CN106503373A - The method for planning track that a kind of Dual-robot coordination based on B-spline curves is assembled - Google Patents
The method for planning track that a kind of Dual-robot coordination based on B-spline curves is assembled Download PDFInfo
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Abstract
The invention provides a kind of Dual-robot coordination assembling method for planning track based on B-spline curves, belongs to trajectory planning field；Which includes task module, principal and subordinate's joint of robot trajectory planning module, Robot dodge strategy module, multiple-objection optimization module, industrial robot driver.A kind of method of the Dual-robot coordination assembling joint trajectory planning method and Coordinative assembling error compensation based on B-spline curves of principal and subordinate's joint of robot trajectory planning module invention；A kind of dual robot deep search Robot dodge strategy of the Robot dodge strategy module invention；Multiple-objection optimization module invention is a kind of to solve based on Swarm Intelligence Algorithm that Dual-robot coordination installation time is less, assembles the multi-objective planning method under the conditions of the kinematical constraint of smooth trajectory；Using technical scheme, it is shorter to obtain installation time, and load segment joint trajectories are smoothed, successful avoiding obstacles and without the Dual-robot coordination assembling track that interferes, reduce cost, it is to avoid the damage of assembly parts.
Description
Technical field
The present invention relates to trajectory planning field.Fill more particularly, to a kind of Dual-robot coordination based on B-spline curves
The method for planning track that matches somebody with somebody.
Background technology
As single robotic asssembly is present, working space is limited, and blind area is assembled in easily presence, and flexibility is inadequate, it is difficult to realize
The deficiencies such as full-automatic assembling work.Therefore, in order to adapt to the complexity of fittage and intelligent, single robotic asssembly is made up
Deficiency, propose Dual-robot coordination assembly system.Although Dual-robot coordination assembly system has, and flexibility is good, adaptability is high
Advantage, but its complexity is consequently increased, obstacle avoidance algorithm between the coordinated movement of various economic factors scheme of double SCM, robot,
The trajectory planning and its optimized algorithm of dual robot is all problem demanding prompt solution.
Content of the invention
In order to solve the above problems, it is contemplated that a kind of Dual-robot coordination assembling method for planning track is disclosed, espespecially
A kind of multiple target dual robot assembling for obtaining minimum run time, assembling smooth trajectory, avoiding obstacles based on B-spline curves
The method of trajectory planning.
For achieving the above object, the technical solution adopted in the present invention is mainly included the following steps that：
Step 1, the kinematics model for setting up double industrial robots, try to achieve the positive and negative solution of MS master-slave industrial robot；
The main robot referred in the Coordinative assembling stage, and joint displacements, speed and acceleration are according to kinematical constraint
The industrial robot of one assembly of clamping to determine；Refer to that joint motions are with main frame in the Coordinative assembling stage from robot
The joint motions of device people and change clamping another assembly industrial robot.
Step 2, the task point posture information for being obtained MS master-slave robot by described task module；
The task module refers to given MS master-slave robot specifically discrete teaching path point, can using the result of step 1
To obtain the task point posture information of MS master-slave robot.
Step 3, the coordinate system for setting up the robot coordinated system of MS master-slave, obtain MS master-slave machine by the method for Coordinate Conversion
Transformation matrix of the ending coordinates system of people relative to itself base coordinate system.
Step 4, row interpolation is clicked through to MS master-slave robot Coordinative assembling joint position using the method for B-spline curves interpolation,
Dual-robot coordination assembling joint trajectories are tried to achieve, and carries out the compensation of Coordinative assembling error, be i.e. joint trajectory planning module；
The Mathematical Modeling of the B-spline curves interpolation method is：
In formula (1)：Q1(u)∈RM×1And Q2(u)∈RM×1MS master-slave joint of robot at respectively normalization moment u
The joint number of displacement, wherein M for robot, dj,1(u)∈RM×1And dj,2(u)∈RM×1Respectively MS master-slave robot B-spline
The control point of joint trajectories curve；Close for slave device people B-spline
The normalization time arrow of section geometric locus, n1+ 1 and n2+ 1 task interpolation point number for being respectively principal and subordinate robot, Nj,k,1(u)
And Nj,k,2U () is respectively k specification B-spline basic function of MS master-slave robot B-spline joint trajectories curve, according to recurrence formula
(2) define：
In formula (2), R=1 represents main robot, and R=2 is represented from robot, and i is batten sequence number, B-spline basic function
Ni,k,RU it is [u that the supporting of () is intervali,ui+k+1], i=0,1 ... n；If run time is ttotal, closed according to MS master-slave robot
Section track B-spline interpolation curve control point and knot vector, by De Buer recurrence formula conversion can obtain on curve
The r ranks of moment t lead arrow, i.e.,：
Can respectively obtain as R=1,2, r=0,1,2,3 in formula (3) MS master-slave robot B-spline joint trajectories with
The joint displacements of time change, speed, acceleration and jerk curve；
As the pose constraint and relative motion constraint between assembly is difficult to ensure that, rigging error can be produced, therefore base
Need to carry out rigging error compensation after B-spline curves interpolation；
The Coordinative assembling error compensating method is：
In formula (4), PositionError is site error, and AttitudeError is attitude error,Respectively
For two vertical lines distance (referring to Fig. 2), α, β γ, α, β*、γ*、*For Eulerian angles.
Step 5, execution dual robot deep search Robot dodge strategy module；
Robot dodge strategy in the dual robot deep search Robot dodge strategy between robot and barrier is as follows：In machine
One interference test point is set on the connecting rod axis of people at spacing intervals, and test point each segment connecting rod will be interfered most
Big Envelope radius be added to barrier thickness on, so as to the collision between robot and barrier is converted into by a series of dry
The position relationship between barrier after relating to test point and expanding judges.
A series of position relationship decision methods that interferes between test point and the barrier after expansion are as follows：By robot
After being reduced to a series of interference test points, the whole working time internal interference test point whether barrier region after expansion is judged
Interior；If so, then connecting rod and barrier have interference situation, judge that robot is collided with barrier；Otherwise continue to judge other
Interfere test point within the whole working time whether in the barrier region after expansion；If all interference test points are in whole work
Make in the time not in the barrier region after expansion, then judge that robot is not collided with barrier, otherwise machine
People collides (referring to Fig. 3) with barrier.
Robot dodge strategy in the dual robot deep search Robot dodge strategy between robot and robot is as follows：By machine
People is reduced to the straightway being made up of pitman shaft, so as to the collision between robot and robot to be reduced to judge whole work
In space, in space, the beeline of two straightways judges to close with the size of the largest enveloping radius sum of corresponding two connecting rods
System.
The simplification judges in whole working space the beeline of two straightways and corresponding two connecting rods in space
The size predicting relation method of largest enveloping radius sum is as follows：The simplified straightway of calculating main frame device people connecting rod i with from machine
(computational methods are with reference to the beeline between two lines section in space for beeline between the simplified straightway of people connecting rod j
Computational methods).Judge within the whole working time beeline whether largest enveloping radius sum less than connecting rod i and connecting rod j,
If so, then connecting rod i and connecting rod j collides, and judges to collide between dual robot；Otherwise connecting rod i and connecting rod j does not occur
Collision, continues to judge whether other connecting rods of main robot i is collided with the connecting rod from robot；When all connecting rods of main robot
With all do not collide from all connecting rods of robot, then judge dual robot between do not collide (referring to Fig. 4).
The dual robot deep search Robot dodge strategy following steps：
S1, the respective starting point of setting MS master-slave robot and impact point, make num1=num2=0；
S2, avoidance intermediate point substantially is artificially determined according to the position relationship that robot in task space and barrier are present
Position, num1=num1+1；
Heuristic search is carried out in S3, the hunting zone that specifies near avoidance intermediate point, avoidance intermediate point, num2 is determined
=num2+1；
S4, carry out B-spline interpolation respectively to the starting point of MS master-slave robot, intermediate point and impact point, generate master-slave machine
The joint trajectories of device people；
S5, whether judged between whole working time inner machine people and barrier, dual robot by avoidance detection method
Collide, if it is not, then the nothing of output MS master-slave robot touches joint trajectories, fob=0 termination algorithm；If so, then execution step
S6；
S6, num2 is judged whether less than num2max, if so, then execution step S3, if it is not, then execution step S7；
S7, judge num1 whether less than num1max, if so, then execution step S2, if it is not, be not then successfully searched main-
From the collisionless joint trajectories of robot, fob=+∞, algorithm terminate；
Wherein num1max is the number of attempt for artificially determining avoidance mid-point position, and num2max is attached in avoidance intermediate point
The random maximum allowable number of times for determining avoidance intermediate point in nearly scope, specific algorithm performs flow process refer to Fig. 5.
Step 6, the optimization aim and constraints that determine Coordinative assembling track, incorporating quantum particle cluster algorithm and avoidance plan
Slightly solved, i.e. multiple objective programming module；
The object and multi object mathematical model is：
Object function：FG=ω1.ft+ω2.fj+ω3.fob(5)
Constraints：
In formula (5～9)：ftFor run time evaluation index, efficiency of assembling is weighed；fjFor joint average pulse, as rail
The smoothness evaluation index of mark；fobFor colliding evaluation index；ω1、ω2、ω3Respectively ft、fj、fobThe power of three evaluation indexes
Value coefficient.
The quanta particle swarm optimization Mathematical Modeling is：
Vacation lets N be population population, and the current location of particle i is designated as Xi=(xi1,xi2,…,xiD), D is the dimension of particle
Number.In each iteration, the desired positions of particle i search are designated as pbesti=(pbesti1,pbesti2,…,pbestiD),
The whole desired positions for planting group hunting are designated as gbesti=(gbesti1,gbesti2,…,gbestiD).Wherein：
In formula (10～11), t is the current iteration number of times of algorithm, r1d(t) and r2dT () is the random number between (0,1)；c1
And c2For the Studying factors of PSO algorithms, c is typically taken1=c2, nowThe random number being generally evenly distributed on (0,1)；In grain
The current optimal location pbest of sub- iiGlobal optimum position gbest with colonyiPress in the hypermatrix constituted for summitThan
Example randomly selects a position as the follow-on desired positions of particle i；The method is referred to as particle cluster algorithm.
In postulated particle group, particle has the behavior of quantum dynamics, is determined the position of each particle by wave function ψ, | ψ
| 2 is the probability density function of particle position.It is assumed that in the t time iteration, particle i is moved in D dimension spaces, and the particle is tieed up in d
Potential well is pbestid (t), then can obtain particle i in the wave function of (t+1) secondary iteration is：
Then the probability density function Q of particle is：
Probability-distribution function T is：
Stochastical sampling is carried out to particle position using DSMC, is obtained in (t+1) secondary iteration, i-th
The location components of son d dimensions：
In formula (15), uid (t) is generally evenly distributed in the random number on (0,1).The value of Lid (t) is determined by formula (16):
LidThe α (t) of (t)=2 | mbestd(t)-xid(t)| (16)
Wherein mbest is referred to as average optimal position, and it is the central point of itself optimal location of all particles, can be by formula (17)
It is calculated：
Then the location updating formula of particle is：
xid(t+1)=pbestid(t)±α(t)|mbestid(t)-xid(t)|ln[1/uid(t)] (18)
In formula (18), parameter alpha is referred to as compression-broadening factor, directly affects the convergence rate of particle.The value of the parameter can
To be fixed, or dynamic change, generally determined by following formula：
A in formula (19)<B, b and a are the initial value and stop value of control parameter α respectively.
The current optimal location pbest of particleiUpdate mode be：
The update mode of global optimum position gbest is：
In formula (21), f is object function.Formula (18) is as the particle cluster algorithm of particle position more new formula
There is quantum particle swarm optimization.
The incorporating quantum particle cluster algorithm and Robot dodge strategy carry out method for solving flow process and refer to Fig. 6.
Step 7, the joint space information for obtaining multiple objective programming module are sent to the driver of MS master-slave robot.
Method for planning track is assembled using above-mentioned Dual-robot coordination, speed, acceleration, an acceleration can be obtained
Continuously, installation time is shorter, load segment joint trajectories smooth, successful avoiding obstacles and without interfere Dual-robot coordination assembling
Track, reduces cost, it is to avoid the damage of assembly parts.
Description of the drawings
Fig. 1 is the rail that the Dual-robot coordination based on quanta particle swarm optimization and B-spline curves proposed by the present invention is assembled
The flow chart of mark planing method；
Fig. 2 is the coordination of the method for planning track that the Dual-robot coordination based on B-spline curves proposed by the present invention is assembled
Rigging error defines schematic diagram；
Fig. 3 is the machine of the method for planning track that the Dual-robot coordination based on B-spline curves proposed by the present invention is assembled
Avoidance rough schematic view between people and barrier；
Fig. 4 is the machine of the method for planning track that the Dual-robot coordination based on B-spline curves proposed by the present invention is assembled
Avoidance rough schematic view between people and robot；
Fig. 5 is the two-shipper of the method for planning track that the Dual-robot coordination based on B-spline curves proposed by the present invention is assembled
Device people's deep search Robot dodge strategy flow chart；
Fig. 6 is the quantum of the method for planning track that the Dual-robot coordination based on B-spline curves proposed by the present invention is assembled
The flow chart that particle cluster algorithm is executed；
Specific embodiment
In order that the object, technical solutions and advantages of the present invention are clearer, the present invention is described below in conjunction with the accompanying drawings in detail
Specific embodiment：
With reference to Fig. 1, the invention discloses a kind of trajectory planning of the robot coordinated assembling of duplexing industry based on B-spline curves
Method, its include task module, MS master-slave joint of robot trajectory planning module, Robot dodge strategy module, multiple-objection optimization mould
Block, industrial robot driver.Dress is coordinated as realizing typical double industrial robot (six degree of freedom) axis holes with task just below
It is described as a example by matching somebody with somebody task.Other satisfactory tasks can be implemented according to this programme, and specific enforcement key step is such as
Under：
Step 1, the kinematics model for setting up double industrial robots, try to achieve the positive and negative solution of MS master-slave industrial robot；
The kinematics model is referred to can set up each link rod coordinate system of MS master-slave robot respectively by D-H methods, lead to
Cross D-H parameter lists and coordinate system transformation matrices derive forward kinematics solution, Inverse Kinematics Solution is derived by PIPER methods then.
Step 2, the task point posture information for being obtained MS master-slave robot by described task module.
Dual-robot coordination fittage is generally divided into two stages：First stage is gripping workpiece；Second stage is association
Adjust assembling stage；First stage only needs to dual robot, and each cut-through thing grips assembly and moves to the assembling that specifies
Position；Second stage needs the dual robot must strictly through discrete assembly path in the case where set relative assembly constraint is kept
Point.Discrete assembly path point is obtained by teaching, and the dual robot Inverse Kinematics solution formula obtained by step 1 goes to seek task
Point attitude.
Step 3, the coordinate system for setting up the robot coordinated system of MS master-slave, obtain MS master-slave machine by the method for Coordinate Conversion
Transformation matrix of the ending coordinates system of people relative to itself base coordinate system.
The robot coordinated system of the MS master-slave include the base coordinate system of dual robot, ending coordinates system, tool coordinates system,
Fittage point coordinates system；MS master-slave robot constitutes the closing loop chain formed by two kinematic chains：One is " main robot
The kinematic chain of pedestal-main robot end assembly A- fittage points ", in addition one is " main robot pedestal-from machine
The kinematic chain of people's pedestal-from robot end-assembly B- fittage points ", according to two kinematic chains, can obtain MS master-slave
Transformation matrix of robot end's coordinate system relative to itself base coordinate system, and then asked according to the inverse kinematics of MS master-slave robot
Corresponding joint angle is solved, and assembling motion is coordinated so as to order about dual robot.
Step 4, row interpolation is clicked through to MS master-slave robot Coordinative assembling joint position using the method for B-spline curves interpolation,
Dual-robot coordination assembling joint trajectories are tried to achieve, and carries out error compensation, be i.e. joint trajectory planning module；
The corresponding joint angles of MS master-slave robot fittage path point can be obtained according to step 1～3, for reality
The flatness of existing MS master-slave joint of robot track, enters row interpolation using the method for B-spline curves interpolation.Specifically interpolation procedure is：
S1, using accumulation chord length method to node time normalize, obtain the node of k B-spline geometric locus of main robot
Vector：Wherein
S2, generalBring intoAsk
Obtain the n that k B-spline geometric locus of main robot meets interpolation condition1+ 1 equation；
S3, arrow boundary condition is cut with reference to main robot, determine the B-spline joint trajectories of main robot；
S4, with step S1, using accumulation chord length method, obtain the knot vector from k B-spline geometric locus of robot；
S3 is obtained knot vector band incoming vector by S5, same to S2
Try to achieve the n that k B-spline geometric locus of main robot meets interpolation condition2+ 1 equation；
S6, with step S3, cut arrow boundary condition in conjunction with from robot, determine the B-spline joint trajectories from robot；
S7, the constraint that MS master-slave robot kinematical constraint is converted into B-spline control point；
The maximum rigging position error of S8, traversal from the time interval of robot B-spline track, if be less than default essence
Degree, then execute the B-spline curves interpolation function from robot；If less than default precision, from robot according to kinematical constraint
Retinue's main robot motion.
Step 5, execution dual robot deep search Robot dodge strategy module；
S1, the respective starting point of setting MS master-slave robot and impact point, make num1=num2=0；
S2, avoidance intermediate point substantially is artificially determined according to the position relationship that robot in task space and barrier are present
Position, num1=num1+1；
Heuristic search is carried out in S3, the hunting zone that specifies near avoidance intermediate point, avoidance intermediate point, num2 is determined
=num2+1；
S4, carry out B-spline interpolation respectively to the starting point of MS master-slave robot, intermediate point and impact point, generate master-slave machine
The joint trajectories of device people；
S5, whether judged between whole working time inner machine people and barrier, dual robot by avoidance detection method
Collide, if it is not, then the nothing of output MS master-slave robot touches joint trajectories, fob=0 termination algorithm；If so, then execution step
S6；
S6, num2 is judged whether less than num2max, if so, then execution step S3, if it is not, then execution step S7；
S7, judge num1 whether less than num1max, if so, then execution step S2, if it is not, be not then successfully searched main-
From the collisionless joint trajectories of robot, fob=+∞, algorithm terminate；
Wherein num1max is the number of attempt for artificially determining avoidance mid-point position, and num2max is attached in avoidance intermediate point
The random maximum allowable number of times for determining avoidance intermediate point in nearly scope, concrete implementation algorithm flow refer to Fig. 5.
Step 6, the optimization aim and constraints that determine Coordinative assembling track, incorporating quantum particle cluster algorithm and avoidance plan
Slightly solved, i.e. multiple objective programming module；
The incorporating quantum particle cluster algorithm and Robot dodge strategy carry out method for solving and are related to algorithm, refer to Fig. 6, specifically
Algorithm performs step as follows：
S1, Initialize installation：Random assignment is carried out to the position of all particles in given range；
S2, judge whether to reach maximum iteration time, if so, then jump out algorithm；If it is not, then to S3；
The MS master-slave B-spline interpolation track constructed by S3, execution Dual-robot coordination assembling method for planning track, i.e. step
4；
S4, execution dual robot deep search policing algorithm, i.e. step 5；
S5, judge collision detection index fobWhether it is 0,；If so, particle cluster algorithm fitness value is then made for infinity, extremely
S9；If it is not, to S6；
S6, use formulaCalculate total run time；
S7, use formulaCalculate average pulse value；
S8, use formula FG=ω1.ft+ω2.fj+ω3.fobCalculate fitness function value；
S9, use formula xid(t+1)=pbestid(t)±α(t)|mbestid(t)-xid(t)|ln[1/uid(t)] update grain
Sub- position, to S2；
By the loop iteration of algorithm, it will obtain a speed, acceleration, acceleration continuously, the execution time is shorter,
The smooth joint trajectories of joint trajectories.
Step 7, the joint space information for obtaining multiple objective programming module are sent to the driver of MS master-slave robot.
Claims (8)
1. a kind of method for planning track that Dual-robot coordination based on B-spline curves is assembled, it is characterised in that following step
Suddenly：
Step 1, the kinematics model for setting up dual robot, try to achieve the positive and negative solution of MS master-slave robot；
Step 2, the task point posture information for being obtained MS master-slave robot by described task module；
Step 3, the coordinate system for setting up the robot coordinated system of MS master-slave, obtain MS master-slave robot by the method for Coordinate Conversion
Transformation matrix of the ending coordinates system relative to itself base coordinate system；
Step 4, row interpolation is clicked through to MS master-slave robot Coordinative assembling joint position using the method for B-spline curves interpolation, tried to achieve
Dual-robot coordination assembles joint trajectories, and carries out error compensation, i.e. joint trajectory planning module；
Step 5, execution dual robot deep search Robot dodge strategy module；
Step 6, the optimization aim and constraints that determine Coordinative assembling track, incorporating quantum particle cluster algorithm and Robot dodge strategy enter
Row is solved, i.e. multiple objective programming module；
Step 7, the joint space information for obtaining multiple objective programming module are sent to the driver of MS master-slave robot.
2. the method for planning track for being assembled according to the Dual-robot coordination based on B-spline curves described in claim 1, which is special
Levy and be：In the step 4, the method for robot coordinated assembling trajectory planning is：Using k non-uniform rational B sample of De Buer
Bar recurrence formula and r ranks lead the time dependent joint displacements of arrow transformation for mula construction MS master-slave robot B-spline joint trajectories,
Speed, acceleration and jerk curve；Further, since the pose constraint and relative motion constraint between assembly is difficult to protect
Card, can produce rigging error, therefore after based on B-spline curves interpolation need to carry out rigging error compensation.
3. the method for planning track for being assembled according to the Dual-robot coordination based on B-spline curves described in claim 1, which is special
Levy and be：In the step 5, the Robot dodge strategy between robot and barrier is as follows：On the connecting rod axis of robot every
One determining deviation arranges an interference test point, and the largest enveloping radius for interfering test point each segment connecting rod is added to barrier
Hinder on the thickness of thing, after the collision between robot and barrier is converted into by a series of interference test points and expansion
Location determination relation between barrier.
4. the method for planning track for being assembled according to the Dual-robot coordination based on B-spline curves described in claim 1, which is special
Levy and be：In the step 5, the Robot dodge strategy between robot and robot is as follows：Robot is reduced to by pitman shaft group
Into straightway, so as to by the collision between robot and robot be reduced to judge in whole working space in space two straight
The size predicting relation of the beeline of line segment and the largest enveloping radius sum of corresponding two connecting rods.
5. the method for planning track for assembling in the Dual-robot coordination based on B-spline curves according to claim 1, its
It is characterised by：In the step 6, optimize dual robot track approach using quanta particle swarm optimization as follows：In order to improve machine
The efficiency of assembling of people, the vibration of reduction joint, protect the parts such as driver and decelerator of robot, set up and meeting kinematics about
Under the conditions of beam and dual robot are collisionless, the optimum Model for Multi-Objective Optimization with optimal smoothing trajectory problem of efficiency of assembling；Adopt
Constrained object function is converted into without constrained objective function with penalty function method；Multiple target is solved using Swarm Intelligence Algorithm excellent
Change model.
6. the method for planning track for being assembled according to the Dual-robot coordination based on B-spline curves described in claim 1, which is special
Levy and be：In the step 6, dual robot deep search Robot dodge strategy following steps：
S1, the respective starting point of setting MS master-slave robot and impact point, make num1=num2=0；
S2, avoidance point midway substantially is artificially determined according to the position relationship that robot in task space and barrier are present
Put, num1=num1+1；
Heuristic search is carried out in S3, the hunting zone that specifies near avoidance intermediate point, avoidance intermediate point, num2=is determined
num2+1；
S4, carry out B-spline interpolation respectively to the starting point of MS master-slave robot, intermediate point and impact point, generate MS master-slave robot
Joint trajectories；
S5, judge whether occur between whole working time inner machine people and barrier, dual robot by avoidance detection method
Collision, if it is not, then the nothing of output MS master-slave robot touches joint trajectories, termination algorithm；If so, then execution step S6；
S6, num2 is judged whether less than num2max, if so, then execution step S3, if it is not, then execution step S7；
S7, num1 is judged whether less than num1max, if so, then execution step S2, if it is not, not then being successfully searched master-slave machine
The collisionless joint trajectories of device people, algorithm terminates；
Wherein num1max is the number of attempt for artificially determining avoidance mid-point position, and num2max is model near the avoidance intermediate point
Enclose the interior random maximum allowable number of times for determining avoidance intermediate point.
7. the method for planning track for being assembled according to the Dual-robot coordination based on B-spline curves described in claim 2, which is special
Levy and be：The rigging error is defined as follows：The cooperation coordinate system between assembly is initially set up before the error of definition assembling,
As Z axis, assembly A sets up assembly A's in starting point O1 of axis direction assembly path section for origin to axis with assembly A
Coordinate system；With the mating surface axis without assembly B during rigging error as Z axis, assembly B rising in axis direction assembly path section
Initial point O2 sets up the coordinate system of assembly B for origin；Axis hole simplified model is set up, Fig. 2 is referred to；
In the case of error free assembling, the Z axis of assembly B coordinate systems are overlapped with the Z axis of assembly A coordinate systems all the time, assembly A and
Relative motion between assembly B is constrained to：Assembly A moves along a straight line along the Z axis of assembly B coordinate systems；
Require a series of fittage point sequence that relative world coordinate systems are given in cartesian space according to fittage；Start
When entering Coordinative assembling, O1 is overlapped with O2；After the completion of assembling, O1 is overlapped with Pn, and O2 is overlapped with P1；The origin O1 of Fig. 2 assembly A exists
Intersection point on the Z axis of assembly B；F is intersection points of the origin O2 of assembly B on the Z axis of WP1；In order in Dual-robot coordination
Rigging error is eliminated in assembling strategy, assembly yield is improved, rigging position error and assembling attitude error is defined；
In assembly path section, two vertical lines are chosen（O1, E）Extremely（O2, F）The maximum of distance is defined as rigging position error
PositionError；Difference of the Eulerian angles of posture changing between current assembly A and assembly B with preferable Eulerian angles is taken
Absolute value summation is defined as assembly definition assembling attitude error AttitudeError；
In the case of ideal fit, the Z axis of assembly B coordinate systems are overlapped with the Z axis of assembly A coordinate systems all the time, so assembling position
Error PositionError is put for 0；Currently between assembly A and assembly B, assembling attitude error AttitudeError is also
0.
8. the method for planning track for being assembled according to the Dual-robot coordination based on B-spline curves described in claim 2, which is special
Levy and be：The rigging error compensation method is：In Coordinative assembling route segment, main robot is all the time according to B-spline interpolation joint
Move track；Traversal is from robot maximum rigging error, if being less than default precision, from robot according to the B-spline from robot
Interpolation joint trajectories are moved；If more than default precision, from robot according to kinematical constraint retinue's main robot motion, carrying out
Error compensation, in order to avoid damaging assembly, and updates from robot rigging error maximum.
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