CN109911241B - Seven-degree polynomial-based multi-section automatic posture adjusting method - Google Patents
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Abstract
The invention discloses a seven-degree polynomial based multi-section automatic posture adjusting method, which specifically comprises the following steps of: step S1: creating a theoretical coordinate system; step S2: measuring actual data of monitoring points of the attitude adjusting system component; step S3: acquiring a rigid transformation matrix of the attitude adjusting system component by adopting a least square method according to theoretical data and actual data of the monitoring points; step S4: according to the starting position and the end position of the rigid transformation matrix motion unit; step S5: calculating the motion track of each driving shaft, S (t) k0+k1·t+k2·t2+k3·t3+k4·t4+k5·t5+k6·t6+k7·t7In the formula: s (t): motion displacement trajectory parameters of the drive shaft; v (t): speed; a (t): acceleration; j (t): the acceleration is added; t: the time from the starting position to the end position of each drive shaft; step S7: and carrying out data communication on the motion trajectory parameters and the motion control system, establishing a motion control instruction, and adjusting the posture and the posture in place. The problem of the manual butt joint time assembly inefficiency, assembly time are long, the product uniformity is poor, can produce the impact to the product of effectual solution.
Description
Technical Field
The invention relates to the technical field of aircraft component assembly, in particular to a seven-degree polynomial based multi-section automatic posture adjusting method.
Background
At present, the traditional method is generally adopted in the assembly and manufacturing process of airplanes in China, manual adjustment is carried out on the large parts of the airplanes mostly by using manual positioners of assembly tools, and the problems of low assembly efficiency, long assembly time and poor product consistency exist. In recent years, with the continuous development of equipment automation, most of parts matching systems based on automatic posture adjustment are gradually put into use under the drive of colleges and universities, but the self-mastering degree of enterprises is not high, and the use stability and universality are not good. At present, a fifth-order polynomial is adopted to fit displacement tracks of all driving shafts, although the smoothness of speed and acceleration in the motion process is met, the acceleration of the motion is not zero at the initial and final positions of the posture adjustment, and the product is impacted. With the continuous advance and development of equipment intellectualization, the development of an automatic docking system with independent intellectual property rights is necessary and urgent.
Disclosure of Invention
The invention aims to provide a seven-degree polynomial-based multi-section automatic posture adjusting method, which effectively solves the problems of low assembly efficiency, long assembly time, poor product consistency and non-zero acceleration of motion when starting and ending positions are automatically butted and impact is generated on products when most parts are manually butted.
The invention is realized by the following technical scheme:
a seven-degree polynomial based multi-section automatic posture adjusting method specifically comprises the following steps:
step S1: creating a theoretical coordinate system;
step S2: measuring actual data of monitoring points of the attitude adjusting system component;
step S3: according to theoretical data and actual data of the monitoring points, a least square method is used for ensuring that the sum of squares of coordinate differences of three-way points of a theoretical space of the monitoring points and an actual space of the monitoring points is minimum, and a rigid transformation matrix of the attitude adjusting system component is obtained;
step S4: according to the starting position and the end position of the rigid transformation matrix motion unit;
step S5: calculating the motion track of each driving shaft, S (t) k0+k1·t+k2·t2+k3·t3+k4·t4+k5·t5+k6·t6+k7·t7
In the formula:
s (t): motion displacement trajectory parameters of the drive shaft;
v (t): speed;
a (t): acceleration;
j (t): the acceleration is added;
t: the time from the starting position to the end position of each drive shaft;
step S7: and carrying out data communication on the motion trajectory parameters and the motion control system, establishing a motion control instruction, and adjusting the posture and the posture in place.
Further, in order to better implement the present invention, step S3 specifically refers to:
acquiring a rigid transformation matrix of the attitude adjusting system component by adopting a least square method according to the theoretical value and the measured value of the monitoring point;
the docking coordinate system is set as the measurement coordinate system of the laser tracker, and the actual coordinates of the key measurement points on the attitude adjustment system component are measured and expressed as: ei＝(Eix，Eiy，Eiz),i＝1…n；
In the above formula, i is the ith measuring point, and n is the number of the measuring points;
calculating the theoretical position of the measuring point in the component coordinate system, and expressing the theoretical position as follows: e.g. of the typei＝(eix，eiy，eiz),i＝1…n；
Translation matrix: p ═ X0Y0Z0]；
Rotating the matrix:
wherein:
alpha, beta and gamma are the rotation angles around the X-axis direction, the Y-axis direction and the Z-axis direction from the theoretical position to the actual position of the rigid body respectively, and X is0，Y0，Z0Respectively translating the values from the theoretical position of the rigid body to the actual position along the X-axis direction, the Y-axis direction and the Z-axis direction;
the X-axis direction, the Y-axis direction and the Z-axis direction are respectively parallel to the STA direction, the BL direction and the WL direction of an airplane coordinate system;
substituting the measured value into
The stiffness change matrix can be found.
Further, in order to better implement the present invention, step S4 specifically refers to:
keeping the relative position between each attitude adjusting system component and the motion unit unchanged, and solving the starting point and the end point of the motion unit according to the theoretical position and the actual position of the monitoring point;
the starting point position of the motion unit carries out position conversion according to the position of the monitoring point measured by the laser tracker;
the end point position of the movement unit is the ball angle position of the tail end of the movement unit at the theoretical position of the posture adjusting system component, and the position conversion is carried out according to the theoretical position of each posture adjusting system component product coordinate system.
Further, in order to better implement the present invention, step S1 specifically refers to: the theoretical coordinate system of the multi-section attitude adjusting system which is coincident with the coordinate system of the airplane is created by means of a right laser tracker system component and a left laser tracker system component which are installed on the site.
Further, in order to better implement the present invention, the method further includes step S6: setting the speed of the starting position and the end position as V (t), the acceleration as A (t) and the jerk as J (t) to be 0; processing the motion process by adopting a normalization method to obtain:
starting point position:
S＝0
V＝0
A＝0
J＝0；
end point position:
S＝1
V＝0
A＝0
J＝0；
according to the boundary conditions, the following are obtained:
displacement: s (t) 35t4-84t5+70t6-20t7；
Speed: v (t) ═ S' (t) ═ 140t3-420t4+420t5-140t6；
Acceleration: a (t) ═ V' (t) ═ 420t2-1680t3+2100t4-840t5；
Acceleration: j (t) ═ a' (t) ═ 840t-5040t2+8400t3-4200t4(ii) a Wherein S' (t) is the speed during the exercise at any time; v '(t) is the velocity at any time during the movement, and A' (t) is the acceleration at any time during the movement.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the invention effectively solves the problems of low assembly efficiency, long assembly time and poor product consistency when large parts are manually butted, and the acceleration of the movement at the initial position and the final position is not zero when automatic butting is adopted, so that the product is impacted;
(2) the invention can ensure the accurate butt joint of two wallboard assemblies, a front-end cockpit assembly and a bottom baseplate assembly on the left side and the right side, has stable motion in the butt joint process and has good expansibility for the butt joint of similar components.
Drawings
FIG. 1 is a diagram of an automated pose adjustment system architecture according to the present invention;
FIG. 2 is a flow chart of the present invention;
the system comprises a left lower computer control cabinet system component, a 2 left wall plate component posture adjusting system component, a 3 cockpit component posture adjusting system component, a 4 right wall plate posture adjusting system component, a 5 right lower computer control cabinet system component, a 6 right laser tracker system component, a 7 upper computer control system component, an 8 lower bottom plate posture adjusting system component and a 9 left laser tracker system component.
Detailed Description
The present invention will be described in further detail with reference to examples, but the embodiments of the present invention are not limited thereto.
Example 1:
the invention is realized by the following technical scheme, as shown in figures 1-2, the multi-section automatic posture adjusting method based on a seventh polynomial is based on a multi-section automatic posture adjusting system, and the multi-section automatic posture adjusting system comprises a left side wall plate assembly posture adjusting system assembly 2 butted with a left side wall plate assembly, a right side wall plate assembly posture adjusting system assembly 4 butted with a right side wall plate assembly, a lower bottom plate posture adjusting system assembly 8 butted with a bottom plate assembly, a cockpit assembly posture adjusting system assembly 3 butted with a front cockpit assembly, a right laser tracker system assembly 9 and a left laser tracker system assembly 6 for installing an airplane assembly posture adjusting site, a left lower computer control cabinet system assembly 1 connected with the left side wall plate assembly posture adjusting system assembly, a right lower computer control cabinet system assembly 5 connected with the right side wall plate assembly posture adjusting system assembly, a left computer control cabinet system assembly 5 connected with the right side wall plate assembly posture adjusting system assembly, And an upper computer control system assembly 7 respectively connected with the left lower computer control cabinet system assembly 1 and the right lower computer control cabinet system assembly 5; the method comprises the following steps: a seventh polynomial is adopted to fit a displacement track during posture adjustment when the posture of the left side wall plate type component posture adjustment system component 2, the right side wall plate type posture adjustment system component 4, the lower floor type posture adjustment system component 8 and the cockpit type component posture adjustment system component 3 is adjusted;
the method specifically comprises the following steps:
step S1: creating a theoretical coordinate system;
step S2: measuring actual data of monitoring points of the attitude adjusting system component;
step S3: according to theoretical data and actual data of the monitoring points, a least square method is used for ensuring that the sum of squares of coordinate differences of three-way points of a theoretical space of the monitoring points and an actual space of the monitoring points is minimum, and a rigid transformation matrix of the attitude adjusting system component is obtained;
step S4: according to the starting position and the end position of the rigid transformation matrix motion unit;
step S5: calculating the motion track of each driving shaft, S (t) k0+k1·t+k2·t2+k3·t3+k4·t4+k5·t5+k6·t6+k7·t7
In the formula:
s (t): motion displacement trajectory parameters of the drive shaft;
v (t): speed;
a (t): acceleration;
j (t): the acceleration is added;
t: the time from the starting position to the end position of each drive shaft;
step S7: carrying out data communication on the motion trajectory parameters and a motion control system, establishing a motion control instruction, and adjusting the posture and the posture in place; the posture adjustment specifically comprises the following steps: the slave station system and the driving system in the left lower computer control cabinet system assembly 1 and the right lower computer control cabinet system assembly 5 are used for realizing the posture adjusting movement of the execution system;
step S8: after one beat gesture adjustment is finished, the actual position of the monitoring point is compared with the theoretical position, and whether the involution requirement is met or not is judged:
if the requirements cannot be met, repeating the operations of the step S3-the step S7;
if the requirements are met, the gesture adjustment of the section is finished, and the gesture adjustment of the next section is executed until all the gestures are adjusted.
The left side wallboard class subassembly is transferred appearance system component, right side wallboard class and is transferred appearance system component, lower part bottom plate class transfer appearance system component and cockpit class subassembly and transfer appearance system component and constitute by the motion unit that has three-dimensional straight line degree of freedom respectively, the X axle direction of three-dimensional motion unit, Y axle direction, Z axle direction are parallel with STA direction, BL direction, the WL direction of aircraft coordinate system respectively.
The number of the degrees of freedom of the three-way motion unit realized by the servo system when realizing single component posture adjustment is 3/2/1/1 respectively, and the rest are follow-up degrees of freedom.
Example 2:
in this embodiment, as shown in fig. 1, the further optimization is performed on the basis of the above embodiment, and the step S3 specifically includes:
according to the theoretical value and the measured value of the monitoring point, the least square method is used for ensuring that the square sum of the coordinate difference values of the three-way points of the theoretical space of the monitoring point and the actual space of the monitoring point is the minimum to obtain a rigid transformation matrix of the attitude adjusting system component;
the docking coordinate system is set as the measurement coordinate system of the laser tracker, and the actual coordinates of the key measurement points on the attitude adjusting system component are measured and expressed as: ei＝(Eix,Eiy,Eiz),i＝1…n；
In the above formula, i is the ith measuring point, and n is the number of the measuring points;
and calculating the theoretical position of the measuring point in the coordinate system, and expressing the theoretical position as follows: e.g. of the typei＝(eix，eiy，eiz),i＝1…n；
Translation matrix: p ═ X0 Y0 Z0]；
Rotating the matrix:
wherein:
alpha, beta and gamma are the rotation angles around the X-axis direction, the Y-axis direction and the Z-axis direction from the theoretical position to the actual position of the rigid body respectively, and X is0，Y0，Z0Respectively translating the values from the theoretical position of the rigid body to the actual position along the X-axis direction, the Y-axis direction and the Z-axis direction;
the X-axis direction, the Y-axis direction and the Z-axis direction are respectively parallel to the STA direction, the BL direction and the WL direction of an airplane coordinate system;
substituting the measured value into
The stiffness change matrix can be found.
Other parts of this embodiment are the same as those of the above embodiment, and thus are not described again.
Example 3:
the present embodiment is further optimized based on the above embodiment, and as shown in fig. 1, the step S4 specifically refers to:
keeping the relative position between each attitude adjusting system component and the motion unit unchanged, and solving the starting point and the end point of the motion unit according to the theoretical position and the actual position of the monitoring point;
the starting point position of the motion unit carries out position conversion according to the position of the monitoring point measured by the laser tracker;
the final position of the movement unit is the position of the ball angle at the tail end of the movement unit under the theoretical position of the attitude adjusting system component, and the position conversion is carried out according to the theoretical position of each attitude adjusting system component under the product coordinate system.
It should be noted that, with the above improvement, the solution and the position conversion provided herein are both prior arts; how to implement the solution and the transformation is not described in detail. Any solving method and position conversion method in the prior art can be used as long as the solving is realized.
Other parts of this embodiment are the same as those of the above embodiment, and thus are not described again.
Example 4:
the present embodiment is further optimized based on the above embodiment, as shown in fig. 1, further, in order to better implement the present invention, the step S1 specifically refers to: a theoretical coordinate system of a multi-section pose adjusting system which is coincident with an airplane coordinate system is established by means of a right-side laser tracker system component and a left-side laser tracker system component which are installed on the site.
Further, in order to better implement the present invention, the method further includes step S6: in order to ensure the stability of the movement process, the speed, the acceleration and the jerk of the air cushion position and the key position are all 0, wherein V (t) is the speed, A (t) is the acceleration and J (t) is the jerk; processing the motion process by adopting a normalization method to obtain:
starting point position:
S＝0
V＝0
A＝0
J＝0；
end point position:
S＝1
V＝0
A＝0
J＝0；
according to the boundary conditions, the following are obtained:
displacement: s (t))＝35t4-84t5+70t6-20t7；
Speed: v (t) ═ S' (t) ═ 140t3-420t4+420t5-140t6；
Acceleration: a (t) ═ V' (t) ═ 420t2-1680t3+2100t4-840t5；
Acceleration: j (t) ═ a' (t) ═ 840t-5040t2+8400t3-4200t4(ii) a Wherein S' (t) is the speed during the exercise at any time; v '(t) is the velocity at any time during the movement, and A' (t) is the acceleration at any time during the movement.
Other parts of this embodiment are the same as those of the above embodiment, and thus are not described again.
Example 5:
this embodiment is the best embodiment of the present invention, as shown in FIG. 1, a seven degree polynomial based multi-segment automated tone
The posture adjusting method specifically comprises the following steps:
step S1: creating a theoretical coordinate system; the step S1 specifically includes: a theoretical coordinate system of a multi-section pose adjusting system which is coincident with an airplane coordinate system is established by means of a right-side laser tracker system component and a left-side laser tracker system component which are installed on the site.
Step S2: measuring actual data of monitoring points of the attitude adjusting system component;
step S3: according to the theoretical data and the actual data of the monitoring points, the least square method is used for ensuring that the sum of squares of the coordinate differences of the three-dimensional points of the theoretical space of the monitoring points and the actual space of the monitoring points is the minimum to obtain a rigid transformation matrix of the attitude adjusting system component; the step S3 specifically includes:
acquiring a rigid transformation matrix of the attitude adjusting system component by adopting a least square method according to the theoretical value and the measured value of the monitoring point;
the docking coordinate system is set as the measurement coordinate system of the laser tracker, and the actual coordinates of the key measurement points on the attitude adjustment system component are measured and expressed as: ei＝(Eix，Eiy，Eiz),i＝1…n；
In the above formula, i is the ith measuring point, and n is the number of the measuring points;
calculating to obtain the theoretical position of the measuring point under the coordinate system of the component, and expressing as follows: e.g. of the typei＝(eix，eiy，eiz),i＝1…n；
Translation matrix: p ═ X0Y0Z0]；
Rotating the matrix:
wherein:
alpha, beta and gamma are the rotation angles around the X-axis direction, the Y-axis direction and the Z-axis direction from the theoretical position to the actual position of the rigid body respectively, and X is0，Y0，Z0Respectively translating the values from the theoretical position of the rigid body to the actual position along the X-axis direction, the Y-axis direction and the Z-axis direction;
the X-axis direction, the Y-axis direction and the Z-axis direction are respectively parallel to the STA direction, the BL direction and the WL direction of an airplane coordinate system;
substituting the measured value into
The stiffness change matrix can be found.
Step S4: according to the starting position and the end position of the rigid transformation matrix motion unit; the step S4 specifically includes:
keeping the relative position between each attitude adjusting system component and the motion unit unchanged, and solving the starting point and the end point of the motion unit according to the theoretical position and the actual position of the monitoring point;
the starting point position of the motion unit carries out position conversion according to the position of the monitoring point measured by the laser tracker;
the end point position of the movement unit is the ball angle position of the tail end of the movement unit at the theoretical position of the posture adjusting system component, and the position conversion is carried out according to the theoretical position of each posture adjusting system component product coordinate system.
Step S5: calculating for each drive axisTrajectory of motion, s (t) ═ k0+k1·t+k2·t2+k3·t3+k4·t4+k5·t5+k6·t6+k7·t7
In the formula:
s (t): motion displacement trajectory parameters of the drive shaft;
v (t): speed;
a (t): acceleration;
j (t): the acceleration is added;
t: the time from the starting position to the end position of each drive shaft;
step S6: setting the speed of the starting position and the end position as V (t), the acceleration as A (t) and the jerk as J (t) to be 0; processing the motion process by adopting a normalization method to obtain:
starting point position:
S＝0
V＝0
A＝0
J＝0；
end point position:
S＝1
V＝0
A＝0
J＝0；
according to the boundary conditions, the following are obtained:
displacement: s (t) 35t4-84t5+70t6-20t7；
Speed: v (t) S' (t) 140t3-420t4+420t5-140t6；
Acceleration: a (t) ═ V' (t) ═ 420t2-1680t3+2100t4-840t5；
Acceleration: j (t) ═ a' (t) ═ 840t-5040t2+8400t3-4200t4。
Wherein S' (t) is the speed during the exercise at any time; v '(t) is the velocity at any time during the movement, and A' (t) is the acceleration at any time during the movement.
Step S7: and carrying out data communication on the motion trajectory parameters and the motion control system, establishing a motion control instruction, and adjusting the posture and the posture in place.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications and equivalent variations of the above embodiments according to the technical spirit of the present invention are included in the scope of the present invention.
Claims (4)
1. A seven-degree polynomial based multi-section automatic posture adjusting method is characterized by comprising the following steps: the method specifically comprises the following steps:
step S1: creating a theoretical coordinate system;
step S2: measuring actual data of monitoring points of the attitude adjusting system component;
step S3: acquiring a rigid transformation matrix of the attitude adjusting system component by adopting a least square method according to theoretical data and actual data of the monitoring points;
step S4: according to the starting position and the end position of the rigid transformation matrix motion unit;
step S5: calculating the motion track of each driving shaft, S (t) k0+k1·t+k2·t2+k3·t3+k4·t4+k5·t5+k6·t6+k7·t7
In the formula:
s (t): motion displacement trajectory parameters of the driving shaft;
v (t): speed;
a (t): acceleration;
j (t): the acceleration is added;
t: the time from the starting position to the end position of each drive shaft;
step S7: carrying out data communication on the motion trajectory parameters and a motion control system, establishing a motion control instruction, and adjusting the posture and the posture in place;
between steps S5 and S7, step S6 is further included: setting the speed of the starting position and the end position as V (t), the acceleration as A (t) and the jerk as J (t) to be 0; processing the motion process by adopting a normalization method to obtain:
starting point position:
S＝0
V＝0
A＝0
J＝0；
end point position:
S＝1
V＝0
A＝0
J＝0；
obtaining the following boundary conditions according to the starting point position and the end point position:
displacement: s (t) 35t4-84t5+70t6-20t7
Speed: v (t) ═ S' (t) ═ 140t3-420t4+420t5-140t6
Acceleration: a (t) ═ V' (t) ═ 420t2-1680t3+2100t4-840t5
Acceleration: j (t) ═ a' (t) ═ 840t-5040t2+8400t3-4200t4；
Wherein S' (t) is the speed during the exercise at any time; v '(t) is the velocity at any time during the movement, and A' (t) is the acceleration at any time during the movement.
2. The posture adjustment method for the multi-section automatic posture adjustment based on the seventh-order polynomial as claimed in claim 1, characterized in that: the step S3 specifically includes:
according to the theoretical value and the measured value of the monitoring point, the least square method is used for ensuring that the square sum of the coordinate difference values of the three-way points of the theoretical space of the monitoring point and the actual space of the monitoring point is the minimum to obtain a rigid transformation matrix of the attitude adjusting system component;
the docking coordinate system is set as the measurement coordinate system of the laser tracker, and the actual coordinates of the key measurement points on the attitude adjustment system component are measured and expressed as: ei＝(Eix,Eiy,Eiz),i＝1…n；
In the above formula, i is the ith measuring point, and n is the number of the measuring points;
calculating the theoretical position of the measuring point in the component coordinate system, and expressing the theoretical position as follows: e.g. of the typei＝(eix,eiy,eiz),i＝1…n；
Translation matrix: p ═ X0 Y0 Z0]；
Rotating the matrix:
wherein:
alpha, beta and gamma are the rotation angles around the X-axis direction, the Y-axis direction and the Z-axis direction from the theoretical position to the actual position of the rigid body respectively, and X is0，Y0，Z0Respectively translating the values from the theoretical position of the rigid body to the actual position along the X-axis direction, the Y-axis direction and the Z-axis direction;
the X-axis direction, the Y-axis direction and the Z-axis direction are respectively parallel to the STA direction, the BL direction and the WL direction of an airplane coordinate system;
substituting the measured value into
The stiffness change matrix can be found.
3. The posture adjustment method for the multi-section automatic posture adjustment based on the seventh-order polynomial as claimed in claim 2, characterized in that: the step S4 specifically includes:
keeping the relative position between each attitude adjusting system component and the motion unit unchanged, and solving the starting point and the end point of the motion unit according to the theoretical position and the actual position of the monitoring point;
the starting point position of the motion unit carries out position conversion according to the position of the monitoring point measured by the laser tracker;
the end point position of the movement unit is the ball angle position of the tail end of the movement unit at the theoretical position of the posture adjusting system component, and the position conversion is carried out according to the theoretical position of each posture adjusting system component product coordinate system.
4. The posture adjustment method for the multi-section automatic posture adjustment based on the seventh-order polynomial as claimed in claim 1, characterized in that: the step S1 specifically includes: the theoretical coordinate system of the multi-section attitude adjusting system which is coincident with the coordinate system of the airplane is created by means of a right laser tracker system component and a left laser tracker system component which are installed on the site.
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| CN111912401B (en) * | 2020-06-30 | 2021-08-03 | 成都飞机工业（集团）有限责任公司 | Working space solving method for airplane large-part attitude adjusting mechanism |
| CN112298600B (en) * | 2020-09-18 | 2022-05-06 | 成都飞机工业（集团）有限责任公司 | Multi-axis full-active attitude adjusting method and device for large airplane component with rotating center of gravity |
| CN112340053B (en) * | 2020-09-18 | 2022-05-10 | 成都飞机工业（集团）有限责任公司 | Large component multi-axis full-active motion posture adjusting method and device |
| CN112340054B (en) * | 2020-09-18 | 2022-05-06 | 成都飞机工业（集团）有限责任公司 | Multi-axis main follow-up attitude adjusting method and attitude adjusting device for large part of airplane |
| CN113988607B (en) * | 2021-10-26 | 2024-05-14 | 成都飞机工业（集团）有限责任公司 | Method, device, equipment and storage medium for analyzing component assembly out-of-tolerance |
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