CN100565406C - A system and method for adjusting the position and attitude of aircraft components based on four locators - Google Patents

Abstract

The invention discloses a system and method for adjusting the position and posture of aircraft components based on four locators. The pose adjustment system includes four three-coordinate locators, spherical process joints, aircraft parts to be adjusted, laser tracker and target reflection ball. Y-direction motion mechanism, Z-direction motion mechanism, displacement sensor. The steps of the pose adjustment method are: 1) establish the global coordinate system OXYZ, calculate the current pose and the target pose of the aircraft component to be adjusted; 2) plan the path of the aircraft component to be adjusted from the current pose to the target pose; 3) According to the path, the trajectories of the motion mechanisms in all directions of the locator are generated; 4) The three locators move in coordination to realize pose adjustment. The invention has the advantages of: 1) it can realize the support of the aircraft component to be adjusted; 2) it can realize the automatic adjustment of the position and attitude of the aircraft component to be adjusted; 3) it can realize the inching adjustment of the position and attitude of the aircraft component to be adjusted.

Description

A system and method for adjusting the position and attitude of aircraft components based on four locators

technical field

The invention relates to a system and method for adjusting the position and posture of aircraft components based on four locators.

Background technique

In the field of aerospace manufacturing, in order to realize the docking assembly of parts, it is necessary to adjust the pose of large rigid body parts such as aircraft fuselage. The aircraft fuselage component is a unique operation object, which has a large volume and mass, and requires high precision in pose adjustment, and the adjustment tooling is not allowed to cause damage to the fuselage surface or internal components. At present, the widely used tandem robot is mainly suitable for occasions with small volume and mass, and low requirements for system rigidity. Commonly used parallel mechanisms are only used in the field of aircraft simulation or parallel machine tool manufacturing. The volume and mass of the moving platform cannot be compared with the fuselage components, and the system stiffness and positioning accuracy cannot meet the adjustment requirements of aircraft fuselage components.

In the traditional frame-based aircraft assembly process, multiple jacks are generally used to support the fuselage, and the pose adjustment of components is realized by manual assisted positioning. This method has problems such as low adjustment accuracy and large assembly stress. The attitude adjustment tool is the key equipment to realize the digital assembly of the aircraft, and it is also the actuator that converts the control command into the actual movement. One of the main characteristics of foreign digital assembly technology is that more and more automatic attitude adjustment tooling is used in the final assembly stage of the aircraft. Based on the industrial field bus, a multi-axis synchronous motion control network is constructed to realize the coordinated movement of multiple mechanical devices, and realize the accurate and stable Pose adjustment and docking of large parts. Therefore, in order to ensure small component stress and deformation, convenient tooling adjustment, and high adjustment accuracy, the document "JoinCell for the G150 Aircraft "(Samuel O.Smith, Dr.Peter B.Zieve and MichaelGurievsky, 2006 SAE International, 2006.1.31) In Gulfstream G150 aircraft assembly, a method using multiple movable jacks to support the fuselage section is given to realize the aircraft Pose adjustment and docking of fuselage components. Each section of the fuselage is supported by 4-6 movable jacks, and through automatic control, the posture adjustment and docking of the fuselage sections are realized. Manufacturers of aircraft digital assembly equipment such as German Baojie Company, Spanish SERRA Company and M.Torris Company have also proposed various three-coordinate support mechanisms to realize posture adjustment and docking assembly of large aircraft components. The document "Segmented Hull Alignment and Docking System—A Realization of a Multi-Robot Coordinated Operating System" (Jing Fengshui, Tan Min, Hou Zengguang, Wang Yunkuan. Acta Automatica Sinica, 2002, 28(5): 708-714) proposed to adopt Coordinated actions of multiple three-degree-of-freedom robots realize alignment and docking of hull segments.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, and provide a system and method for adjusting the position and posture of aircraft components based on four locators.

The aircraft component pose adjustment system based on four locators includes four three-coordinate locators, spherical process joints, laser trackers, aircraft components to be adjusted, and target reflective balls, which are supported by four three-coordinate positioners through spherical process joints. To adjust the aircraft parts, the target reflective ball is installed on the aircraft part to be adjusted, and the laser tracker is used to track the spatial position of the target reflective ball. The three-coordinate positioner includes the base plate, the X-direction movement mechanism, the Y-direction movement The sensor is equipped with an X-direction movement mechanism, a Y-direction movement mechanism, and a Z-direction movement mechanism on the base plate from bottom to top, and a conical surface cavity matched with a spherical process joint is provided at the upper end of the Z-direction movement mechanism. With displacement sensor;

The aircraft component to be adjusted is a frame beam structure, the spherical process joint is installed on the frame beam of the aircraft component to be adjusted, and the center of gravity of the aircraft component to be adjusted is located in a quadrangle formed by four locators.

The pose adjustment method of aircraft components based on four locators includes the following steps:

1) Place the aircraft parts to be adjusted on the four three-coordinate positioners through the spherical process joint,

2) Send instructions to the laser tracker to establish a global coordinate system OXYZ at the work site, and consolidate a local coordinate system O'X'Y'Z' on the aircraft components to be adjusted;

3) Use the coordinates of the origin O' of the local coordinate system under the global coordinate system OXYZ to express the position of the aircraft component to be adjusted, and use flip, pitch, and roll to express the attitude of the aircraft component to be adjusted;

4) Calculate the current pose and target pose of the aircraft components to be adjusted in the global coordinate system;

5) Plan the path of the aircraft component to be adjusted from the current pose to the target pose;

6) Generate the track of the all-directional motion mechanism of the positioner according to the path;

7) According to the trajectories of the positioner's motion mechanism in all directions, the four positioners move in coordination to realize pose adjustment;

8) Monitor the displacement sensors of each positioner online, and compensate the position of the positioner's motion mechanism in all directions according to the readings of the displacement sensors.

The steps of sending instructions to the laser tracker to establish a global coordinate system OXYZ at the work site, and to consolidate a local coordinate system O'X'Y'Z' on the aircraft components to be adjusted:

1) Install 6-8 target reflective spheres on the foundation of the work site, among which 3-4 are a group, specify the X-axis direction of the global coordinate system, and the other 3-4 are a group, specify the Y-axis direction of the global coordinate system , select the center of a target reflective sphere as the coordinate origin, and establish the global coordinate system OXYZ according to the right-hand rule;

2) Install 3 to 10 target reflective spheres on the aircraft component to be adjusted. The center of the target reflective sphere is not on the same straight line. Measure the coordinates of the sphere center of the target reflective sphere in the global coordinate system OXYZ, and the coordinates of the aircraft component to be adjusted. Design model comparison, and establish a local coordinate system O'X'Y'Z' according to the comparison results.

The steps of calculating the current pose and the target pose of the aircraft component to be adjusted under the global coordinate system:

1) Calculate the coordinates of the origin O′ of the local coordinate system of the aircraft component to be adjusted in the global coordinate system OXYZ under the current or target pose, and express the current or target position of the aircraft component to be adjusted P=[P _x , P _y , P _z ] ^T ;

2) Let the three coordinate axes of the local coordinate system of the aircraft component to be adjusted start from the state where they coincide with the coordinate axes of the global coordinate system, and rotate a, b, and c radians around the X, Y, and Z axes of the global coordinate system in turn to reach the current or target attitude, and express the current or target attitude RPY=[a, b, c] ^T of the aircraft component to be adjusted with this angle sequence;

3) Combining the current or target position and the current or target attitude, write out the current or target attitude of the aircraft component to be adjusted L=[P _x , P _y , P _z , a, b, c] ^T .

The step of planning the path of the aircraft component to be adjusted from the current pose to the target pose: processing the path as a translation and a rotation to reach the target pose from the current pose;

The steps of generating the trajectory of the positioner's anisotropic motion mechanism according to the path:

1) For the translation path of the aircraft component to be adjusted, the time-based 3-5 polynomial method is used to plan the position adjustment amount, so that the anisotropic motion mechanism of the positioner can obtain better dynamic characteristics;

2) For the rotation path of the aircraft component to be adjusted, the time-based 3-5 degree polynomial method is used to plan the angle adjustment amount, so that the anisotropic motion mechanism of the positioner can obtain better dynamic characteristics.

The online monitoring of the displacement sensors of each positioner, and the steps of compensating the position of the positioner's motion mechanism in all directions according to the readings of the displacement sensors:

1) When the reading of the displacement sensor of a positioner is -0.05 ~ -0.1mm, the position adjustment is interrupted, and the laser tracker is requested to re-detect the coordinates of the center of each target reflective ball 9 on the aircraft component to be adjusted, which is consistent with the position of the aircraft component to be adjusted. Design model comparison, and calculate the coordinates of the spherical center of the spherical process joint in the global coordinate system according to the comparison results;

2) The position of each locator in the global coordinate system at any time is determined, corresponding to the coordinates of the spherical center of the spherical process joint. When the reading of the locator displacement sensor is -0.05 ~ -0.1mm , there is an error between the position of the positioner's omnidirectional movement mechanism and the spherical center coordinates of the spherical process joint. After calculating the error amount, the position of the positioner's omnidirectional movement mechanism is compensated, so that the reading of the displacement sensor of the positioner is at 0～-0.05mm range.

The invention has the advantages of: 1) it can realize the support of the aircraft component to be adjusted; 2) it can realize the automatic adjustment of the position and attitude of the aircraft component to be adjusted; 3) it can realize the inching adjustment of the position and attitude of the aircraft component to be adjusted.

Description of drawings

The accompanying drawing is a schematic structural diagram of an aircraft component pose adjustment system based on four locators;

In the figure: base plate 1, X-direction movement mechanism 2, Y-direction movement mechanism 3, Z-direction movement mechanism 4, displacement sensor 5, spherical process joint 6, laser tracker 7, aircraft parts to be adjusted 8, and target reflection ball 9.

Detailed ways

As shown in the accompanying drawings, the aircraft component pose adjustment system based on four locators includes four three-coordinate locators, a spherical process joint 6, a laser tracker 7, an aircraft component to be adjusted 8, and a target reflective ball 9. A three-coordinate locator supports the aircraft part 8 to be adjusted through the spherical process joint 6, and a target reflective ball 9 is installed on the aircraft part 8 to be adjusted, and a laser tracker 7 is used to track the spatial position of the target reflective ball 9. The three-coordinate locator includes a base plate 1. X-direction movement mechanism 2, Y-direction movement mechanism 3, Z-direction movement mechanism 4, displacement sensor 5, X-direction movement mechanism 2, Y-direction movement mechanism 3, Z-direction movement mechanism are arranged on the base plate 1 from bottom to top Mechanism 4, the upper end of the Z-direction movement mechanism 4 is provided with a conical surface cavity matched with the spherical process joint 6, and a displacement sensor 5 is installed in the conical surface cavity;

The aircraft part 8 to be adjusted is a frame beam structure, the spherical process joint 6 is installed on the frame beam of the aircraft part 8 to be adjusted, and the center of gravity of the aircraft part 8 to be adjusted is located in a quadrilateral formed by four locators.

The pose adjustment method of aircraft components based on four locators includes the following steps:

1) Place the aircraft part 8 to be adjusted on the four three-coordinate positioners through the spherical process joint 6,

2) Send an instruction to the laser tracker 7 to make it establish a global coordinate system OXYZ at the work site, and consolidate a local coordinate system O'X'Y'Z' on the aircraft component 8 to be adjusted;

3) The coordinates of the origin O' of the local coordinate system under the global coordinate system OXYZ are used to express the position of the aircraft part 8 to be adjusted, and the attitude of the aircraft part 8 to be adjusted is expressed by rollover, pitch and roll;

4) Calculate the current pose and target pose of the aircraft part 8 to be adjusted in the global coordinate system;

5) Plan the path of the aircraft part 8 to be adjusted from the current pose to the target pose;

6) Generate the track of the all-directional motion mechanism of the positioner according to the path;

7) According to the trajectories of the positioner's motion mechanism in all directions, the four positioners move in coordination to realize pose adjustment;

8) Monitor the displacement sensors 5 of each positioner online, and compensate the position of the positioner's motion mechanism in all directions according to the readings of the displacement sensors 5 .

The steps of sending an instruction to the laser tracker 7 to make it establish a global coordinate system OXYZ at the work site, and to consolidate a local coordinate system O'X'Y'Z' on the aircraft component 8 to be adjusted:

1) Install 6 to 8 target reflective balls 9 on the foundation of the work site, among which 3 to 4 are a group, specify the X-axis direction of the global coordinate system, and the other 3 to 4 are a group, specify the Y axis of the global coordinate system Direction, select the center of a target reflective sphere as the coordinate origin, and establish the global coordinate system OXYZ according to the right-hand rule;

2) Install 3 to 10 target reflective spheres 9 on the aircraft component 8 to be adjusted. The centers of the target reflective spheres are not on the same straight line. Measure the coordinates of the sphere centers of the target reflective spheres in the global coordinate system OXYZ, which is consistent with the coordinates of the aircraft to be adjusted. The design models of the components 8 are compared, and the local coordinate system O'X'Y'Z' is established according to the comparison results.

The steps of calculating the current pose and the target pose of the aircraft part 8 to be adjusted under the global coordinate system:

1) Calculate the coordinates of the origin O' of the local coordinate system of the aircraft part 8 to be adjusted under the global coordinate system OXYZ under the current or target pose, expressing the current or target position of the aircraft part 8 to be adjusted P=[P _x , P _y , P _z ] ^T ;

2) Let the three coordinate axes of the local coordinate system of the aircraft part 8 to be adjusted start from the state where they coincide with the coordinate axes of the global coordinate system, and rotate a, b, and c radians around the X, Y, and Z axes of the global coordinate system in turn to reach the current or Target attitude, and express the current or target attitude RPY=[a, b, c] ^T of aircraft part 8 to be adjusted with this angle sequence;

3) Combining the current or target position and the current or target attitude, write out the current or target attitude of the aircraft component 8 to be adjusted L=[P _x , P _y , P _z , a, b, c] ^T .

The step of planning the path of the aircraft part 8 to be adjusted from the current pose to the target pose: processing the path as a translation and a rotation, from the current pose to the target pose:

Suppose the current pose of aircraft part 8 to be adjusted is:

L ₀ =[x ₀ , y ₀ , z ₀ , a ₀ , b ₀ , c ₀ ] ^T

The target pose of aircraft part 8 to be adjusted is:

L _f =[x _f , y _f , z _f , a _f , b _f , c _f ] ^T

Then the translation adjustment amount of aircraft part 8 to be adjusted is:

P = [P _x P _y P _z ] ^T = [x _f , y _f , z _f ] ^T -[x ₀ , y ₀ , z ₀ ] ^T

The attitude adjustment amount of aircraft part 8 to be adjusted is:

RPY=[abc] ^T =[a _f , b _f , c _f ] ^T -[a ₀ , b ₀ , c ₀ ] ^T

Then, according to the RPY angle, calculate the attitude adjustment w expressed by the equivalent angular displacement vector. The calculation process is as follows:

First, calculate the attitude adjustment matrix R of the aircraft part 8 to be adjusted according to the RPY angle, and the calculation formula is:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; b</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; a</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; a</span>}\\ \mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; b</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; a</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; a</span>}\\ <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; b</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; a</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; a</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Where R is a 3×3 attitude transformation matrix:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}& {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Then calculate the equivalent angular displacement w=dθ=θ[d ₁ d ₂ d ₃ ] ^T according to R, where d is the equivalent rotation axis, θ is the equivalent rotation angle, and the calculation formula is:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

According to the formula, it can be solved:

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ $\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}\\ {\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Let the aircraft part 8 to be adjusted complete the translation adjustment amount P and the attitude adjustment amount w, and then reach the target pose from the current pose.

The steps of generating the trajectory of the positioner's anisotropic motion mechanism according to the path:

For the position adjustment amount P, if it is completed within the time T ₁ , then:

P ₀ =0, P _T1 =P; v ₀ =0, v _T1 =0; a ₀ =0, a _T1 =0

Among them, P, v, and a are displacement, velocity, and acceleration respectively, P ₀ , P _T1 are displacements at time 0 and T ₁ respectively, and v ₀ , v _T1 , a ₀ , a _T1 have similar meanings.

Suppose the expression of the position adjustment curve is: P(t)＝k ₀ +k ₁ t+k ₂ t ² +k ₃ t ³ +k ₄ t ⁴ +k ₅ t ⁵ , then the coefficients of the polynomial satisfy six constraints:

$\left.\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 20</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

The formula contains 6 unknowns, 6 equations, and its solution is:

$\left.\begin{array}{c}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 20</span>}\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 20</span>}\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 12</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="4"\; label="k"\; filenames="C2008101616680013H1.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 30</span>}\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 30</span>}\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 16</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

According to the formula, the coefficients of the curve P(t) can be solved, and the curve has smooth changing speed and acceleration. The time _T1 is determined according to the physical characteristics of the pose adjustment system shown in the attached figure. During this time, the maximum speed and acceleration achieved by the positioner 1 will not exceed the maximum value allowed by the system.

For the angle adjustment θ, if it is completed within the time T ₂ , then:

θ ₀ = 0, θ _T2 = θ;

ω ₀ =0, ω _T2 =0; γ ₀ =0, γ _T2 =0

Among them, θ, ω, and γ are angular displacement, angular velocity, and angular acceleration, respectively, and θ ₀ , θ _T2 are angular displacements at time 0 and T ₂ , respectively. ω ₀ , ω _T2 , γ ₀ , and γ _T2 have similar meanings. Suppose the expression of the angle adjustment curve is: θ(t)＝l ₀ +l ₁ t+l ₂ t ² +l ₃ t ³ +l ₄ t ⁴ +l ₅ t ⁵ , according to these known conditions, it can be solved as follows:

$\left.\begin{array}{c}{\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 20</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 20</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 12</span>}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="4"\; label="l"\; filenames="C2008101616680013H1.png"\; state="\{\{state\}\}">l</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 30</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 30</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 16</span>}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}\\ {\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; 12</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

According to the formula, various coefficients of the curve θ(t) can be solved, and the curve has smoothly changing angular velocity and angular acceleration. The time _T2 is also determined according to the physical characteristics of the posture adjustment system shown in the attached figure. During this time, the maximum speed and acceleration that the positioner 1 can achieve will not exceed the maximum value allowed by the system.

According to the formula:

w(t)=dθ(t) (8)

Solve the angular displacement curve w(t), and substitute w(t) into the formula (3) to get the attitude transformation matrix function R(t):

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

The position adjustment curve P(t) and the attitude transformation matrix function R(t) are the automatic attitude adjustment path of the aircraft part 7 to be adjusted.

Based on the principle of inverse kinematics, the planned position adjustment curve P(t) and attitude transformation matrix function R(t) can be transformed into the trajectory of the relevant attitude adjustment point, which has a smooth changing speed and acceleration. The conversion method is as follows:

As shown in the attached figure, assuming that the joint points A, B, C, and D have initial coordinates A ₀ , B ₀ , C ₀ , and D ₀ in the current pose, then the joint point trajectories A(t), B(t), C(t), D(t) are:

A(t)＝R(t)A ₀ +P(t)

B(t)＝R(t)B ₀ +P(t)

C(t)＝R(t)C ₀ +P(t)

D(t)＝R(t)D ₀ +P(t)

(10)

Pose adjustment includes two processes: first, translation is performed, which is completed in T ₁ time; then, rotation is performed, and it is completed in T ₂ time. Therefore, the total time is T ₁ +T ₂ .

The displacement sensor 5 of each locator is monitored online, and the steps of compensating the position of the locator's motion mechanism in all directions according to the readings of the displacement sensor 5 are as follows:

1) When the reading of the displacement sensor 5 of a positioner is -0.05 ~ -0.1mm, the position adjustment is interrupted, and the laser tracker 7 is requested to re-detect the coordinates of the center of each target reflective ball 9 on the aircraft component 8 to be adjusted, which is consistent with the position to be adjusted. Comparing the design models of the aircraft component 8, and calculating the coordinates of the spherical center of the spherical process joint 6 in the global coordinate system according to the comparison results;

2) The position of each locator’s motion mechanism in all directions under the global coordinate system at any time is determined, corresponding to the coordinates of the spherical center of the spherical process joint 6, when the reading of the locator’s displacement sensor 5 is between -0.05 and -0.1 mm, there is an error between the position of the anisotropic movement mechanism of the locator and the coordinates of the spherical center of the spherical process joint 6. After calculating the error amount, the position of the anisotropic movement mechanism of the locator is compensated so that the displacement of the locator The sensor reading 5 is within the range of 0 to -0.05mm.

Claims (8)

1. aircraft part pose Adjustment System based on four locater, it is characterized in that comprising 4 three-coordinate positioners, spherical process connection (6), laser tracker (7), aircraft components to be adjusted (8), target reflection sphere (9), support aircraft components to be adjusted (8) by 4 three-coordinate positioners by spherical process connection (6), at aircraft components to be adjusted (8) target reflection sphere (9) is installed, adopt laser tracker (7) to follow the tracks of the locus of target reflection sphere (9), three-coordinate positioner comprises base plate (1), X is to motion (2), Y is to motion (3), Z is to motion (4), displacement transducer (5), on going up from descending, base plate (1) is provided with X successively to motion (2), Y is to motion (3), Z is to motion (4), be provided with the circular conical surface chamber of matching at Z to motion (4) upper end, displacement transducer (5) is housed in the circular conical surface chamber with spherical process connection (6).

2. a kind of aircraft part pose Adjustment System according to claim 1 based on four locater, it is characterized in that described aircraft components to be adjusted (8) is the frame girder construction, spherical process connection (6) is installed on the frame beam of aircraft components to be adjusted (8), and the center of gravity of aircraft components to be adjusted (8) is positioned at the quadrilateral that four locater is formed.

3. aircraft part pose method of adjustment based on four locater is characterized in that may further comprise the steps:

1) aircraft components to be adjusted (8) is placed on 4 three-coordinate positioners by spherical process connection (6),

2) send instruction to laser tracker (7), make it set up global coordinate system OXYZ in the working site, and go up fixed local coordinate system O ' X ' Y ' Z ' at aircraft components to be adjusted (8);

3) adopt the coordinate of local coordinate system initial point O ' under global coordinate system OXYZ to express the position of aircraft components to be adjusted (8), adopt upset, pitching, inclination to express the attitude of aircraft components to be adjusted (8);

4) under global coordinate system, calculate the current pose and the object pose of aircraft components to be adjusted (8);

5) cook up the path of aircraft components to be adjusted (8) from current pose to object pose;

6) generate each track of steady arm according to this path to motion;

7) according to each track to motion of steady arm, the four locater coordinated movement of various economic factors realizes the pose adjustment;

8) displacement transducer of each steady arm of on-line monitoring (5), each compensates to the position of motion to steady arm according to displacement transducer (5) reading.

4. a kind of aircraft part pose method of adjustment according to claim 3 based on four locater, it is characterized in that described to laser tracker (7) transmission instruction, make it set up global coordinate system OXYZ in the working site, and go up fixed local coordinate system O ' X ' Y ' Z ' step at aircraft components to be adjusted (8):

1) 6～8 target reflection spheres (9) is installed on the ground of working site, wherein 3～4 is one group, specify the X-direction of global coordinate system, other 3～4 is one group, specify the Y direction of global coordinate system, the centre of sphere of a selected target reflection sphere is set up global coordinate system OXYZ as true origin according to right hand rule;

2) go up installation 3～10 target reflection spheres (9) at aircraft components to be adjusted (8), the centre of sphere of target reflection sphere is not on same straight line, the coordinate of the centre of sphere of measurement target drone reflection sphere under global coordinate system OXYZ, with the comparison that designs a model of aircraft components to be adjusted (8), set up local coordinate system O ' X ' Y ' Z ' according to comparison result.

5. a kind of aircraft part pose method of adjustment based on four locater according to claim 3 is characterized in that described current pose and the object pose step that calculates aircraft components to be adjusted (8) under global coordinate system:

1) calculate current or object pose under, the coordinate of aircraft components to be adjusted (8) local coordinate system initial point O ' under global coordinate system OXYZ expressed the current or target location P=[P of aircraft components to be adjusted (8) _x, P _y, P _z] ^T

2) make the state of three coordinate axis from overlapping of aircraft components to be adjusted (8) local coordinate system with each coordinate axis of global coordinate system, arrive current or targeted attitude around global coordinate system X, Y, the rotation of Z axle a, b, c radian successively, and express the current or targeted attitude RPY=[a of aircraft components to be adjusted (8) with this angle sequence, b, c] ^T

3) comprehensive current or target location, current or targeted attitude write out the current pose or the object pose L=[P of aircraft components to be adjusted (8) _x, P _y, P _z, a, b, c] ^T

6. a kind of aircraft part pose method of adjustment according to claim 3 based on four locater, it is characterized in that the described path step of aircraft components to be adjusted (8) of cooking up: the path is treated to a translation and once rotation, arrives object pose from current pose from current pose to object pose.

7. a kind of aircraft part pose method of adjustment based on four locater according to claim 3 is characterized in that described each track step to motion that generates steady arm according to this path:

1), adopt time-based 3～5 order polynomial rules to draw position adjustment amount, so that each of steady arm obtains dynamics preferably to motion for the path for translation of aircraft components to be adjusted (8);

2), adopt time-based 3～5 order polynomial rules to draw the angular setting amount, so that each of steady arm obtains dynamics preferably to motion for the rotate path of aircraft components to be adjusted (8).

8. a kind of aircraft part pose method of adjustment according to claim 3 based on four locater, the displacement transducer (5) that it is characterized in that described each steady arm of on-line monitoring, each compensates step to the position of motion to steady arm according to displacement transducer (5) reading:

1) when certain steady arm displacement transducer (5) reading be-0.05～-during 0.1mm, the interruption pose is adjusted, request laser tracker (7) detects the coordinate that aircraft components to be adjusted (8) is gone up each target reflection sphere (9) centre of sphere again, with the comparison that designs a model of aircraft components to be adjusted (8), calculate the coordinate of the centre of sphere under global coordinate system of spherical process connection (6) according to comparison result;

2) each steady arm each all determine in the position under the global coordinate system to motion any time, corresponding with the coordinate of the centre of sphere of spherical process connection (6), when the reading of steady arm displacement transducer (5)-0.05～-during 0.1mm, each of this steady arm has error to the position of motion and the sphere centre coordinate of spherical process connection (6), after calculating the margin of error, each compensates to the position of motion to this steady arm, make the displacement transducer reading (5) of this steady arm 0～-the 0.05mm interval in.

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