CN112077836B - Overhead boom error correction method based on four-flexible-cable traction parallel actuator - Google Patents

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

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CN112077836B
CN112077836B CN202010937266.4A CN202010937266A CN112077836B CN 112077836 B CN112077836 B CN 112077836B CN 202010937266 A CN202010937266 A CN 202010937266A CN 112077836 B CN112077836 B CN 112077836B
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point
corner
rope
coordinate
value
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CN112077836A (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

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Control And Safety Of Cranes (AREA)

Abstract

The invention provides an overhead boom error correction method based on four-flexible-cable traction parallel actuators, which comprises the following steps: establishing a three-dimensional space coordinate system x-y-z; determining coordinate measurement calibration values of all the hanging points; dragging the actuator E to different space target position points according to a set dragging rule, and recording the length value of each rope; solving an equation set to obtain coordinate solution values of all the hanging points; comparing the coordinate solution value of each lifting point with the corresponding coordinate measurement calibration value to obtain a lifting point calibration error value; and (3) superposing half of the calibration error value of each lifting point into the corresponding coordinate measurement calibration value to obtain the final corrected coordinate value of each lifting point. The method can reduce the length error of the rope caused by the position of the hanging point of the overhead boom, so that the control precision of the overhead boom is improved. In addition, in the whole realization process, the algorithm is simple, and the method is very suitable for being applied to various stage spaces.

Description

Overhead boom error correction method based on four-flexible-cable traction parallel actuator
Technical Field
The invention belongs to the technical field of development of innovative stage performance technologies, and particularly relates to an overhead boom error correction method based on a four-flexible-rope traction parallel actuator.
Background
The four-flexible-cable traction parallel actuator performance system of the stage has the structure that: the four corner areas of the performance area are respectively provided with an overhead boom, the top of each overhead boom, namely, the position of a lifting point is provided with a winch, the rope outlet end of each winch extends out of a rope, and the other end of each rope is connected to an actuator after passing through a pulley; therefore, the four ropes drive the actuator to move randomly in a space range through parallel movement.
In general, the actuator can move freely in the three-dimensional space formed by the stage performance area and the overhead boom by controlling the length of the rope to be zoomed, and the rope to be zoomed is in important connection with the positions of the overhead booms in four corner areas.
In normal use, the rope length is generally calculated according to the position of the lifting point of the overhead boom in the corner area and the target position of the actuator, so that the instruction of rope scaling of the winch is performed by using the calculated rope length value, and the actuator is moved to the target position to the greatest extent. However, in actual use, due to changes in working environment or irregularities in performance areas, etc., the position of the suspension point of the overhead boom is generally determined by manual measurement, and this approach brings the following problems: (1) Due to the environmental problems and different measuring methods of measuring staff, the position of the lifting point of the overhead boom obtained by manual measurement generates a height error, and the error can directly influence the calculated value of the scaling length of the rope, thereby causing the deviation of the target position of the four-flexible-rope traction parallel actuator in the space range. For better control of the performance system, accurate determination of the position of each overhead boom suspension point is required.
In the existing performance system, most researchers and experimenters manually add experience constant values, so that the measured positions of the lifting points of the overhead boom are corrected, and the corrected values of the positions of the lifting points of the overhead boom are obtained. However, the addition of the empirical values is disadvantageous in that the addition of the empirical values causes the experimental values to be mutually exclusive, and the performance system is a four-flexible-cable parallel system, so that the parameters are mutually restricted and mutually restrained to be mutually fed back, and the final control effect is still poor due to the addition of the empirical values.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention provides an overhead boom error correction method based on a four-flexible-rope traction parallel actuator, which can effectively solve the problems.
The technical scheme adopted by the invention is as follows:
the invention provides an overhead boom error correction method based on a four-flexible-cable traction parallel actuator, which comprises the following steps of:
step 1, in a stage performance space, the ground plane of a stage performance area is a stage horizontal plane, four corner points of the stage horizontal plane are overhead boom bottom mounting positions, wherein the four corner points of the stage horizontal plane are arranged anticlockwise, and the four corner points are expressed as: corner a, corner b, corner c and corner d; corner a, corner b, corner c and corner d are connected end to form a rectangle;
the 1 st overhead boom is installed at the corner point a, the top suspension point of the 1 st overhead boom is denoted as suspension point a, and thus the 1 st overhead boom is denoted as: aA; the 2 nd overhead boom is mounted at the corner B, the top suspension point of the 2 nd overhead boom being denoted as suspension point B, and thus the 2 nd overhead boom being denoted as: bB; the 3 rd overhead boom is mounted at the corner C, the top suspension point of the 3 rd overhead boom being denoted suspension point C, and thus the 3 rd overhead boom being denoted as: a cC; the 4 th overhead boom is mounted at the corner D, the top suspension point of the 4 th overhead boom being denoted as suspension point D, and thus the 4 th overhead boom being denoted as: dD; the hanging point A, the hanging point B, the hanging point C and the hanging point D are connected end to form a rectangle;
step 2, a hoisting point A, a hoisting point B, a hoisting point C and a hoisting point D are respectively provided with 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;
the actuator E is connected with the rope coiling machine A through the 1 st rope, and the length L of the 1 st rope can be recorded in real time through the encoder A 1 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope winder B through the 2 nd rope, and the length L of the 2 nd rope can be recorded in real time through the encoder B 2 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope coiling machine C through the 3 rd rope, and the length L of the 3 rd rope can be recorded in real time through the encoder C 3 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope coiling machine D through the 4 th rope, and the length L of the 4 th rope can be recorded in real time through the encoder D 4 ；
Step 3, at stage level, namely: determining a diagonal intersection point O by using a rectangular area surrounded by the corner a, the corner b, the corner c and the corner d, and establishing a three-dimensional space coordinate system x-y-z by taking the O point as a coordinate origin; wherein, the coordinate value of the O point is O (0, 0); the x direction is the direction parallel to the connecting line from the corner a to the corner b; the y direction is the direction parallel to the connecting line from the corner b to the corner c; the z direction is the direction parallel to the connecting line from the corner point a to the hanging point A;
step 4, corner a, corner B, corner C, corner D, hanging point A, hanging point B, hanging point C and hanging point D are enclosed into a rectangle under ideal conditions, the length of the rectangle is L, the width is W, and the height is H; the length L is the distance between the corner a and the corner b; the width W is the distance from the corner b to the corner c; the height H is the distance from the corner a to the connecting line of the hanging point A;
the ideal coordinates of the corner point a areThe ideal coordinates of corner b are +.>The ideal coordinates of the corner point c are +.>The ideal coordinates of the corner d are +.>
The ideal coordinates of the suspension point A areThe ideal coordinates of the hanging point B are +.>The ideal coordinates of the lifting point C are +.>The ideal coordinates of the suspension point D are +.>
Due to the installation errors of the 1 st, 2 nd, 3 rd and 4 th overhead booms, andmeasurement errors exist in each lifting point and each corner point, so that coordinate measurement calibration values of each lifting point are respectively as follows: the coordinate measurement calibration value of the hanging point A isThe coordinate measurement calibration value of the lifting point B is +.>The coordinate measurement calibration value of the lifting point C is +.> The coordinate measurement calibration value of the hanging point D isWherein, +Δ is the error value of the installation calibration;
step 5, setting coordinate solutions of the hanging points as follows: the coordinate solution of the suspension point a is a (x 1 ，y 1 ，z 1 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the hanging point B is B (x 2 ，y 2 ，z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the lifting point C is C (x 3 ，y 3 ，z 3 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the suspension point D is D (x 4 ，y 4 ，z 4 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution value of each lifting point is to be evaluated;
firstly, manually dragging an actuator E to be positioned at a point O of a coordinate origin; then, dragging the actuator E to different space target position points according to a set dragging rule;
whenever the drag actuator E reaches a certain spatial target position point (x 0 ，y 0 ，z 0 ) At this time, the spatial target position point (x 0 ，y 0 ，z 0 ) Is known and, by means of the encoders, the respective rope length values are recorded, respectively: 1 st rope length L 10 The length of the 2 nd rope is L 20 3 rd rope length L 30 Length of 4 th rope L 40 ；
By establishing a spatial target position point (x 0 ，y 0 ，z 0 ) The corresponding equation:
(x 1 -x 0 ) 2 +(y 1 -y 0 ) 2 +(z 1 -z 0 ) 2 ＝L 10 2
(x 2 -x 0 ) 2 +(y 2 -y 0 ) 2 +(z 2 -z 0 ) 2 ＝L 20 2
(x 3 -x 0 ) 2 +(y 3 -y 0 ) 2 +(z 3 -z 0 ) 2 ＝L 30 2
(x 4 -x 0 ) 2 +(y 4 -y 0 ) 2 +(z 4 -z 0 ) 2 ＝L 40 2
assuming that the actuator is dragged to n space target position points altogether, n equations can be obtained; solving an equation set formed by n equations to obtain a coordinate solution value A (x 1 ，y 1 ，z 1 ) Coordinate solution value B (x 2 ，y 2 ，z 2 ) Coordinate calculation value C (x of suspension point C 3 ，y 3 ，z 3 ) And a coordinate solution value D (x 4 ，y 4 ，z 4 )；
Step 6, comparing the coordinate calculated 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 stepsCalibration error value of lifting point B>Calibration error value of lifting point C>And the calibration error value of the lifting point D +.>
And 7, superposing half of the calibration error value of each lifting point into the corresponding coordinate measurement calibration value to obtain the coordinate value of each lifting point after final correction, namely: the corrected coordinate value of the hanging point A is A j (x 1j ，y 1j ，z 1j ) The corrected coordinate value of the hanging point B is B j (x 2j ，y 2j ，z 2j ) The corrected coordinate value of the lifting point C is C j (x 3j ，y 3j ，z 3j ) And the corrected coordinate value of the lifting point D is D j (x 4j ，y 4j ，z 4j )；
And 8, during actual performance, generating control instructions for the rope winding machine A, the rope winding machine B, the rope winding machine C and the rope winding machine D according to the coordinate values corrected by the lifting points and the target position of the actuator E, further controlling the automatic action of each rope winding machine, and controlling the actuator E to move to the target position so as to realize the space attitude control of the actuator E.
Preferably, in step 5, according to a set drag rule, the drag actuator E reaches different spatial target position points, specifically:
the drag actuator E moves to different target positions along the positive direction of the x axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the negative direction of the x axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the positive direction of the y axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the negative y-axis direction at intervals of 1 unit length;
the drag actuator E moves to different target positions along the positive direction of the z axis at intervals of 1 unit length;
at intervals of 1 unit length, the drag actuator E moves to different target positions in the negative z-axis direction.
The overhead boom 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 a coordinate origin, then enabling an actuator to move from the coordinate origin by unit length, after the actuator is moved, enabling four flexible ropes pulled by an overhead boom to generate different rope lengths, recording the rope lengths, then calculating the coordinate value of a lifting point of a rope pulling end of the overhead boom by using a mathematical model, and then comparing and correcting the coordinate value obtained by using the coordinate value actually tested with the coordinate value calculated by using the mathematical model. In addition, in the whole realization process, the algorithm is simple, and the method is very suitable for being applied to various stage spaces.
Drawings
FIG. 1 is a geometric schematic of three-dimensional space dimensions of a stage area provided by the present invention;
fig. 2 is a schematic flow chart of an overhead boom error correction method based on a four-flexible-cable traction parallel actuator.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects solved by the invention more clear, the 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 for purposes of illustration only and are not intended to limit the scope of the invention.
In the prior art, because the measurement error exists in the position of the lifting point of the overhead boom, the correction mode is adopted by adding an empirical value, and errors in position calibration and system control can still be caused, so that the motion precision of an actuator is greatly influenced.
Based on the above, the invention provides an overhead boom error correction method based on a four-flexible-cable traction parallel actuator, and referring to fig. 2 and 1, the method comprises the following steps:
step 1, in a stage performance space, the ground plane of a stage performance area is a stage horizontal plane, four corner points of the stage horizontal plane are overhead boom bottom mounting positions, wherein the four corner points of the stage horizontal plane are arranged anticlockwise, and the four corner points are expressed as: corner a, corner b, corner c and corner d; corner a, corner b, corner c and corner d are connected end to form a rectangle;
the 1 st overhead boom is installed at the corner point a, the top suspension point of the 1 st overhead boom is denoted as suspension point a, and thus the 1 st overhead boom is denoted as: aA; the 2 nd overhead boom is mounted at the corner B, the top suspension point of the 2 nd overhead boom being denoted as suspension point B, and thus the 2 nd overhead boom being denoted as: bB; the 3 rd overhead boom is mounted at the corner C, the top suspension point of the 3 rd overhead boom being denoted suspension point C, and thus the 3 rd overhead boom being denoted as: a cC; the 4 th overhead boom is mounted at the corner D, the top suspension point of the 4 th overhead boom being denoted as suspension point D, and thus the 4 th overhead boom being denoted as: dD; the hanging point A, the hanging point B, the hanging point C and the hanging point D are connected end to form a rectangle;
step 2, a hoisting point A, a hoisting point B, a hoisting point C and a hoisting point D are respectively provided with 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;
the actuator E is connected with the rope coiling machine A through the 1 st rope, and the length L of the 1 st rope can be recorded in real time through the encoder A 1 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope winder B through the 2 nd rope, and the length L of the 2 nd rope can be recorded in real time through the encoder B 2 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope coiling machine C through the 3 rd rope, and the length L of the 3 rd rope can be recorded in real time through the encoder C 3 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope coiling machine D through the 4 th rope, and the length L of the 4 th rope can be recorded in real time through the encoder D 4 ；
Step 3, at stage level, namely: the rectangular area surrounded by the corner a, the corner b, the corner c and the corner d utilizes the convenience of the stage horizontal plane, utilizes a tool to determine a diagonal intersection point O in the stage horizontal plane, and uses the point O as a coordinate origin to establish a three-dimensional space coordinate system x-y-z; the point O is the geometric center coordinate origin of the whole stage horizontal plane, and the coordinate value of the point O is O (0, 0); the x direction is the direction parallel to the connecting line from the corner a to the corner b; the y direction is the direction parallel to the connecting line from the corner b to the corner c; the z direction is the direction parallel to the connecting line from the corner point a to the hanging point A;
step 4, corner a, corner B, corner C, corner D, hanging point A, hanging point B, hanging point C and hanging point D are enclosed into a rectangle under ideal conditions, the length of the rectangle is L, the width is W, and the height is H; the length L is the distance between the corner a and the corner b; the width W is the distance from the corner b to the corner c; the height H is the distance from the corner a to the connecting line of the hanging point A;
according to the actual size of the stage, the length L, the width W and the height H can obtain the coordinate values of each lifting point of the overhead boom in fig. 1, and under the ideal condition, the ideal coordinates of each corner point and each lifting point are respectively:
the ideal coordinates of the corner point a areThe ideal coordinates of corner b are +.>The ideal coordinates of the corner point c are +.>The ideal coordinates of the corner d are +.>
The ideal coordinates of the suspension point A areThe ideal coordinates of the hanging point B are +.>The ideal coordinates of the lifting point C are +.>The ideal coordinates of the suspension point D are +.>
Because there is an installation error in the 1 st overhead boom, the 2 nd overhead boom, the 3 rd overhead boom and the 4 th overhead boom, and there is a measurement error in each hanging point and corner point, the coordinate measurement calibration values of each hanging point are respectively: the coordinate measurement calibration value of the hanging point A isThe coordinate measurement calibration value of the lifting point B is +.>The coordinate measurement calibration value of the lifting point C is +.> The coordinate measurement calibration value of the hanging point D isWherein, +Δ is the error value of the installation calibration;
step 5, setting coordinate solutions of the hanging points as follows: the coordinate solution of the suspension point a is a (x 1 ，y 1 ，z 1 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the hanging point B is B (x 2 ，y 2 ，z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the lifting point C is C (x 3 ，y 3 ，z 3 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the suspension point D is D (x 4 ，y 4 ，z 4 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution value of each lifting point is to be evaluated;
firstly, manually dragging an actuator E to be positioned at a point O of a coordinate origin; then, dragging the actuator E to different space target position points according to a set dragging rule;
whenever the drag actuator E reaches a certain spatial target position point (x 0 ，y 0 ，z 0 ) At this time, the spatial target position point (x 0 ，y 0 ，z 0 ) Is known and, by means of the encoders, the respective rope length values are recorded, respectively: 1 st rope length L 10 The length of the 2 nd rope is L 20 3 rd rope length L 30 Length of 4 th rope L 40 ；
By establishing a spatial target position point (x 0 ，y 0 ，z 0 ) The corresponding equation:
(x 1 -x 0 ) 2 +(y 1 -y 0 ) 2 +(z 1 -z 0 ) 2 ＝L 10 2
(x 2 -x 0 ) 2 +(y 2 -y 0 ) 2 +(z 2 -z 0 ) 2 ＝L 20 2
(x 3 -x 0 ) 2 +(y 3 -y 0 ) 2 +(z 3 -z 0 ) 2 ＝L 30 2
(x 4 -x 0 ) 2 +(y 4 -y 0 ) 2 +(z 4 -z 0 ) 2 ＝L 40 2
assuming that the actuator is dragged to n space target position points altogether, n equations can be obtained; solving an equation set formed by n equations to obtain a coordinate solution value A (x 1 ，y 1 ，z 1 ) Coordinate solution value B (x 2 ，y 2 ，z 2 ) Coordinate calculation value C (x of suspension point C 3 ，y 3 ，z 3 ) And a coordinate solution value D (x 4 ，y 4 ，z 4 )；
In this step, according to a set dragging rule, the actuator E is dragged to reach different spatial target position points, specifically:
the drag actuator E moves to different target positions along the positive direction of the x axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the negative direction of the x axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the positive direction of the y axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the negative y-axis direction at intervals of 1 unit length;
the drag actuator E moves to different target positions along the positive direction of the z axis at intervals of 1 unit length;
at intervals of 1 unit length, the drag actuator E moves to different target positions in the negative z-axis direction.
For example, the position coordinates of the moving actuator E are moved by 1 unit length each time, with the geometric center origin coordinates O of the performance area as a starting point and the coordinate system O-xyz as a scale, and the detailed steps are as follows:
(1) If the actuator E point is moved to the origin O, the new coordinates of the actuator E point are E (x 0 ＝0，y 0 ＝0，z 0 =0), and the length of the rope after movement is measured to be (L 11 ，L 21 ，L 31 ，L 41 ) Substituting the class value into the equation of the above formula yields:
(x 1 -0) 2 +(y 1 -0) 2 +(z 1 -0) 2 ＝L 11 2
(x 2 -0) 2 +(y 2 -0) 2 +(z 2 -0) 2 ＝L 21 2
(x 3 -0) 2 +(y 3 -0) 2 +(z 3 -0) 2 ＝L 31 2
(x 4 -0) 2 +(y 4 -0) 2 +(z 4 -0) 2 ＝L 41 2
the formula can be simplified as:
(x 1 ) 2 +(y 1 ) 2 +(z 1 ) 2 ＝L 11 2
(x 2 ) 2 +(y 2 ) 2 +(z 2 ) 2 ＝L 21 2
(x 3 ) 2 +(y 3 ) 2 +(z 3 ) 2 ＝L 31 2
(x 4 ) 2 +(y 4 ) 2 +(z 4 ) 2 ＝L 41 2
(2) When the actuator E point is moved by 1 unit length along the positive direction of the y axis, the new coordinate of the actuator E point is E (x 0 ＝0，y 0 ＝1，z 0 =0), and the length of the rope after movement is measured to be (L 12 ，L 22 ，L 32 ，L 42 ) Substituting the class value into the equation of the above formula can obtain:
(x 1 -0) 2 +(y 1 -1) 2 +(z 1 -0) 2 ＝L 12 2
(x 2 -0) 2 +(y 2 -1) 2 +(z 2 -0) 2 ＝L 22 2
(x 3 -0) 2 +(y 3 -1) 2 +(z 3 -0) 2 ＝L 32 2
(x 4 -0) 2 +(y 4 -1) 2 +(z 4 -0) 2 ＝L 42 2
the formula can be simplified as:
(x 1 ) 2 +(y 1 -1) 2 +(z 1 ) 2 ＝L 12 2
(x 2 ) 2 +(y 2 -1) 2 +(z 2 ) 2 ＝L 22 2
(x 3 ) 2 +(y 3 -1) 2 +(z 3 ) 2 ＝L 32 2
(x 4 ) 2 +(y 4 -1) 2 +(z 4 ) 2 ＝L 42 2
(3) Moving the actuator E point by 1 unit length along the negative direction of the y axis, the new coordinate of the actuator E point is E (x 0 ＝0，y 0 ＝-1，z 0 =0), and the length of the rope after movement is measured to be (L 13 ，L 23 ，L 33 ，L 43 ) Substituting the class value into the equation of the above formula yields:
(x 1 -0) 2 +(y 1 +1) 2 +(z 1 -0) 2 ＝L 13 2
(x 2 -0) 2 +(y 2 +1) 2 +(z 2 -0) 2 ＝L 23 2
(x 3 -0) 2 +(y 3 +1) 2 +(z 3 -0) 2 ＝L 33 2
(x 4 -0) 2 +(y 4 +1) 2 +(z 4 -0) 2 ＝L 43 2
the formula can be simplified as:
(x 1 ) 2 +(y 1 +1) 2 +(z 1 ) 2 ＝L 13 2
(x 2 ) 2 +(y 2 +1) 2 +(z 2 ) 2 ＝L 23 2
(x 3 ) 2 +(y 3 +1) 2 +(z 3 ) 2 ＝L 33 2
(x 4 ) 2 +(y 4 +1) 2 +(z 4 ) 2 ＝L 43 2
(4) When the actuator E point is moved by 1 unit length along the positive direction of the x axis, the new coordinate of the actuator E point is E (x 0 ＝1，y 0 ＝0，z 0 =0), and the length of the rope after movement isThe overdetering is known as (L 14 ，L 24 ，L 34 ，L 44 ) Substituting the class value into the equation of the above formula yields:
(x 1 -1) 2 +(y 1 -0) 2 +(z 1 -0) 2 ＝L 14 2
(x 2 -1) 2 +(y 2 -0) 2 +(z 2 -0) 2 ＝L 24 2
(x 3 -1) 2 +(y 3 -0) 2 +(z 3 -0) 2 ＝L 34 2
(x 4 -1) 2 +(y 4 -0) 2 +(z 4 -0) 2 ＝L 44 2
the formula can be simplified as:
(x 1 -1) 2 +(y 1 ) 2 +(z 1 ) 2 ＝L 14 2
(x 2 -1) 2 +(y 2 ) 2 +(z 2 ) 2 ＝L 24 2
(x 3 -1) 2 +(y 3 ) 2 +(z 3 ) 2 ＝L 34 2
(x 4 -1) 2 +(y 4 ) 2 +(z 4 ) 2 ＝L 44 2
(2) Moving the actuator E point by 1 unit length along the negative direction of the x axis, the new coordinate of the actuator E point is E (x 0 ＝-1，y 0 ＝0，z 0 =0), and the length of the rope after movement is measured to be (L 15 ，L 25 ，L 35 ，L 45 ) Substituting the class value into the equation of the above formula yields:
(x 1 +1) 2 +(y 1 -0) 2 +(z 1 -0) 2 ＝L 15 2
(x 2 +1) 2 +(y 2 -0) 2 +(z 2 -0) 2 ＝L 25 2
(x 3 +1) 2 +(y 3 -0) 2 +(z 3 -0) 2 ＝L 35 2
(x 4 +1) 2 +(y 4 -0) 2 +(z 4 -0) 2 ＝L 45 2
the formula can be simplified as:
(x 1 +1) 2 +(y 1 ) 2 +(z 1 ) 2 ＝L 15 2
(x 2 +1) 2 +(y 2 ) 2 +(z 2 ) 2 ＝L 25 2
(x 3 +1) 2 +(y 3 ) 2 +(z 3 ) 2 ＝L 35 2
(x 4 +1) 2 +(y 4 ) 2 +(z 4 ) 2 ＝L 45 2
step 6, comparing the coordinate calculated 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 stepsCalibration error value of lifting point B>Calibration error value of lifting point C>And the calibration error value of the lifting point D +.>
Step 7, adopt the followingSuperposing half of the calibration error value of each lifting point into the corresponding coordinate measurement calibration value to obtain the coordinate value of each lifting point after final correction, namely: the corrected coordinate value of the hanging point A is A j (x 1j ，y 1j ，z 1j ) The corrected coordinate value of the hanging point B is B j (x 2j ，y 2j ，z 2j ) The corrected coordinate value of the lifting point C is C j (x 3j ，y 3j ，z 3j ) And the corrected coordinate value of the lifting point D is D j (x 4j ，y 4j ，z 4j )；
In practical application, the ideal coordinate value (A i ，B i ，C i ，D i ) Due to the interference of stage technology, construction, environment and the like, a true ideal value is difficult to obtain. Therefore, in general, the measured calibration values (A ', B', C ', D') after calibration of the ideal coordinate values are regarded as ideal coordinate values, i.e., (A) i ＝A′，B i ＝B′，C i ＝C′，D i =d'). The correction of the errors then also pertains to 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 resolving value, and half of the error value is added to the measurement calibration value to calibrate the control system of the whole device, and finally the corrected coordinate value (A j ，B j ，C j ，D j )。
And 8, during actual performance, generating control instructions for the rope winding machine A, the rope winding machine B, the rope winding machine C and the rope winding machine D according to the coordinate values corrected by the lifting points and the target position of the actuator E, further controlling the automatic action of each rope winding machine, and controlling the actuator E to move to the target position so as to realize the space attitude control of the actuator E.
The invention provides an overhead boom error correction method based on a four-flexible-rope 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 a coordinate origin, then enabling an actuator to move from the coordinate origin by unit length, after the actuator is moved, enabling four flexible ropes pulled by an overhead boom to generate different rope lengths, recording the rope lengths, then calculating the coordinate value of a lifting point of a rope pulling end of the overhead boom by using a mathematical model, and then comparing and correcting the coordinate value obtained by using the coordinate value actually tested with the coordinate value calculated by using the mathematical model. In addition, in the whole realization process, the algorithm is simple, and the method is very suitable for being applied to various stage spaces.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which is also intended to be covered by the present invention.

Claims (2)

1. An overhead boom error correction method based on a four-flexible-rope traction parallel actuator is characterized by comprising the following steps of:
step 1, in a stage performance space, the ground plane of a stage performance area is a stage horizontal plane, four corner points of the stage horizontal plane are overhead boom bottom mounting positions, wherein the four corner points of the stage horizontal plane are arranged anticlockwise, and the four corner points are expressed as: corner a, corner b, corner c and corner d; corner a, corner b, corner c and corner d are connected end to form a rectangle;
the 1 st overhead boom is installed at the corner point a, the top suspension point of the 1 st overhead boom is denoted as suspension point a, and thus the 1 st overhead boom is denoted as: aA; the 2 nd overhead boom is mounted at the corner B, the top suspension point of the 2 nd overhead boom being denoted as suspension point B, and thus the 2 nd overhead boom being denoted as: bB; the 3 rd overhead boom is mounted at the corner C, the top suspension point of the 3 rd overhead boom being denoted suspension point C, and thus the 3 rd overhead boom being denoted as: a cC; the 4 th overhead boom is mounted at the corner D, the top suspension point of the 4 th overhead boom being denoted as suspension point D, and thus the 4 th overhead boom being denoted as: dD; the hanging point A, the hanging point B, the hanging point C and the hanging point D are connected end to form a rectangle;
step 2, a hoisting point A, a hoisting point B, a hoisting point C and a hoisting point D are respectively provided with 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;
the actuator E is connected with the rope coiling machine A through the 1 st rope, and the length L of the 1 st rope can be recorded in real time through the encoder A 1 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope winder B through the 2 nd rope, and the length L of the 2 nd rope can be recorded in real time through the encoder B 2 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope coiling machine C through the 3 rd rope, and the length L of the 3 rd rope can be recorded in real time through the encoder C 3 The method comprises the steps of carrying out a first treatment on the surface of the The actuator E is connected with the rope coiling machine D through the 4 th rope, and the length L of the 4 th rope can be recorded in real time through the encoder D 4 ；
Step 3, at stage level, namely: determining a diagonal intersection point O by using a rectangular area surrounded by the corner a, the corner b, the corner c and the corner d, and establishing a three-dimensional space coordinate system x-y-z by taking the O point as a coordinate origin; wherein, the coordinate value of the O point is O (0, 0); the x direction is the direction parallel to the connecting line from the corner a to the corner b; the y direction is the direction parallel to the connecting line from the corner b to the corner c; the z direction is the direction parallel to the connecting line from the corner point a to the hanging point A;
step 4, the corner a, the corner B, the corner C, the corner D, the hanging point A, the hanging point B, the hanging point C and the hanging point D are enclosed into a cuboid under ideal conditions, wherein the length of the cuboid is L, the width of the cuboid is W, and the height of the cuboid is H; the length L is the distance between the corner a and the corner b; the width W is the distance from the corner b to the corner c; the height H is the distance from the corner a to the connecting line of the hanging point A;
the ideal coordinates of the corner point a areThe ideal coordinates of corner b are +.>The ideal coordinates of the corner point c are +.>The ideal coordinates of the corner d are +.>
The ideal coordinates of the suspension point A areThe ideal coordinates of the hanging point B are +.>The ideal coordinates of the lifting point C are +.>The ideal coordinates of the suspension point D are +.>
Because there is an installation error in the 1 st overhead boom, the 2 nd overhead boom, the 3 rd overhead boom and the 4 th overhead boom, and there is a measurement error in each hanging point and corner point, the coordinate measurement calibration values of each hanging point are respectively: the coordinate measurement calibration value of the hanging point A isThe coordinate measurement calibration value of the lifting point B is +.>The coordinate measurement calibration value of the lifting point C is +.> The coordinate measurement calibration value of the hanging point D isWherein, +Δ is the error value of the installation calibration;
step 5, setting coordinate solutions of the hanging points as follows: the coordinate solution of the suspension point a is a (x 1 ,y 1 ,z 1 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the hanging point B is B (x 2 ,y 2 ,z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the lifting point C is C (x 3 ,y 3 ,z 3 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution of the suspension point D is D (x 4 ,y 4 ,z 4 ) The method comprises the steps of carrying out a first treatment on the surface of the The coordinate solution value of each lifting point is to be evaluated;
firstly, manually dragging an actuator E to be positioned at a point O of a coordinate origin; then, dragging the actuator E to different space target position points according to a set dragging rule;
whenever the drag actuator E reaches a certain spatial target position point (x 0 ,y 0 ,z 0 ) At this time, the spatial target position point (x 0 ,y 0 ,z 0 ) Is known and, by means of the encoders, the respective rope length values are recorded, respectively: 1 st rope length L 10 The length of the 2 nd rope is L 20 3 rd rope length L 30 Length of 4 th rope L 40 ；
By establishing a spatial target position point (x 0 ,y 0 ,z 0 ) The corresponding equation:
(x 1 -x 0 ) 2 +(y 1 -y 0 ) 2 +(z 1 -z 0 ) 2 ＝L 10 2
(x 2 -x 0 ) 2 +(y 2 -y 0 ) 2 +(z 2 -z 0 ) 2 ＝L 20 2
(x 3 -x 0 ) 2 +(y 3 -y 0 ) 2 +(z 3 -z 0 ) 2 ＝L 30 2
(x 4 -x 0 ) 2 +(y 4 -y 0 ) 2 +(z 4 -z 0 ) 2 ＝L 40 2
assume that together willThe actuator drags to n space target position points, so n equations can be obtained; solving an equation set formed by n equations to obtain a coordinate solution value A (x 1 ,y 1 ,z 1 ) Coordinate solution value B (x 2 ,y 2 ,z 2 ) Coordinate calculation value C (x of suspension point C 3 ,y 3 ,z 3 ) And a coordinate solution value D (x 4 ,y 4 ,z 4 )；
Step 6, comparing the coordinate calculated 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 stepsCalibration error value of lifting point B>Calibration error value of lifting point C>And the calibration error value of the lifting point D +.>
And 7, superposing half of the calibration error value of each lifting point into the corresponding coordinate measurement calibration value to obtain the coordinate value of each lifting point after final correction, namely: the corrected coordinate value of the hanging point A is A j (x 1j ,y 1j ,z 1j ) The corrected coordinate value of the hanging point B is B j (x 2j ,y 2j ,z 2j ) The corrected coordinate value of the lifting point C is C j (x 3j ,y 3j ,z 3j ) And the corrected coordinate value of the lifting point D is D j (x 4j ,y 4j ,z 4j )；
And 8, during actual performance, generating control instructions for the rope winding machine A, the rope winding machine B, the rope winding machine C and the rope winding machine D according to the coordinate values corrected by the lifting points and the target position of the actuator E, further controlling the automatic action of each rope winding machine, and controlling the actuator E to move to the target position so as to realize the space attitude control of the actuator E.
2. The method for correcting the error of the overhead boom based on the four-flexible-wire traction parallel actuator according to claim 1, wherein in the step 5, the actuator E is dragged to different space target position points according to a set dragging rule, specifically:
the drag actuator E moves to different target positions along the positive direction of the x axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the negative direction of the x axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the positive direction of the y axis at intervals of 1 unit length;
the dragging actuator E moves to different target positions along the negative y-axis direction at intervals of 1 unit length;
the drag actuator E moves to different target positions along the positive direction of the z axis at intervals of 1 unit length;
at intervals of 1 unit length, the drag actuator E moves to different target positions in the negative z-axis direction.
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