CN103496449A - Pose adjustment track planning method for plane side wall component assembling - Google Patents

Pose adjustment track planning method for plane side wall component assembling Download PDF

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CN103496449A
CN103496449A CN201310384485.4A CN201310384485A CN103496449A CN 103496449 A CN103496449 A CN 103496449A CN 201310384485 A CN201310384485 A CN 201310384485A CN 103496449 A CN103496449 A CN 103496449A
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coordinate
aircraft
alpha
pose
cos
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CN103496449B (en
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李卫东
王洪雨
万敏
涂晓君
龚会民
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Chengdu Aircraft Industrial Group Co Ltd
Beihang University
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Chengdu Aircraft Industrial Group Co Ltd
Beihang University
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Abstract

The invention provides a pose adjustment track planning method for plane side wall component assembling. The method includes the steps that (1) a fixed target mirror is installed on a tool base, the coordinate of the target mirror is measured by means of a laser tracking instrument, and a fixed coordinate system A is built; (2) a target mirror is installed on a plane side wall component, and a follow-up coordinate system B is built on the plane side wall component; (3) each positioning device is provided with a target mirror and a drive coordinate system Mi is built; (4) the pose of the follow-up coordinate system B in the fixed coordinate system A is calculated, and the initial pose of the plane side wall component is obtained; (5) target mirrors are installed on four clamping points, the coordinates of the target mirrors are measured by means of the laser tracking instrument, the initial coordinates of the clamping points in the fixed coordinate system A are obtained, and the position vector at the drive coordinate system M is inversed solved; (6) a rotating motion track is planned; (7) a translational motion track is planned. According to the method, difficulty of a pose adjustment system in controlling multi-shaft coordination drive is effectively reduced, and the pose adjustment track planning problem that in the assembling process, the beginning and end poses of the plane side wall components are known but motion paths are undetermined is solved.

Description

A kind of aircraft side member assembling posture adjustment method for planning track
(1) technical field
The invention provides a kind of aircraft side member assembling posture adjustment method for planning track, it is based on six-degree-of-freedom parallel connection mechanism aircraft side member assembling posture adjustment method for planning track, belongs to aircraft components assembly technique field.
(2) technical background
Nearly ten or twenty is over year, and the Aviation Manufacturing Enterprises that Boeing and Air Passenger company be representative of take is greatly developed the digitalisation assembly technique, generally adopts Digital-flexible Assembly Tool.The digital tool of a large amount of like this highly versatiles can repeated usage, not only the production cycle be can shorten, improve fitting process, assembly quality and work efficiency thereof greatly improved, and the assembling that goes for concentrating different aircraft products or parts due to its commonality and alerting ability, reduced significantly frock quantity.At present, the aircraft assembly technique of China is compared with developed countries also very backward.Each main engine plants are basically still following and take in the past few decades the handicraft workshop pattern and be main aircraft assembly technique, adopt a large amount of standard frocks and special-purpose assembly tooling.
Aircraft components mostly adopts a plurality of steady arms to be supported in the posture adjustment fitting process, by automation, controls, and realizes pose posture adjustment and the docking of parts.Flexible assembly fixture based on multi-point support has the advantages such as stiffness/weight ratio is large, load-carrying capacity strong, fast response time as a kind of typical case's application of parallel institution, but be based on the posture adjustment assembly system of steady arm, generally all need the multiaxis redundant drive, control method is had higher requirement.
Trajectory planning is a key issue must considering in many Design of Motion Control System processes, the mechanism's task of whether finishing the work on request that rationally whether will be directly connected to of its planning.A good trajectory planning even can make some performance figure of mechanism be optimized, and such as time, energy consumption, propulsive effort (moment) etc., these are all the common trajectory planning targets of parallel institution.Multi-shaft motion control system is carried out to rational trajectory planning, reduce the control difficulty necessary.
(3) summary of the invention
1, purpose:
The objective of the invention is to propose a kind of aircraft side member assembling posture adjustment method for planning track, it is the Aircraft-Oriented side member flexible assembly pose_adjuster in conjunction with autonomous Design, propose a kind ofly based on the complete uncertain pose of the known and motion path of side member pose at the whole story, to adjust method for planning track, to reduce the pose_adjuster multiaxis, coordinate the control difficulty driven.
2, technical scheme:
(1) first introduce the flexible assembly pose_adjuster: as shown in Figure 1, this six-degree-of-freedom parallel connection mechanism aircraft side member flexible assembly pose_adjuster, before and after mainly being by four, the accurate three-coordinate positioner of two rows, high level matches with low level layout forms.See Fig. 2, the aircraft side member is considered as to moving platform, with four steady arms, jointly form the 4-PPPS parallel institution, can realize the 6DOF pose adjustment of aircraft side member space.Annexation between them is: each PPPS props up chain end and the aircraft side member connects to form typed ball bearing pair by ball pivot, then by three mutually orthogonal moving sets, with silent flatform, is connected successively.Front-seat two steady arms are for supporting aircraft side member lower portion; Two steady arms of rear row are for supporting side walls component top position.Every three-coordinate positioner comprises that 4 parts: x is to moving assembly, y to moving assembly, z to moving assembly and process connection.Between aircraft side member and steady arm, by process connection, be connected, this process connection can be considered ball and socket.The steady arm x, y, z to movement carry out precision by servomotor and drive.
Described PPPS side chain is fast by ball pivot, hold-down arm, cross holder, column, guide rail, base form.The hold-down arm end is connected with the aircraft side member by ball pivot, and hold-down arm and cross holder are fast, the cross holder is fast and column, column and base are connected to form moving sets by guide rail slide block successively.
Described silent flatform refer to the adjustment level fixing with ground the assembly jig base,
Moving sets in the present invention adopts ball-screw and nut structure to realize single degree of freedom transmission campaign, and nut and driven assembly are fixed, and each moving assembly all moves along rolling linear guide.
In the present invention, unidirectional guide rail is parallel to each other, and the guide rail of different directions is mutually orthogonal.
(2) a kind of aircraft side member assembling of the present invention posture adjustment method for planning track, the method step is as follows:
Step 1: the fixed target mirror is installed on the tooling base of aircraft components erecting yard, is utilized laser tracker to measure target mirror coordinate, set up a fixed coordinate system o-xyz on tooling base, be designated as { A};
Step 2: the target mirror is installed on the aircraft side member, and { coordinate in A} is set up one with moving coordinate system o '-x ' y ' z ' on the aircraft side member, is designated as { B} at fixed coordinate system to utilize laser tracker to measure the target mirror; Its origin of coordinates is at { the position vector p in A} a=(p xp yp z) t, at { the attitude matrix R in A} aB;
Step 3: the target mirror is installed on every steady arm, is utilized laser tracker to measure the target mirror at fixed coordinate system { coordinate o in A} i, set up one and drive system of axes o on every steady arm i-x iy iz i, be designated as { M i(i=1,2,3,4), the origin of coordinates is { position vector in A} is m i a;
Step 4: calculate that { { pose in A}, be the initial pose of aircraft side member to B}, is designated as U at fixed coordinate system with moving coordinate system 0;
Step 5: four nip points, the target mirror is installed, is utilized laser tracker to measure target mirror coordinate, { initial coordinate in A}, be designated as q at fixed coordinate system to obtain bite i a, (i=1,2,3,4); Anti-drive solution moving coordinate system { the position vector q under M} i m;
Step 6: trajectory planning rotatablely moves; First set the boundary condition of this trajectory planning, set the posture adjustment time T, given aircraft side member object pose U tand posture adjustment process kinematic boundary condition, be designated as:
1) pose boundary condition: U (0)=U 0, U (T)=U t;
2) velocity boundary conditions: v (0)=v 0, v (T)=v t;
3) acceleartion boundary condition: a (0)=a 0, a (T)=a t;
Calculate each steady arm driving amount;
Step 7: motion of translation trajectory planning; First set the boundary condition of this trajectory planning, set the posture adjustment time T, given aircraft side member object pose U tand posture adjustment process kinematic boundary condition, be designated as:
1) pose boundary condition: U (0)=U 0, U (T)=U t;
2) velocity boundary conditions: v (0)=v 0, v (T)=v t;
3) acceleartion boundary condition: a (0)=a 0, a (T)=a t.
Calculate each steady arm driving amount.
Wherein, " set up a fixed coordinate system o-xyz on tooling base, be designated as { A} " described in step 1, its method for building up is:
A target mirror f first is installed on base 0, its position gets final product about the base middle part, as fixed coordinate system { the initial point o of A}; O point vertical direction and with guide's x parallel direction on a target mirror f is installed respectively z, f x.With vector as the x axle, with vector direction, as the z direction of principal axis, is determined the y direction of principal axis according to right-hand rule, as shown in Figure 1.
Wherein, " set up on the aircraft side member with moving coordinate system { B} " described in step 2, its method for building up is;
In aircraft side member approximate center, one target mirror f is installed o 'as moving coordinate system the initial point o ' of B}, and on the aircraft side member roughly with target mirror f o 'installation target mirror f vertically and on horizontal direction z ', f x '.With vector as x ' axle, with vector direction, as z ' direction of principal axis, is determined y ' direction of principal axis according to right-hand rule.
Wherein, " setting up and driving system of axes o on every steady arm described in step 3 i-x iy iz i, be designated as { M i", the method for its foundation is;
In the column bottom, one target mirror f is installed o ias driving system of axes { M iinitial point o i, x i, y i, z iall with fixed coordinate system, { the x, y, z direction of principal axis of A} is corresponding consistent for direction of principal axis.
Wherein, " calculating that { { pose in A}, be the initial pose of aircraft side member to B}, is designated as U at fixed coordinate system with moving coordinate system described in step 4 0", the method for its calculating is:
Utilize target mirror f on laser tracker instrumentation airplane side member o 'fixed coordinate system the position in A}, and as the aircraft side member at fixed coordinate system { the initial position vector p in A} a=(p xp yp z) t.If under initial condition, with moving coordinate system, { with respect to fixed coordinate system, { Eulerian angles of A}z, x, z rotation order are α (0), β (0), γ (0) to B}.With moving coordinate system B} with respect to fixed coordinate system the attitude transition matrix of A} is:
R AB = cos α cos γ - sin α cos β sin γ - cos α sin γ - sin α cos β cos γ sin α sin β sin α cos γ + cos α cos β sin γ - sin α sin γ + cos α cos β cos γ - cos α sin β sin β sin γ sin β cos γ cos β
Can obtain initial pose U 0=[p x(0) p y(0) p z(0) α (0) β (0) γ (0)] t.
Wherein, at " the anti-drive solution moving coordinate system { M described in step 5 iunder position vector q i m", its anti-method of separating is:
To steady arm i (i=1~4), its bite is in { the position vector in A} { in B}, position vector is q i b, have:
q i A = R AB q i B + p A - - - ( 1 )
{ M iand the A} coordinate axle is parallel to each other, and in whole side member posture adjustment process, { M iwith { A} is relative static, so R a mibe 3 * 3 identity matrixs.Bite is at { M iin position vector be q i mihave
q i A = R A M i q i M i + m i A - - - ( 2 )
Simultaneous formula (1) and formula (2) can obtain
q i M i = R AB q i B + p A - m i A - - - ( 3 )
By q i mito driving system of axes { M ithree main shaft coordinate projections can obtain each joint variable of steady arm i.To (3) formula differentiate, can draw the joint velocity vector of steady arm i and the relation between acceleration and side member pose.
q · i M i q · · i M i = R · AB p · A R · · AB p · · A q i B 1 - - - ( 4 )
Wherein, " trajectory planning rotatablely moves " described in step 6, the method for its trajectory planning is:
Adopt five order polynomials to carry out matching to the track that rotatablely moves, take Eulerian angles α as example, the rotatablely move equation of locus of side member from initial pose to the object pose process can be expressed as:
α ( t ) α · ( t ) α · · ( t ) = 1 t t 2 t 3 t 4 t 5 0 1 2 t 3 t 2 4 t 3 5 t 4 0 0 2 6 t 12 t 2 20 t 3 a 0 a 1 a 2 a 3 a 4 a 5 - - - ( 5 )
Kinematic boundary condition substitution (6) formula can be solved:
α ( t ) = 6 Δα T R 5 t 5 - 15 Δα T R 4 t 4 + 10 Δα T R 3 t 3 + α 0 - - - ( 6 )
T in formula rfor the time of rotatablely moving, α 0for initial attitude Eulerian angles, α 0=α (0), Δ α=α (T r)-α (0).
Utilize similarly method for planning track of α (t), the track that can try to achieve β and γ is:
β ( t ) γ ( t ) 6 Δβ T R 5 - 15 Δβ T R 4 20 Δβ T R 3 β 0 6 Δγ T R 5 - 15 Δγ T R 4 20 Δγ T R 3 γ 0 t 5 t 4 t 3 1 - - - ( 7 )
Can obtain the side member track U that rotatablely moves by formula (6), (7) r(t) be:
U R(t)=[p x(0) p y(0) p z(0) α(t) β(t) γ(t)] T (8)
[p in formula x(0) p y(0) p z(0)] t=p a(0), be the position vector of side member at initial pose place.The path of motion that formula (8) substitution formula (3), (4) can be tried to achieve to each joint of steady arm in the side member rotary movement is:
q i M i ( t ) = R AB ( t ) q i B + p A ( 0 ) - m i A q · i M i ( t ) = R · AB ( t ) q i B q · · i M i ( t ) = R · · AB ( t ) q i B - - - ( 9 )
Wherein, " calculating each steady arm driving amount " described in step 6, its method of calculating is:
By what try to achieve in formula (9) respectively to { M ithe change in coordinate axis direction projection can obtain the corresponding driving amount driven.
Wherein, at " motion of translation trajectory planning " described in step 7, the method for its trajectory planning is:
After side member completes the attitude adjustment, will be in targeted attitude [α (T r) β (T r) γ (T r)] t, only need to carry out motion of translation along three directions of x, y, z respectively and can complete the pose adjustment.Motion of translation for side member adopts " accelerating-at the uniform velocity-deceleration " velocity mode, with segmental cubic polynomials, carries out trajectory planning.In the motion of translation trajectory planning, make accelerator and moderating process symmetry.The track U of motion of translation p(t) be:
U P(t)=[p x(t) p y(t) p z(t) α(T R) β(T R) γ(T R)] T (10)
T in formula pfor the side member motion of translation time.Formula (10) substitution formula (3), (4) can be tried to achieve to the path of motion in each joint of steady arm in side member motion of translation process.
q i M i ( t ) = R AB ( T R ) q i B + p A ( t ) - m i A q · i M i ( t ) = p · A ( t ) q · · i M i ( t ) = p · · A ( t ) - - - ( 11 )
Wherein, " calculating each steady arm driving amount " described in step 7, its method of calculating is:
By what try to achieve in formula (11) respectively to { M ithe change in coordinate axis direction projection can obtain the corresponding driving amount driven.
3, advantage and effect
The present invention, in conjunction with the Aircraft-Oriented side member flexible assembly pose_adjuster of autonomous Design, is decomposed into attitude by the adjustment of aircraft side member pose and adjusts whole two stages of peaceful transposition.Take the time as variable, carry out successively the adjustment of six spatial coordinates variablees, effectively reduce the pose_adjuster multiaxis and coordinate the control difficulty driven.Solved in fitting process that aircraft side member pose at the whole story is known and the complete uncertain pose of motion path is adjusted trajectory planning problem.
(4) accompanying drawing explanation
Fig. 1 is aircraft side member assembly tooling schematic diagram involved in the present invention.
Fig. 2 is aircraft side member assembly tooling kinematic sketch of mechanism involved in the present invention.
Fig. 3 is operational flowchart of the present invention.
In figure, nomenclature is as follows:
1 process connection, 2 line slideways, 3 hold-down arms, 4 cross trays, 5 columns, 6 slide blocks, 7 line slideways, 8 tooling bases, 9 aircraft side member, 10z is to moving sets, and 11y is to moving sets, 12 typed ball bearing pair, 13x is to moving sets, 14 tooling bases.
(5) specific embodiment
See Fig. 1 to Fig. 3, a kind of aircraft side member assembling of the present invention posture adjustment method for planning track, its concrete implementation step is as follows:
Step 1: the fixed target mirror is installed on the tooling base of aircraft components erecting yard, is utilized laser tracker to measure target mirror coordinate, set up a fixed coordinate system o-xyz on tooling base, be designated as { A};
Step 2: the target mirror is installed on the aircraft side member, and { coordinate in A} is set up one with moving coordinate system o '-x ' y ' z ' on the aircraft side member, is designated as { B} at fixed coordinate system to utilize laser tracker to measure the target mirror.Its origin of coordinates is at { the position vector p in A} a=(p xp yp z) t, at { the attitude matrix R in A} aB;
Step 3: the target mirror is installed on every steady arm, is utilized laser tracker to measure the target mirror at fixed coordinate system { coordinate o in A} i, set up one and drive system of axes o on every steady arm i-x iy iz i, be designated as { M i(i=1,2,3,4), the origin of coordinates is { position vector in A} is m i a;
Step 4: calculate that { { pose in A}, be the initial pose of aircraft side member to B}, is designated as U at fixed coordinate system with moving coordinate system 0;
Step 5: four nip points, the target mirror is installed, is utilized laser tracker to measure target mirror coordinate, { initial coordinate in A}, be designated as q at fixed coordinate system to obtain bite i a, (i=1,2,3,4).Anti-drive solution moving coordinate system { the position vector q under M} i m;
Step 6: trajectory planning rotatablely moves.Set the posture adjustment time T, given aircraft side member object pose U tand posture adjustment process kinematic boundary condition.Be designated as:
1) pose boundary condition: U (0)=U 0, U (T)=U t;
2) velocity boundary conditions: v (0)=v 0, v (T)=v t;
3) acceleartion boundary condition: a (0)=a 0, a (T)=a t.
Calculate each steady arm driving amount;
Step 7: motion of translation trajectory planning.Set the posture adjustment time T, given aircraft side member object pose U tand posture adjustment process kinematic boundary condition.Be designated as:
1) pose boundary condition: U (0)=U 0, U (T)=U t;
2) velocity boundary conditions: v (0)=v 0, v (T)=v t;
3) acceleartion boundary condition: a (0)=a 0, a (T)=a t.
Calculate each steady arm driving amount.
Wherein, described in step 1 tooling base set up fixed coordinate system the method for A} is:
A target mirror f first is installed on base 0, its position gets final product about the base middle part, as fixed coordinate system { the initial point o of A}; O point vertical direction and with guide's x parallel direction on a target mirror f is installed respectively z, f x.With vector as the x axle, with vector direction, as the z direction of principal axis, is determined the y direction of principal axis according to right-hand rule, as shown in Figure 1.
Wherein, with moving coordinate system, { method of B} is setting up on the aircraft side member described in step 2;
In aircraft side member approximate center, one target mirror f is installed o 'as moving coordinate system the initial point o ' of B}, and on the aircraft side member roughly with target mirror f o 'installation target mirror f vertically and on horizontal direction z ', f x '.With vector as x ' axle, with vector direction, as z ' direction of principal axis, is determined y ' direction of principal axis according to right-hand rule, as shown in Figure 1.
Wherein, setting up on steady arm and driving system of axes { M described in step 3 imethod be;
In the column bottom, one target mirror f is installed o ias driving system of axes { M iinitial point o i, x i, y i, z iall with fixed coordinate system, { the x, y, z direction of principal axis of A} is corresponding consistent for direction of principal axis.
Wherein, in calculating described in step 4, with moving coordinate system, { B} is at fixed coordinate system { the initial pose U in A} 0method be:
Utilize target mirror f on laser tracker instrumentation airplane side member o 'fixed coordinate system the position in A}, and as the aircraft side member at fixed coordinate system { the initial position vector p in A} a=(p xp yp z) t.If under initial condition, with moving coordinate system, { with respect to fixed coordinate system, { Eulerian angles of A}z, x, z rotation order are α (0), β (0), γ (0) to B}.With moving coordinate system B} with respect to fixed coordinate system the attitude transition matrix of A} is:
R AB = cos α cos γ - sin α cos β sin γ - cos α sin γ - sin α cos β cos γ sin α sin β sin α cos γ + cos α cos β sin γ - sin α sin γ + cos α cos β cos γ - cos α sin β sin β sin γ sin β cos γ cos β
Can obtain initial pose U 0=[p x(0) p y(0) p z(0) α (0) β (0) γ (0)] t
Wherein, at anti-drive solution moving coordinate system { M described in step 5 iunder position vector q i mmethod be:
To steady arm i (i=1~4), its bite is at { the position vector q in A} i a=(q ix aq iy aq iz a) t, { in B}, position vector is q i b, have:
q i A = R AB q i B + p A - - - ( 1 )
{ M iand the A} coordinate axle is parallel to each other, and in whole side member posture adjustment process, { M iwith { A} is relative static, so R a mibe 3 * 3 identity matrixs.Bite is at { M iin position vector be q i mi, have
q i A = R A M i q i M i + m i A - - - ( 2 )
Simultaneous formula (1) and formula (2) can obtain
q i M i = R AB q i B + p A - m i A - - - ( 3 )
By q i mito driving system of axes { M ithree main shaft coordinate projections can obtain each joint variable of steady arm i.To (3) formula differentiate, can draw the joint velocity vector of steady arm i and the relation between acceleration and side member pose.
q · i M i q · · i M i = R · AB p · A R · · AB p · · A q i B 1 - - - ( 4 )
Wherein, the method at the trajectory planning that rotatablely moves described in step 6 is:
Set kinematic boundary condition in test as follows:
1) pose boundary condition: U 0(0,0,0,0,0,0) t, U t=(0,0,0,0.015 ,-0.02,0.03) t
2) velocity boundary conditions: v (0)=0, v (T)=0;
3) acceleartion boundary condition: α (0)=0, α (T)=0.
Adopt five order polynomials to carry out matching to the track that rotatablely moves, take Eulerian angles α as example, the rotatablely move equation of locus of side member from initial pose to the object pose process can be expressed as:
α ( t ) α · ( t ) α · · ( t ) = 1 t t 2 t 3 t 4 t 5 0 1 2 t 3 t 2 4 t 3 5 t 4 0 0 2 6 t 12 t 2 20 t 3 a 0 a 1 a 2 a 3 a 4 a 5 - - - ( 5 )
Kinematic boundary condition substitution (6) formula can be solved:
α ( t ) = 6 Δα T R 5 t 5 - 15 Δα T R 4 t 4 + 10 Δα T R 3 t 3 + α 0 - - - ( 6 )
Carry out successively the adjustment of Eulerian angles α, β, γ in test, adjust time series T r=(18,25,30), initial attitude Eulerian angles α 0=(0,0,0), targeted attitude Eulerian angles α (T r)=(0.015 ,-0.02,0.03), Δ α=α (T r)-α (0)=(0.015 ,-0.02,0.03).
Utilize similarly method for planning track of α (t), the track that can try to achieve β and γ is:
β ( t ) γ ( t ) = 6 Δβ T R 5 - 15 Δβ T R 4 20 Δβ T R 3 β 0 6 Δγ T R 5 - 15 Δγ T R 4 20 Δγ T R 3 γ 0 t 5 t 4 t 3 1 - - - ( 7 )
Can obtain the side member track U that rotatablely moves by formula (6), (7) r(t) be:
U R(t)=[p x(0) p y(0) p z(0) α(t) β(t) γ(t)] T (8)
[p in formula x(0) p y(0) p z(0)] t=P a(0), be the position vector of side member at initial pose place.The path of motion that formula (8) substitution formula (3), (4) can be tried to achieve to each joint of steady arm in the side member rotary movement is:
q i M i ( t ) = R AB ( t ) q i B + p A ( 0 ) - m i A q · i M i ( t ) = R · AB ( t ) q i B q · · i M i ( t ) = R · · AB ( t ) q i B - - - ( 9 )
Wherein, " calculating each steady arm driving amount " described in step 6, its method of calculating is:
By what try to achieve in formula (9) respectively to { M ithe change in coordinate axis direction projection can obtain the corresponding driving amount driven.
Wherein, the method at the trajectory planning of motion of translation described in step 7 is:
After side member completes the attitude adjustment, will be in targeted attitude [α (T r) β (T r) γ (T r)] t, only need to carry out motion of translation along three directions of x, y, z respectively and can complete the pose adjustment, the track U of motion of translation p(t) be:
U p(t)=[p x(t) p y(t) p z(t) α(T R) β(T R) γ(T R))] T (10)
Set kinematic boundary condition in test as follows:
1) pose boundary condition: U 0=(0,0,0,0,0,0) t, U t=(30 ,-45,25,0,0,0) t
2) velocity boundary conditions: v (0)=0, v (T)=0;
3) acceleartion boundary condition: α (0)=0, α (T)=0.
Carry out successively the adjustment of x, y, x in test, adjust time series T p=(24,35,22)
In aircraft side member motion of translation process, the path of motion of the path of motion of steady arm and aircraft side member is identical.Adopt " accelerating an at the uniform velocity deceleration " velocity mode, with segmental cubic polynomials, carry out trajectory planning.In the motion of translation trajectory planning, make accelerator and moderating process symmetry.The motion of translation of take in the x-direction is example (y to z to identical), and the acceleration/accel of side member, speed, location track are respectively shown in formula (11), (12), (13).
p · · x ( t ) = b 0 t + b 1 t ∈ [ 0 , T P 6 ] - b 0 t + b 2 t ∈ [ T P 6 , T P 3 ] 0 t ∈ [ T P 3 , 2 T P 3 ] - b 0 t + b 3 t ∈ [ 2 T P 3 , 5 T P 6 ] b 0 t + b 4 t ∈ [ 5 T P 6 , T P ] - - - ( 11 )
p · x ( t ) = 1 2 b 0 t 2 + b 1 t + b 5 t ∈ [ 0 , T p 6 ] - 1 2 b 0 t 2 + b 2 t + b 6 t ∈ [ T p 6 , T p 3 ] b 7 t ∈ [ T p 3 , 2 T p 3 ] - 1 2 b 0 t 2 + b 3 t + b 8 t ∈ [ 2 T p 3 , 5 T p 6 ] 1 2 b 0 t 2 + b 4 t + b 9 t ∈ [ 5 T p 6 , T p ] - - - ( 12 )
p x ( t ) = 1 6 b 0 t 3 + 1 2 b 1 t 2 + b 5 t + b 10 t ∈ [ 0 , T P 6 ] - 1 6 b 0 t 3 + 1 2 b 2 t 2 + b 6 t + b 11 t ∈ [ T P 6 , T P 3 ] b 7 t + b 12 t ∈ [ T P 3 , 2 T P 3 ] - 1 6 b 0 t 3 + 1 2 b 3 t 2 + b 8 t + b 13 t ∈ [ 2 T P 3 , 5 T P 6 ] 1 6 b 0 t 3 + 1 2 b 4 t 2 + b 9 t + b 14 t ∈ [ 5 T P 6 , T P ] - - - ( 13 )
By 6 kinematic boundary condition substitution formulas (11), (12), (13), be combined in the continuity of side member displacement, speed and acceleration trajectory in the motion of translation process respectively simultaneously, can solve that to obtain the motion of translation equation of locus as follows:
p · · x ( t ) = 54 Δ p x T P 3 t - 54 Δ p x T P 3 t + 18 Δ p x T P 2 0 - 54 Δ p x T P 3 t + 36 Δ p x T P 2 54 Δ p x T P 3 t - 54 Δ p x T P 2 - - - ( 14 )
p · x ( t ) = 27 Δ p x T P 3 t 2 - 27 Δ p x T P 3 t 2 + 18 Δ p x T P 2 t - 3 Δ p x 2 T P 3 Δ p x 2 T P - 27 Δ p x T P 3 t 2 + 36 Δ p x T P 2 t - 21 Δ p x 2 T P 27 Δ p x T P 3 t 2 - 54 Δ p x T P 2 t + 27 Δ p x T P - - - ( 15 )
p x ( t ) = 9 Δ p x T P 3 t 3 + p x 0 - 9 Δ p x T P 3 t 3 + 9 Δ p x T P 2 t 2 - 3 Δ p x 2 T P t + Δ p x 12 + p x 0 3 Δ p x 2 T P t - Δ p x 4 + p x 0 - 9 Δ p x T P 3 t 3 + 18 Δ p x T P 2 t 2 - 21 Δ p x 2 T P t + 29 Δ p x 12 + p x 0 9 Δ p x T P 3 t 3 - 27 Δ p x T P 2 t 2 + 27 Δ p x T P t - 8 Δ p x + p x 0 - - - ( 16 )
T in formula pfor side member motion of translation time, p x0for the position coordinate at initial pose place, p x0=p x(0), Δ p x=p x(T p)-p x(0).P yand p (t) z(t) the same p of trajectory planning x(t), by p x(t), p y(t), p z(t) substitution formula (10) can obtain the track of side member motion of translation.
Wherein, " calculating each steady arm driving amount " described in step 7, its method of calculating is:
By what try to achieve in formula (11) respectively to { M ithe change in coordinate axis direction projection can obtain the corresponding driving amount driven.

Claims (10)

1. an aircraft side member is assembled the posture adjustment method for planning track, and it is characterized in that: the method step is as follows:
Step 1: the fixed target mirror is installed on the tooling base of aircraft components erecting yard, is utilized laser tracker to measure target mirror coordinate, set up a fixed coordinate system o-xyz on tooling base, be designated as { A };
Step 2: the target mirror is installed on the aircraft side member, is utilized laser tracker to measure target mirror coordinate in fixed coordinate system { A }, set up one with moving coordinate system o '-x ' y ' z ' on the aircraft side member, be designated as { B}; Its origin of coordinates is at { the position vector p in A} a=(p xp yp z) t, the attitude matrix R in { A } aB;
Step 3: the target mirror is installed on every steady arm, is utilized laser tracker to measure target mirror coordinate o in fixed coordinate system { A } i, set up one and drive system of axes o on every steady arm i-x iy iz i, be designated as { M i, i=1,2,3,4, the position vector of the origin of coordinates in { A } is m i a;
Step 4: calculate the pose in fixed coordinate system { A } with moving coordinate system { B }, be the initial pose of aircraft side member, be designated as U 0;
Step 5: four nip points, the target mirror is installed, is utilized laser tracker to measure target mirror coordinate, obtain the initial coordinate of bite in fixed coordinate system { A }, be designated as q i a, i=1,2,3,4; Position vector q under anti-drive solution moving coordinate system { M } i m;
Step 6: trajectory planning rotatablely moves; First set the boundary condition of this trajectory planning, set the posture adjustment time T, given aircraft side member object pose U tand posture adjustment process kinematic boundary condition, be designated as:
1) pose boundary condition: U (0)=U 0, U (T)=U t;
2) velocity boundary conditions: v (0)=v 0, v (T)=v t;
3) acceleartion boundary condition: a (0)=a 0, a (T)=a t;
Calculate each steady arm driving amount;
Step 7: motion of translation trajectory planning; First set the boundary condition of this trajectory planning, set the posture adjustment time T, given aircraft side member object pose U tand posture adjustment process kinematic boundary condition, be designated as:
1) pose boundary condition: U (0)=U 0, U (T)=U t;
2) velocity boundary conditions: v (0)=v 0, v (T)=v t;
3) acceleartion boundary condition: a (0)=a 0, a (T)=a t;
Calculate each steady arm driving amount.
2. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
" set up a fixed coordinate system o-xyz on tooling base, be designated as { A } " described in step 1, its method for building up is: a target mirror f first is installed on base 0, its position gets final product at the base middle part, as the initial point o of fixed coordinate system { A }; O point vertical direction and with guide's x parallel direction on a target mirror f is installed respectively z, f x, with vector as the x axle, with vector direction, as the z direction of principal axis, is determined the y direction of principal axis according to right-hand rule.
3. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
" setting up with moving coordinate system { B } on the aircraft side member " described in step 2, its method for building up is: a target mirror f is installed in aircraft side member center o 'as the initial point o ' of moving coordinate system { B }, on the aircraft side member with target mirror f o 'installation target mirror f vertically and on horizontal direction z ', f x ', with vector as x ' axle, with vector direction, as z ' direction of principal axis, is determined y ' direction of principal axis according to right-hand rule.
4. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
" setting up and driving system of axes o on every steady arm described in step 3 i-x iy iz i, be designated as { M i", the method for its foundation is: in the column bottom, one target mirror f is installed o 1as driving system of axes { M iinitial point o i, x i, y i, z iall with fixed coordinate system, { the x, y, z direction of principal axis of A} is corresponding consistent for direction of principal axis.
5. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
" calculating the pose in fixed coordinate system { A } with moving coordinate system { B }, being the initial pose of aircraft side member, being designated as U described in step 4 0", the method for its calculating is:
Utilize target mirror f on laser tracker instrumentation airplane side member o 'fixed coordinate system the position in A}, and as the aircraft side member at fixed coordinate system { the initial position vector p in A} a=(p xp yp z) t; If under initial condition, with moving coordinate system { B }, with respect to the Eulerian angles of fixed coordinate system { A } z, x, z rotation order, be a (0), β (0), γ (0), with moving coordinate system { B } with respect to fixed coordinate system the attitude transition matrix of A} is:
R AB = cos α cos γ - sin α cos β sin γ - cos α sin γ - sin α cos β cos γ sin α sin β sin α cos γ + cos α cos β sin γ - sin α sin γ + cos α cos β cos γ - cos α sin β sin β sin γ sin β cos γ cos β
Obtain initial pose U 0=[p x(0) p y(0) p z(0) α (0) β (0) γ (0)] t.
6. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
At " the anti-drive solution moving coordinate system { M described in step 5 iunder position vector q i m", its anti-method of separating is:
To steady arm I (i=1~4), its bite is in { the position vector in A} { in B}, position vector is q i b, have:
q i A = R AB q i B + p A - - - ( 1 )
{ M iand the A} coordinate axle is parallel to each other, and in whole side member posture adjustment process, { M iwith { A} is relative static, so R a mibe 3 * 3 identity matrixs, bite is at { M i) in position vector be q i mi, have
q i A = R A M i q i M i + m i A - - - ( 2 )
Simultaneous formula (1) and formula (2)
q i M i = R AB q i B + p A - m i A - - - ( 3 )
By q i mito driving system of axes { M ithree main shaft coordinate projections obtain each joint variable of steady arm i; To (3) formula differentiate, draw the joint velocity vector of steady arm i and the relation between acceleration and side member pose:
q . i M i q . . i M i = R . AB p . A R . . AB p . . A q i B 1 - - - ( 4 )
7. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
" trajectory planning rotatablely moves " described in step 6, the method for this trajectory planning is:
Adopt five order polynomials to carry out matching to the track that rotatablely moves, take Eulerian angles α as example, the rotatablely move equation of locus of side member from initial pose to the object pose process is expressed as:
α ( t ) α . ( t ) α . . ( t ) = 1 t t 2 t 3 t 4 t 5 0 1 2 t 3 t 2 4 t 3 5 t 4 0 0 2 6 t 12 t 2 20 t 3 a 0 a 1 a 2 a 3 a 4 a 5 - - - ( 5 )
Kinematic boundary condition substitution (6) formula is solved:
α ( t ) = 6 Δα T R 5 t 5 - 15 Δα T R 4 t 4 + 10 Δα T R 3 t 3 + α 0 - - - ( 6 )
T in formula rfor the time of rotatablely moving, α 0for initial attitude Eulerian angles, α 0=α (0), Δ α=α (T r)-α (0);
Utilize similarly method for planning track of α (t), the track of trying to achieve β and γ is:
β ( t ) γ ( t ) = 6 Δβ T R 5 - 15 Δβ T R 4 20 Δβ T R 3 β 0 6 Δγ T R 5 - 15 Δγ T R 4 20 Δγ T R 3 γ 0 t 5 t 4 t 3 1 - - - ( 7 )
By formula (6), (7) the side member track U that rotatablely moves r(t) be:
U R(t)=[p x(0) p y(0) p z(0) α(t) β(t) γ(t)] T (8)
[p in formula x(0) p y(0) p z(0)] t=p a(0), be the position vector of side member at initial pose place; The path of motion of formula (8) substitution formula (3), (4) being tried to achieve to each joint of steady arm in the side member rotary movement is:
q i M i ( t ) = R AB ( t ) q i B + p A ( 0 ) - m i A q · i M i ( t ) = R · AB ( t ) q i B q · · i M i ( t ) = R · · AB ( t ) q i B - - - ( 9 )
8. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
" calculating each steady arm driving amount " described in step 6, its method of calculating is: by what try to achieve in formula (9) respectively to { M ithe change in coordinate axis direction projection obtain the corresponding driving amount driven.
9. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
At " motion of translation trajectory planning " described in step 7, the method for this trajectory planning is:
After side member completes the attitude adjustment, will be in targeted attitude [α (T r) β (T r) γ (T r)] t, only need to carry out motion of translation along three directions of x, y, z respectively and complete the pose adjustment; Motion of translation for side member adopts " accelerating-at the uniform velocity-deceleration " velocity mode, with segmental cubic polynomials, carries out trajectory planning; In the motion of translation trajectory planning, make accelerator and moderating process symmetry, the track U of motion of translation p(t) be:
U P(t)=[p x(t) p y(t) p z(t) α(T R) β(T R) γ(T R)] T (10)
T in formula pfor the side member motion of translation time; Formula (10) substitution formula (3), (4) are tried to achieve to the path of motion in each joint of steady arm in side member motion of translation process;
q i M i ( t ) = R AB ( T R ) q i B + p A ( t ) - m i A q · i M i ( t ) = p · A ( t ) q · · i M i ( t ) = p · · A ( t ) - - - ( 11 )
10. a kind of aircraft side member according to claim 1 is assembled the posture adjustment method for planning track, it is characterized in that:
" calculating each steady arm driving amount " described in step 7, its method of calculating is:
By what try to achieve in formula (11) respectively to { M ithe change in coordinate axis direction projection obtain the corresponding driving amount driven.
CN201310384485.4A 2013-08-29 2013-08-29 A kind of aircraft side walls parts assembling posture adjustment method for planning track Expired - Fee Related CN103496449B (en)

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