure that: the method comprises the following steps that four corner areas of a performance area are respectively provided with an elevated suspender, the top of each elevated suspender, namely a hoisting point, is provided with a winch, a rope extends out of the rope outlet end of each winch, and the other end of each rope is connected to an actuator through a pulley; therefore, the four ropes move in parallel to drive the actuator to move randomly in a space range.
Generally, the actuator can move freely in a three-dimensional space formed by the stage performance area and the overhead suspension rod by controlling the length of the rope to zoom, and the zooming of the rope is in important connection with the positions of the overhead suspension rods in four corner areas.
In the conventional use, the length of the rope is generally calculated according to the lifting point position of the elevated suspender in the corner area and the target position of the actuator, so that the calculated length value of the rope is used for carrying out a rope scaling command of the winch, and the actuator is further moved to the target position to the greatest extent. However, in practical use, the position of the suspension point of the overhead boom is generally determined by manual measurement due to changes in working environment or irregularities in the performance area, which causes the following problems: (1) due to environmental problems and different measurement methods of measuring personnel, height errors are generated at the positions of the suspension points of the overhead hanger rods obtained by manual measurement, and the calculated values of the scaling lengths of the ropes can be directly influenced by the height errors, so that the deviation of the target positions of the four-flexible-cable traction parallel actuator in a space range is caused. For better control of the performance system, precise determination of the individual overhead boom suspension point positions is required.
In the existing performance system, most researchers and experimenters manually add empirical constant values to correct the measured position of the suspension point of the overhead suspension rod, so as to obtain the corrected value of the suspension point of the overhead suspension rod. However, the addition of the experience value makes the experience value be lost, and since the performance system is a four-wire parallel system, and the parameters are restricted and feedback mutually, the final control effect is still poor.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an overhead suspender error correction method based on a four-flexible-cable traction parallel actuator, which can effectively solve the problems.
The technical scheme adopted by the invention is as follows:
the invention provides an overhead suspender error correction method based on a four-flexible-cable traction parallel actuator, which comprises the following steps of:
step 1, in the stage performance space, the ground plane in the stage performance area is the stage horizontal plane, and four angular points of the stage horizontal plane are overhead jib bottom mounted position, and wherein, four angular points of the stage horizontal plane are according to anticlockwise range, represent in proper order and be: an angular point a, an angular point b, an angular point c and an angular point d; the angular points a, b, c and d are connected end to form a rectangle;
at the corner a, the 1 st overhead boom is installed, and the top suspension point of the 1 st overhead boom is denoted as suspension point a, and therefore, the 1 st overhead boom is denoted as: aA; at the corner B, a 2 nd overhead boom is mounted, the top suspension point of the 2 nd overhead boom being denoted as suspension point B, and thus the 2 nd overhead boom is denoted as: bB; at the corner C, a 3 rd overhead boom is mounted, the top suspension point of the 3 rd overhead boom being denoted as suspension point C, and therefore the 3 rd overhead boom is denoted as: cC; at the corner point D, a 4 th overhead boom is mounted, the top suspension point of the 4 th overhead boom being denoted as suspension point D, and therefore the 4 th overhead boom being denoted as: dD; the hoisting point A, the hoisting point B, the hoisting point C and the hoisting point D are connected end to form a rectangle;
step 2, respectively installing a rope winder A provided with an encoder A, a rope winder B provided with an encoder B, a rope winder C provided with an encoder C and a rope winder D provided with an encoder D at a lifting point A, a lifting point B, a lifting point C and a lifting point D;
the actuator E is connected with the rope winder A through the 1 st rope, and the length L of the 1 st rope can be recorded in real time through the encoder A1(ii) a The actuator E is connected with the rope winder B through a 2 nd rope, and the length L of the 2 nd rope can be recorded in real time through the encoder B2(ii) a The actuator E is connected with the rope winder C through the 3 rd rope, and the length L of the 3 rd rope can be recorded in real time through the encoder C3(ii) a HandleThe line driving device E is connected with the rope winder D through a 4 th rope, and the length L of the 4 th rope can be recorded in real time through the encoder D4；
Step 3, at the stage level, namely: determining a diagonal intersection point O in a rectangular area defined by the angular point a, the angular point b, the angular point c and the angular point d, and establishing a three-dimensional space coordinate system x-y-z by taking the point O as a coordinate origin; wherein, the coordinate value of the O point is O (0, 0, 0); the x direction is parallel to a connecting line from the corner a to the corner b; the y direction is a direction parallel to a connecting line from the corner b to the corner c; the z direction is parallel to the connecting line from the angular point a to the lifting point A;
step 4, enclosing the angular points a, B, C, D, A, B, C and D into a rectangle in an ideal condition, wherein the length of the rectangle is L, the width of the rectangle is W, and the height of the rectangle is H; wherein, the length L is the distance from the corner a to the connecting line of the corner b; the width W is the distance from the corner b to the connecting line of the corner c; the height H is the distance from the corner a to the connecting line of the lifting point A;
the ideal coordinate of the corner point a is
Figure BDA0002672396970000031
The ideal coordinate of the corner point b is
Figure BDA0002672396970000032
Ideal coordinates of the corner point c are
Figure BDA0002672396970000033
Ideal coordinates of the corner point d are
Figure BDA0002672396970000034
The ideal coordinate of the hanging point A is
Figure BDA0002672396970000035
The ideal coordinate of the lifting point B is
Figure BDA0002672396970000036
Ideal coordinates of the hoisting point C are
Figure BDA0002672396970000037
The ideal coordinate of the hanging point D is
Figure BDA0002672396970000038
Because there is installation error in 1 st overhead jib, 2 nd overhead jib, 3 rd overhead jib and 4 th overhead jib to, there is measuring error in each hoisting point and angular point, consequently, the coordinate measurement calibration value of each hoisting point is respectively: the coordinate measurement calibration value of the lifting point A is
Figure BDA0002672396970000039
The coordinate measurement calibration value of the lifting point B is
Figure BDA00026723969700000310
The coordinate measurement calibration value of the lifting point C is
Figure BDA00026723969700000311
Figure BDA00026723969700000312
The coordinate measurement calibration value of the lifting point D is
Figure BDA00026723969700000313
Wherein, + Δ is an error value of installation calibration;
and 5, setting coordinate calculation values of the lifting points as follows: the coordinate solution of the lifting point A is A (x)1，y1，z1) (ii) a The coordinate solution value of the lifting point B is B (x)2，y2，z2) (ii) a The coordinate solution value of the lifting point C is C (x)3，y3，z3) (ii) a The coordinate solution of the lifting point D is D (x)4，y4，z4) (ii) a The coordinate calculation value of each lifting point is to-be-evaluated;
firstly, manually dragging an actuator E to be positioned at a coordinate origin point O; then, dragging the actuator E to reach different space target position points according to a set dragging rule;
whenever the actuator E is dragged to reach a certain spatial target position point (x)0，y0，z0) Time, space target position point(x0，y0，z0) And by each encoder, a respective rope length value can be recorded, respectively: length of 1 st rope is L10The 2 nd rope has a length L20And the 3 rd rope has a length L30Length of 4 th rope is L40；
Establishing a target location point (x) in space by0，y0，z0) The corresponding equation:
(x1-x0)2+(y1-y0)2+(z1-z0)2＝L10 2
(x2-x0)2+(y2-y0)2+(z2-z0)2＝L20 2
(x3-x0)2+(y3-y0)2+(z3-z0)2＝L30 2
(x4-x0)2+(y4-y0)2+(z4-z0)2＝L40 2
assuming that the actuator is dragged to n space target position points, therefore, n equations can be obtained; solving an equation set formed by n equations to obtain a coordinate calculation value A (x) of the lifting point A1，y1，z1) Coordinate solution value B (x) of suspension point B2，y2，z2) Coordinate solution value C (x) of suspension point C3，y3，z3) And the coordinate solution value D (x) of the lifting point D4，y4，z4)；
Step 6, comparing the coordinate calculation value of each lifting point with the corresponding coordinate measurement calibration value, and respectively obtaining the calibration error value of the lifting point A according to the following formula
Figure BDA0002672396970000041
Calibration error value of lifting point B
Figure BDA0002672396970000042
Calibration error value of lifting point C
Figure BDA0002672396970000043
And the calibration error value of the lifting point D
Figure BDA0002672396970000044
Figure BDA0002672396970000051
And 7, superposing half of the calibration error value of each lifting point to the corresponding coordinate measurement calibration value by adopting the following formula to obtain a coordinate value of each lifting point after final correction, namely: the corrected coordinate value of the lifting point A is Aj(x1j，y1j，z1j) The corrected coordinate value of the lifting point B is Bj(x2j，y2j，z2j) The corrected coordinate value of the lifting point C is Cj(x3j，y3j，z3j) The corrected coordinate value of the sum point D is the sum Dj(x4j，y4j，z4j)；
Figure BDA0002672396970000061
And 8, during actual performance, generating control instructions for the rope winder A, the rope winder B, the rope winder C and the rope winder D according to the coordinate values after the correction of the lifting points and the target position of the actuator E, further controlling each rope winder to automatically act, controlling the actuator E to move to the target position, and realizing the spatial attitude control of the actuator E.
Preferably, in step 5, according to a set dragging rule, the actuator E is dragged to reach different spatial target position points, specifically:
dragging the actuator E to move to different target positions along the positive direction of the x axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the negative direction of the x axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the positive direction of the y axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the negative direction of the y axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the positive direction of the z axis at intervals of 1 unit length;
and (4) at intervals of 1 unit length, dragging the actuator E to move to different target positions along the negative direction of the z axis.
The overhead suspender error correction method based on the four-flexible-cable traction parallel actuator provided by the invention has the following advantages:
the method comprises the steps of firstly taking the geometric center of a stage theater as an origin of coordinates by utilizing convenience and easiness in measurement of a stage horizontal plane, then enabling an actuator to move in unit length from the origin of coordinates, recording the lengths of ropes by utilizing four flexible cables pulled by an overhead suspender after the actuator is moved, then calculating a coordinate value of a hanging point of a rope outlet end pulled by the overhead suspender by utilizing a mathematical model, and then carrying out contrast correction by utilizing a coordinate value actually tested and the coordinate value calculated by the mathematical model. In addition, in the whole implementation process, the algorithm is simple, and the method is very suitable for being applied to various stage spaces.
Drawings
FIG. 1 is a geometric block diagram of the stage-wide three-dimensional space dimensions provided by the present invention;
fig. 2 is a schematic flow chart of an overhead boom error correction method based on a four-wire traction parallel actuator provided by the invention.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects solved by the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In the prior art, because the position of a suspension point of an overhead suspension rod has a measurement error, the mode of adding an empirical value for correction still causes errors in position calibration and system control, thereby bringing great influence to the motion precision of an actuator.
Based on the above, the invention provides an overhead boom error correction method based on four-wire traction parallel actuator, referring to fig. 2 and fig. 1, comprising the following steps:
step 1, in the stage performance space, the ground plane in the stage performance area is the stage horizontal plane, and four angular points of the stage horizontal plane are overhead jib bottom mounted position, and wherein, four angular points of the stage horizontal plane are according to anticlockwise range, represent in proper order and be: an angular point a, an angular point b, an angular point c and an angular point d; the angular points a, b, c and d are connected end to form a rectangle;
at the corner a, the 1 st overhead boom is installed, and the top suspension point of the 1 st overhead boom is denoted as suspension point a, and therefore, the 1 st overhead boom is denoted as: aA; at the corner B, a 2 nd overhead boom is mounted, the top suspension point of the 2 nd overhead boom being denoted as suspension point B, and thus the 2 nd overhead boom is denoted as: bB; at the corner C, a 3 rd overhead boom is mounted, the top suspension point of the 3 rd overhead boom being denoted as suspension point C, and therefore the 3 rd overhead boom is denoted as: cC; at the corner point D, a 4 th overhead boom is mounted, the top suspension point of the 4 th overhead boom being denoted as suspension point D, and therefore the 4 th overhead boom being denoted as: dD; the hoisting point A, the hoisting point B, the hoisting point C and the hoisting point D are connected end to form a rectangle;
step 2, respectively installing a rope winder A provided with an encoder A, a rope winder B provided with an encoder B, a rope winder C provided with an encoder C and a rope winder D provided with an encoder D at a lifting point A, a lifting point B, a lifting point C and a lifting point D;
the actuator E is connected with the rope winder A through the 1 st rope, and the length L of the 1 st rope can be recorded in real time through the encoder A1(ii) a The actuator E is connected with the rope winder B through a 2 nd rope, and the length L of the 2 nd rope can be recorded in real time through the encoder B2(ii) a The actuator E is connected with the rope winder C through the 3 rd rope, and the length L of the 3 rd rope can be recorded in real time through the encoder C3(ii) a The actuator E is connected with the rope winder D through a 4 th rope, and the length L of the 4 th rope can be recorded in real time through the encoder D4；
Step 3, at the stage level, namely: determining a diagonal intersection point O in the stage horizontal plane by using the convenience of the stage horizontal plane and a tool in a rectangular area surrounded by the angular points a, b, c and d, and establishing a three-dimensional space coordinate system x-y-z by taking the point O as a coordinate origin; wherein, the O point is the origin of the geometric center coordinate of the horizontal plane of the whole stage, and the coordinate value is O (0, 0, 0); the x direction is parallel to a connecting line from the corner a to the corner b; the y direction is a direction parallel to a connecting line from the corner b to the corner c; the z direction is parallel to the connecting line from the angular point a to the lifting point A;
step 4, enclosing the angular points a, B, C, D, A, B, C and D into a rectangle in an ideal condition, wherein the length of the rectangle is L, the width of the rectangle is W, and the height of the rectangle is H; wherein, the length L is the distance from the corner a to the connecting line of the corner b; the width W is the distance from the corner b to the connecting line of the corner c; the height H is the distance from the corner a to the connecting line of the lifting point A;
according to the actual size, length L, width W and height H of the stage, the coordinate values of each suspension point of the overhead boom in fig. 1 can be obtained, and assuming that the measurement installation and calibration are error-free, the ideal coordinates of each corner point and suspension point are, respectively:
the ideal coordinate of the corner point a is
Figure BDA0002672396970000091
The ideal coordinate of the corner point b is
Figure BDA0002672396970000092
Ideal coordinates of the corner point c are
Figure BDA0002672396970000093
Ideal coordinates of the corner point d are
Figure BDA0002672396970000094
The ideal coordinate of the hanging point A is
Figure BDA0002672396970000095
The ideal coordinate of the lifting point B is
Figure BDA0002672396970000096
Ideal coordinates of the hoisting point C are
Figure BDA0002672396970000097
The ideal coordinate of the hanging point D is
Figure BDA0002672396970000098
Because there is installation error in 1 st overhead jib, 2 nd overhead jib, 3 rd overhead jib and 4 th overhead jib to, there is measuring error in each hoisting point and angular point, consequently, the coordinate measurement calibration value of each hoisting point is respectively: the coordinate measurement calibration value of the lifting point A is
Figure BDA0002672396970000099
The coordinate measurement calibration value of the lifting point B is
Figure BDA00026723969700000910
The coordinate measurement calibration value of the lifting point C is
Figure BDA00026723969700000911
Figure BDA00026723969700000912
The coordinate measurement calibration value of the lifting point D is
Figure BDA00026723969700000913
Wherein, + Δ is an error value of installation calibration;
and 5, setting coordinate calculation values of the lifting points as follows: the coordinate solution of the lifting point A is A (x)1，y1，z1) (ii) a The coordinate solution value of the lifting point B is B (x)2，y2，z2) (ii) a The coordinate solution value of the lifting point C is C (x)3，y3，z3) (ii) a The coordinate solution of the lifting point D is D (x)4，y4，z4) (ii) a The coordinate calculation value of each lifting point is to-be-evaluated;
firstly, manually dragging an actuator E to be positioned at a coordinate origin point O; then, dragging the actuator E to reach different space target position points according to a set dragging rule;
whenever the actuator E is dragged to reach a certain spatial target position point (x)0，y0，z0) Time, space target location point (x)0，y0，z0) And by each encoder, a respective rope length value can be recorded, respectively: length of 1 st rope is L10The 2 nd rope has a length L20And the 3 rd rope has a length L30Length of 4 th rope is L40；
Establishing a target location point (x) in space by0，y0，z0) The corresponding equation:
(x1-x0)2+(y1-y0)2+(z1-z0)2＝L10 2
(x2-x0)2+(y2-y0)2+(z2-z0)2＝L20 2
(x3-x0)2+(y3-y0)2+(z3-z0)2＝L30 2
(x4-x0)2+(y4-y0)2+(z4-z0)2＝L40 2
assuming that the actuator is dragged to n space target position points, therefore, n equations can be obtained; solving an equation set formed by n equations to obtain a coordinate calculation value A (x) of the lifting point A1，y1，z1) Coordinate solution value B (x) of suspension point B2，y2，z2) Coordinate solution value C (x) of suspension point C3，y3，z3) And the coordinate solution value D (x) of the lifting point D4，y4，z4)；
In this step, according to a set dragging rule, dragging the actuator E to reach different spatial target position points specifically:
dragging the actuator E to move to different target positions along the positive direction of the x axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the negative direction of the x axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the positive direction of the y axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the negative direction of the y axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the positive direction of the z axis at intervals of 1 unit length;
and (4) at intervals of 1 unit length, dragging the actuator E to move to different target positions along the negative direction of the z axis.
For example, if the position coordinates of the actuator E are moved by 1 unit length each time, starting from the geometric center origin coordinates O of the performance area and using the coordinate system O-xyz as a scale, the detailed steps are as follows:
(1) if the point E of the actuator is moved to the original point O, the new coordinate of the point E of the actuator is E (x)0＝0，y0＝0，z00) and the length of the rope after the movement is known as (L) by measurement11，L21，L31，L41) Then substituting the value into the equation above can obtain:
(x1-0)2+(y1-0)2+(z1-0)2＝L11 2
(x2-0)2+(y2-0)2+(z2-0)2＝L21 2
(x3-0)2+(y3-0)2+(z3-0)2＝L31 2
(x4-0)2+(y4-0)2+(z4-0)2＝L41 2
this formula can be simplified as:
(x1)2+(y1)2+(z1)2＝L11 2
(x2)2+(y2)2+(z2)2＝L21 2
(x3)2+(y3)2+(z3)2＝L31 2
(x4)2+(y4)2+(z4)2＝L41 2
(2) moving the point E of the actuator by 1 unit length along the positive direction of the y axis, and then the new coordinate of the point E of the actuator is E (x)0＝0，y0＝1，z00) and the length of the rope after the movement is known as (L) by measurement12，L22，L32，L42) Then, substituting the class value into the equation above can obtain:
(x1-0)2+(y1-1)2+(z1-0)2＝L12 2
(x2-0)2+(y2-1)2+(z2-0)2＝L22 2
(x3-0)2+(y3-1)2+(z3-0)2＝L32 2
(x4-0)2+(y4-1)2+(z4-0)2＝L42 2
this formula can be simplified as:
(x1)2+(y1-1)2+(z1)2＝L12 2
(x2)2+(y2-1)2+(z2)2＝L22 2
(x3)2+(y3-1)2+(z3)2＝L32 2
(x4)2+(y4-1)2+(z4)2＝L42 2
(3) moving the point E of the actuator by 1 unit length along the negative direction of the y axis, and then the new coordinate of the point E of the actuator is E (x)0＝0，y0＝-1，z00) and the length of the rope after the movement is known as (L) by measurement13，L23，L33，L43) Then substituting the value into the equation above can obtain:
(x1-0)2+(y1+1)2+(z1-0)2＝L13 2
(x2-0)2+(y2+1)2+(z2-0)2＝L23 2
(x3-0)2+(y3+1)2+(z3-0)2＝L33 2
(x4-0)2+(y4+1)2+(z4-0)2＝L43 2
this formula can be simplified as:
(x1)2+(y1+1)2+(z1)2＝L13 2
(x2)2+(y2+1)2+(z2)2＝L23 2
(x3)2+(y3+1)2+(z3)2＝L33 2
(x4)2+(y4+1)2+(z4)2＝L43 2
(4) moving the point E of the actuator by 1 unit length along the positive direction of the x axis, and then the new coordinate of the point E of the actuator is E (x)0＝1，y0＝0，z00) and the length of the rope after the movement is known as (L) by measurement14，L24，L34，L44) Then substituting the value into the equation above can obtain:
(x1-1)2+(y1-0)2+(z1-0)2＝L14 2
(x2-1)2+(y2-0)2+(z2-0)2＝L24 2
(x3-1)2+(y3-0)2+(z3-0)2＝L34 2
(x4-1)2+(y4-0)2+(z4-0)2＝L44 2
this formula can be simplified as:
(x1-1)2+(y1)2+(z1)2＝L14 2
(x2-1)2+(y2)2+(z2)2＝L24 2
(x3-1)2+(y3)2+(z3)2＝L34 2
(x4-1)2+(y4)2+(z4)2＝L44 2
(2) moving the point E of the actuator by 1 unit length along the negative direction of the x axis, and then the new coordinate of the point E of the actuator is E (x)0＝-1，y0＝0，z00) and the length of the rope after the movement is known as (L) by measurement15，L25，L35，L45) Then substituting the value into the equation above can obtain:
(x1+1)2+(y1-0)2+(z1-0)2＝L15 2
(x2+1)2+(y2-0)2+(z2-0)2＝L25 2
(x3+1)2+(y3-0)2+(z3-0)2＝L35 2
(x4+1)2+(y4-0)2+(z4-0)2＝L45 2
this formula can be simplified as:
(x1+1)2+(y1)2+(z1)2＝L15 2
(x2+1)2+(y2)2+(z2)2＝L25 2
(x3+1)2+(y3)2+(z3)2＝L35 2
(x4+1)2+(y4)2+(z4)2＝L45 2
step 6, comparing the coordinate calculation value of each lifting point with the corresponding coordinate measurement calibration value, and respectively obtaining the calibration error value of the lifting point A according to the following formula
Figure BDA0002672396970000131
Calibration error value of lifting point B
Figure BDA0002672396970000132
Calibration error value of lifting point C
Figure BDA0002672396970000133
And the calibration error value of the lifting point D
Figure BDA0002672396970000134
Figure BDA0002672396970000141
And 7, superposing half of the calibration error value of each lifting point to the corresponding coordinate measurement calibration value by adopting the following formula to obtain a coordinate value of each lifting point after final correction, namely: the corrected coordinate value of the lifting point A is Aj(x1j，y1j，z1j) The corrected coordinate value of the lifting point B is Bj(x2j，y2j，z2j) The corrected coordinate value of the lifting point C is Cj(x3j，y3j，z3j) The corrected coordinate value of the sum point D is the sum Dj(x4j，y4j，z4j)；
Figure BDA0002672396970000151
In practical application, the ideal coordinate value (A) of each suspension pointi，Bi，Ci，Di) Due to the interference of stage process, construction, environment and the like, it is difficult to obtain a true ideal value. Therefore, in general, the measurement calibration values (A ', B', C ', D') after calibration of the ideal coordinate values are identified as the ideal coordinate values, i.e., (A)i＝A′，Bi＝B′，Ci＝C′，DiD'). The correction of the error is then also associated with the correction of the measured calibration values (a ', B', C ', D').
According to the above steps, the invention obtains the error value between the measurement calibration value and the coordinate calculation value, and superimposes half of the error value on the measurement calibration value, so as to correct the whole device control system, and finally obtain the corrected coordinate value (A)j，Bj，Cj，Dj)。
And 8, during actual performance, generating control instructions for the rope winder A, the rope winder B, the rope winder C and the rope winder D according to the coordinate values after the correction of the lifting points and the target position of the actuator E, further controlling each rope winder to automatically act, controlling the actuator E to move to the target position, and realizing the spatial attitude control of the actuator E.
The invention provides an overhead suspender error correction method based on a four-flexible-cable traction parallel actuator, which mainly comprises the following steps:
the method comprises the steps of firstly taking the geometric center of a stage theater as an origin of coordinates by utilizing convenience and easiness in measurement of a stage horizontal plane, then enabling an actuator to move in unit length from the origin of coordinates, recording the lengths of ropes by utilizing four flexible cables pulled by an overhead suspender after the actuator is moved, then calculating a coordinate value of a hanging point of a rope outlet end pulled by the overhead suspender by utilizing a mathematical model, and then carrying out contrast correction by utilizing a coordinate value actually tested and the coordinate value calculated by the mathematical model. In addition, in the whole implementation process, the algorithm is simple, and the method is very suitable for being applied to various stage spaces.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements should also be considered within the scope of the present invention.

Claims (2)

1. An overhead suspender error correction method based on a four-flexible-cable traction parallel actuator is characterized by comprising the following steps:
step 1, in the stage performance space, the ground plane in the stage performance area is the stage horizontal plane, and four angular points of the stage horizontal plane are overhead jib bottom mounted position, and wherein, four angular points of the stage horizontal plane are according to anticlockwise range, represent in proper order and be: an angular point a, an angular point b, an angular point c and an angular point d; the angular points a, b, c and d are connected end to form a rectangle;
at the corner a, the 1 st overhead boom is installed, and the top suspension point of the 1 st overhead boom is denoted as suspension point a, and therefore, the 1 st overhead boom is denoted as: aA; at the corner B, a 2 nd overhead boom is mounted, the top suspension point of the 2 nd overhead boom being denoted as suspension point B, and thus the 2 nd overhead boom is denoted as: bB; at the corner C, a 3 rd overhead boom is mounted, the top suspension point of the 3 rd overhead boom being denoted as suspension point C, and therefore the 3 rd overhead boom is denoted as: cC; at the corner point D, a 4 th overhead boom is mounted, the top suspension point of the 4 th overhead boom being denoted as suspension point D, and therefore the 4 th overhead boom being denoted as: dD; the hoisting point A, the hoisting point B, the hoisting point C and the hoisting point D are connected end to form a rectangle;
step 2, respectively installing a rope winder A provided with an encoder A, a rope winder B provided with an encoder B, a rope winder C provided with an encoder C and a rope winder D provided with an encoder D at a lifting point A, a lifting point B, a lifting point C and a lifting point D;
the actuator E is connected with the rope winder A through the 1 st rope, and the length L of the 1 st rope can be recorded in real time through the encoder A1(ii) a The actuator E is connected with the rope winder B through a 2 nd rope, and the length L of the 2 nd rope can be recorded in real time through the encoder B2(ii) a The actuator E is connected with the rope winder C through the 3 rd rope, and the length L of the 3 rd rope can be recorded in real time through the encoder C3(ii) a The actuator E is connected with the rope winder D through a 4 th rope, and the length L of the 4 th rope can be recorded in real time through the encoder D4；
Step 3, at the stage level, namely: determining a diagonal intersection point O in a rectangular area defined by the angular point a, the angular point b, the angular point c and the angular point d, and establishing a three-dimensional space coordinate system x-y-z by taking the point O as a coordinate origin; wherein, the coordinate value of the O point is O (0, 0, 0); the x direction is parallel to a connecting line from the corner a to the corner b; the y direction is a direction parallel to a connecting line from the corner b to the corner c; the z direction is parallel to the connecting line from the angular point a to the lifting point A;
step 4, enclosing the angular points a, B, C, D, A, B, C and D into a rectangle in an ideal condition, wherein the length of the rectangle is L, the width of the rectangle is W, and the height of the rectangle is H; wherein, the length L is the distance from the corner a to the connecting line of the corner b; the width W is the distance from the corner b to the connecting line of the corner c; the height H is the distance from the corner a to the connecting line of the lifting point A;
the ideal coordinate of the corner point a is
Figure FDA0002672396960000021
The ideal coordinate of the corner point b is
Figure FDA0002672396960000022
Ideal coordinates of the corner point c are
Figure FDA0002672396960000023
Ideal coordinates of the corner point d are
Figure FDA0002672396960000024
The ideal coordinate of the hanging point A is
Figure FDA0002672396960000025
The ideal coordinate of the lifting point B is
Figure FDA0002672396960000026
Ideal coordinates of the hoisting point C are
Figure FDA0002672396960000027
The ideal coordinate of the hanging point D is
Figure FDA0002672396960000028
Because there is installation error in 1 st overhead jib, 2 nd overhead jib, 3 rd overhead jib and 4 th overhead jib to, there is measuring error in each hoisting point and angular point, consequently, the coordinate measurement calibration value of each hoisting point is respectively: the coordinate measurement calibration value of the lifting point A is
Figure FDA0002672396960000029
The coordinate measurement calibration value of the lifting point B is
Figure FDA00026723969600000210
The coordinate measurement calibration value of the lifting point C is
Figure FDA00026723969600000211
Figure FDA00026723969600000212
The coordinate measurement calibration value of the lifting point D is
Figure FDA00026723969600000213
Wherein, + Δ is an error value of installation calibration;
and 5, setting coordinate calculation values of the lifting points as follows: the coordinate solution of the lifting point A is A (x)1，y1，z1) (ii) a The coordinate solution value of the lifting point B is B (x)2，y2，z2) (ii) a The coordinate solution value of the lifting point C is C (x)3，y3，z3) (ii) a The coordinate solution of the lifting point D is D (x)4，y4，z4) (ii) a The coordinate calculation value of each lifting point is to-be-evaluated;
firstly, manually dragging an actuator E to be positioned at a coordinate origin point O; then, dragging the actuator E to reach different space target position points according to a set dragging rule;
whenever the actuator E is dragged to reach a certain spatial target position point (x)0，y0，z0) Time, space target location point (x)0，y0，z0) And by each encoder, a respective rope length value can be recorded, respectively: length of 1 st rope is L10The 2 nd rope has a length L20And the 3 rd rope has a length L30Length of 4 th rope is L40；
Establishing a target location point (x) in space by0，y0，z0) The corresponding equation:
(x1-x0)2+(y1-y0)2+(z1-z0)2＝L10 2
(x2-x0)2+(y2-y0)2+(z2-z0)2＝L20 2
(x3-x0)2+(y3-y0)2+(z3-z0)2＝L30 2
(x4-x0)2+(y4-y0)2+(z4-z0)2＝L40 2
assuming that the actuator is dragged to n space target position points, therefore, n equations can be obtained; solving an equation set formed by n equations to obtain a coordinate calculation value A (x) of the lifting point A1，y1，z1) Coordinate solution value B (x) of suspension point B2，y2，z2) Coordinate solution value C (x) of suspension point C3，y3，z3) And the coordinate solution value D (x) of the lifting point D4，y4，z4)；
Step 6, comparing the coordinate calculation value of each lifting point with the corresponding coordinate measurement calibration value, and respectively obtaining the calibration error value of the lifting point A according to the following formula
Figure FDA0002672396960000031
Calibration error value of lifting point B
Figure FDA0002672396960000032
Calibration error value of lifting point C
Figure FDA0002672396960000033
And the calibration error value of the lifting point D
Figure FDA0002672396960000034
Figure FDA0002672396960000035
And 7, superposing half of the calibration error value of each lifting point to the corresponding coordinate measurement calibration value by adopting the following formula to obtain the coordinate value of each lifting point after final correctionNamely: the corrected coordinate value of the lifting point A is Aj(x1j，y1j，z1j) The corrected coordinate value of the lifting point B is Bj(x2j，y2j，z2j) The corrected coordinate value of the lifting point C is Cj(x3j，y3j，z3j) The corrected coordinate value of the sum point D is the sum Dj(x4j，y4j，z4j)；
Figure FDA0002672396960000041
And 8, during actual performance, generating control instructions for the rope winder A, the rope winder B, the rope winder C and the rope winder D according to the coordinate values after the correction of the lifting points and the target position of the actuator E, further controlling each rope winder to automatically act, controlling the actuator E to move to the target position, and realizing the spatial attitude control of the actuator E.
2. The method for correcting the error of the overhead boom based on the four-wire traction parallel actuator according to claim 1, wherein in step 5, according to a set traction rule, the actuator E is dragged to reach different spatial target position points, specifically:
dragging the actuator E to move to different target positions along the positive direction of the x axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the negative direction of the x axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the positive direction of the y axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the negative direction of the y axis at intervals of 1 unit length;
dragging the actuator E to move to different target positions along the positive direction of the z axis at intervals of 1 unit length;
and (4) at intervals of 1 unit length, dragging the actuator E to move to different target positions along the negative direction of the z axis.
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