CN106826829B - A kind of industrial robot fairing motion profile generation method of Controllable Error - Google Patents
A kind of industrial robot fairing motion profile generation method of Controllable Error Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
Abstract
A kind of industrial robot fairing motion profile generation method of Controllable Error, include the following steps: S1, generate MOVEB movement instruction, industrial robot motion track, including tracing point and posture and the tracing point error threshold and action error threshold of user's input are described；High-order B-spline curves are carried out interpolation to tracing point according to the high error threshold of track point tolerance chord, realize the G of robot trajectory's point respectively by the interpolation of S2, robot trajectory's point using high-order B-spline interpolation algorithm2Interpolation and G3Interpolation obtains having high continuity and guarantees the interpolation track for meeting the high error requirements of track point tolerance chord；The interpolation of S3, robot pose obtain segmentation G2And G3Continuous robot pose curve；S4, the motion profile after robot interpolation is obtained jointly by tracing point interpolation curve and robot pose curve.The real-time continuous interpolation of motion profile of the present invention calculates simple, efficient, accurate, reduction machine vibration and abrasion.
Description
Technical field
The invention belongs to industrial robot applied technical fields, and in particular to a kind of industrial robot fairing of Controllable Error
Motion profile generation method.
Background technique
Industrial robot is widely used in the complex jobs such as welding, assembly, carrying, polishing, spraying and machining.Making
Industrial robot controls the motion profile of robot by movement instruction in industry.The existing identifiable movement of industrial robot refers to
Enabling mainly includes linear motion instruction, circular motion instruction and axial coordinate movement instruction, as in ABB robot respectively with MOVEL,
MOVEC and MOVEJ indicates three of the above instruction.Simple motion track can write axial coordinate movement instruction by teaching machine, mainly
It is accurate to a little applied to only requiring, track is any between points but time shortest operation (such as spot welding robot).It is most of
Complicated motion profile needs to obtain by discrete programming software, and main includes linear motion instruction and circular motion instruction.
But the motion profile of straightway and arc representation only has G in junction0Continuity, during robot manipulating task, for essence
The necessary reduction of speed of given trace point is really reached, therefore greatly reduces operating efficiency；In addition, velocity and acceleration may discontinuously be led
Vibration when robot motion is caused, to accelerate wear and tear in machines and influence operation quality.
In order to improve the continuity of robot motion track, it joined in existing movement instruction and approach instruction.Such as Fig. 1 institute
Show, indicates that, accurately by given trace point, z10 indicates the rounding off of error 10mm using fine instruction in ABB robot, but
It is that this approaches instruction and not can guarantee the track high error of point tolerance chord and meets the requirements；An Chuan robot indicates parabola with MOVES
Instruction, although parabolic line can accurately pass through given trace point, not can guarantee action error meet demand.
From the foregoing, it will be observed that can not be generated just with existing straight line and circular motion instruction while meet track point tolerance chord
High error and there is high continuous motion profile.Then occur in existing research some in off-line programing stage interpolated movements rail
Mark and method in interpolated movements track inside the control system.It is that raising is successional preferably square with smooth curve interpolation tracing point
Method, but trajectory interpolation need to meet the high error requirements of track point tolerance chord.Control errors have important practical significance, such as
Require pad in the spraying profile requirement within the scope of the point tolerance of track, in spraying process between two o'clock in action in welding process
In error range.Two error thresholds are arranged by user according to processing technology, any one error is unsatisfactory for all causing product
It is off quality.
Existing interpolation method largely only considered tracing point control errors, not consider action control errors: such as existing non-
Patent document " the industrial robot trajectory planning research based on Based on Interpolating Spline " passes through B sample three times during off-line programing
Curve interpolation tracing point, it is then that interpolation curve is discrete and post-process as straight line or circular motion instruction.Although this method is logical
Cross the continuity that interpolation improves track, but it is discrete after can also have error and be unsatisfactory for the deficiency low with continuity.Non- patent text
Offer " Real-time Coplanar NURBS Curve Fitting and Interpolation for 6-DOF Robot
Arm " in realize a kind of real-time NURBS interpolation of robot control system and discrete algorithm, but this method does not guarantee that action misses
Difference, and it is poor by the method stability that matrix inversion calculates control vertex, it cannot be guaranteed that action error is met the requirements.
The fairing interpolation of robot motion track includes track point interpolation and posture interpolation, the fairing interpolation sum number of tracing point
The fairing interpolation for controlling small line segment in Milling Process is similar: non-patent literature " A real-time look-ahead
interpolation methodology with curvature-continuous B-spline transition
Scheme for CNC machining of short line segments " propose three axis cutters in a kind of numerical control processing
The G of track2Continuous bridging algorithm solves the above problems, and can be obtained that tracing point smoothly transits and the real-time of continual curvature conformal is inserted
It is worth track.But the bridge joint track that this method obtains cannot achieve high-precision interpolation, and point tolerance smaller BridgeCurve in track is shorter,
Too short bridge joint track cannot achieve the smooth of speed.Non-patent literature " A real-time curvature-smooth
interpolation scheme and motion planning for CNC machining of short line
Segments " above method is improved, propose the G of cutter path3Continuous interpolation algorithm can obtain meeting tracing point mistake
The real-time conforming interpolation track of difference and action error and curvature fairing, can effectively improve processing efficiency and processing quality, and
Reduce machine vibration.This method achieves preferable application in three-axis numerical control processing, but is not suitable for five-axis robot and industry
In robot application.
The posture of motion profile discontinuously also will affect the precision and efficiency of processing, and existing posture interpolation method has quaternary number
Method, the method based on matrix exponent method and direct interpolation Eulerian angles.Existing non-patent literature " Interpolation method
For robot trajectory planning " in the interpolation of robot pose is directly realized to Eulerian angles interpolation, but directly
Do not have coordinate invariance to Eulerian angles interpolation, Eulerian angles cannot continuously correspond to the continuous of tracing point posture.
High continuity and high-precision requirement cannot be met simultaneously in view of robot motion track in the prior art, need one
The generation method of kind industrial robot fairing motion profile.
Summary of the invention
The technical problem to be solved by the present invention is to for robot in the prior art, there are poor continuities and error to be unsatisfactory for
The problem of leading to low working efficiency, off quality and machine vibration, provides a kind of industrial robot fairing fortune of Controllable Error
Dynamic orbit generation method, calculate it is simple, efficiently, it is accurate, robot motion track can meet high continuity and high-precision simultaneously
It is required that industrial robot error (the high error of track point tolerance chord) meets the conformal motion profile that real-time implementation requires fairing.
The technical solution taken by the invention to solve the above technical problem is:
A kind of industrial robot fairing motion profile generation method of Controllable Error, includes the following steps:
S1, generate MOVEB movement instruction: MOVEB movement instruction is used to describe industrial robot motion track, including track
Point and posture and the tracing point error threshold and action error threshold of user's input；
The interpolation of S2, robot trajectory's point: the industrial robot motion track that MOVEB movement instruction is indicated imports machine
People's control system, using high-order B-spline interpolation algorithm, by high-order B-spline curves according to the high error threshold of track point tolerance chord
Interpolation is carried out to tracing point, realizes the G of robot trajectory's point respectively2Interpolation (has G2Continuous cubic Bézier curves) and G3It inserts
Value (has G3Continuous four B-spline interpolation), it obtains that there is high continuity and guarantees to meet track point tolerance chord high mistake
The interpolation track that difference requires；
The interpolation of S3, robot pose: the segmentation G of robot pose is realized respectively by B-spline interpolation algorithm2And G3It inserts
Value, and unit orthogonalization process is carried out to the posture of the robot trajectory after interpolation, obtain segmentation G2And G3Continuous robot appearance
State curve；
S4, the motion profile after robot interpolation is generated: the tracing point interpolation curve and step that S2 is obtained through the above steps
The robot pose curve that rapid S3 is obtained obtains the motion profile after robot interpolation jointly.
According to the above scheme, the data content of MOVEB movement instruction includes X, Y, Z, I, J, K, U, V, W in the step S1,
D, E totally ten one variables, wherein the coordinate of the tracing point under (X, Y, Z) representational tool coordinate system, (I, J, K) indicates above-mentioned track
The Z axis unit vector for the tool coordinates system established at point, the X-axis unit vector of (U, V, W) representational tool coordinate system, D, E difference
Indicate action error threshold and tracing point error threshold.
It according to the above scheme,, will when robot control system parses MOVEB movement instruction in the step S2 and step S3
Tracing point error threshold and the identical one section of continuous path of action error threshold form one group of carry out interpolation.
According to the above scheme, in the step S2, the interpolation of robot trajectory's point specifically comprises the following steps:
Step 1: primary iteration parameter determines, one group of robot initial trace point is obtained from MOVEB movement instructionAction error threshold D and tracing point error threshold E；The number of iterations is denoted as k=0, calculates initial change
For tracing pointWith primary iteration action error threshold
Step 2: it specifically includes:
1. establishing each inner track point (not including the iteration tracing point of head and the tail endpoint)Place
B-spline curves are bridged, in entire step 2, omit the number of iterations k, i.e.,It is equal to Pi,It is equal to diIt (conveniently retouches
State):
The number for bridging B-spline curves is p, shares 2p+1 control point, respectively A1,i, A2,i…Ap,i,Qi,Bp,i,…
B2,i,B1,i, knot vector is { 0,0.5,1 }, and the multiplicity of three nodes is respectively p+1, p, p+1；The bridge joint B-spline curves etc.
Valence is in two symmetrical p Bezier curves；
2. establishing in QiSymmetrical two p Bezier curves, the control point of two Bezier curves is respectively A1,i,
A2,i…Ap,i,QiAnd Qi,Bp,i,…B2,i,B1,i, wherein A1,i, A2,i…Ap,iWith Pi-1PiCollinearly, Bp,i,…B2,i,B1,iWith PiPi+1
Collinearly, QiFor Ap,iBp,iMidpoint；
3. dividing G2And G3Two kinds of situations of interpolation provide guarantee bridge joint B-spline curves G everywhere2Or G3Continuous control point:
Ifhi=| Ap,iPi|,θi=< T0,i,T1,i>
Wherein T0,iFor Pi-1PiUnit vector；T1,iFor Ap,iBp,iUnit vector；hiFor line segment Ap,iPiLength；θi
For vector T0,iAnd T1,iAngle；
I) in G2When interpolation, G2The control vertex of BridgeCurve meets the following conditions:
Qi=Pi-hiT0,i+hicosθiT1,i
A3,i=Qi-hicosθiT1,i
A2,i=A3,i-hiT0,i
A1,i=A2,i-βihiT0,i
Ii) in G3When interpolation, G3The control vertex of BridgeCurve meets the following conditions:
Qi=Pi-hiT0,i+hicosθiT1,i
A4,i=Qi-hicosθiT1,i
A3,i=A4,i-αihiT0,i
A1,i=A2,i-βihiT0,i
αi≥0.7,0<βi≤0.5
In G2When interpolation, hi,βiFor two BridgeCurve parameters；In G3When interpolation, hi,αi,βiJoin for three BridgeCurves
Number.BridgeCurve parameter determines the position at BridgeCurve control point, following steps 5. in by objective function optimization ask
Solution obtains, B1,i,B2,i,…,Bp,iIt is obtained by the symmetry of bridge joint B-spline curves；
4. more gently establishing optimization object function with BridgeCurve for target, and provide conformal and action control errors pacts
Beam condition:
The G of two Bezier curves construction2BridgeCurve and G3BridgeCurve is in intersection point QiThe maximum curvature at place, and it is maximum
Curvature is respectivelyWithTo obtain gentler BridgeCurve, it is desirable that
kg2maxAnd kg3maxIt is smaller, that is, require step is 3. middle to bridge parameter of curve hiIt is bigger, therefore objective function is defined as to solve bridge joint
Parameter of curve hi, i=1,2 ... N-1's and greatest problem, i.e., as shown in following formula (1):
To realize conformal constraint, it is desirable that intersection is not present in the BridgeCurve between two tracing points, wherein G2Continuously
And G3Continuously bridge conformal constraint are as follows:
|Pi-1B1,i-1|+|A1,iPi|≤|Pi-1Pi|, i=2 ... N-1 (2)
|A1,1P1|≤|P0P1| (3)
|PN-1B1,N-1|≤|PN-1PN| (4)
To realize action error constraints, P need to be only controllediQiDistance be not more than iteration action error threshold di, it may be assumed that
|PiQi|≤di (5)
5. solve optimization problem, that is, formula (1) simultaneously require BridgeCurve parameter meet constraint equation (2), (3), (4),
(5), BridgeCurve parameter is solved to get the bridge joint track of iteration tracing point is arrived；
Step 3: the tracing point max value of error Δ of bridge joint track and initial trace point is calculatedk, and judge ΔkWhether it is less than
Tracing point error threshold E, the calculation method of track point tolerance are to calculate tracing point and two Bezier curve intersection pointsAway from
From.In this step 3 plus k subscript parameter with not plus k subscript parameter be equal, the error for the secondary iteration of description kth is not examined in step 2
It surveys, does not omit k:
WhereinIt is located atAngular bisector on, according to the symmetry of interpolation curve, pass through calculatingSize and angular bisector vector obtain, calculation method are as follows:
If Δk> E illustrates that BridgeCurve does not meet tracing point error requirements, enters step four update iteration tracing points and changes
For action error threshold；Otherwise, iteration is exited in interpolation success, exports interpolation track；
Step 4: iterative parameter is updated, the adjustment vector of iteration tracing point is enabled are as follows:Iteration tracing point adjusted are as follows:Iteration action error threshold are as follows:Update the number of iterations: k=k+1 goes to step two.
According to the above scheme, in the step S3, the interpolation of robot pose specifically comprises the following steps:
Step 1: offset point, note are calculatedThe X-axis unit vector of the tool coordinates system at place isZ axis unit vector isIt willOne section of fixed range m is deviated along X-axis, obtains X-axis offset
Point is denoted asIt willOne section of fixed range n is deviated along Z axis, Z axis offset point is obtained and is denoted as
Step 2: deviating point interpolation to X-axis offset point and Z axis, is deviated respectively to X-axis using the method for track point interpolation
Point, Z axis offset pointInterpolation is carried out, piecewise interpolation curve O (t), R (t) are obtained；
Step 3: the posture of the track after calculating interpolation, the piecewise interpolation curve of note robot trajectory's point are P (t), interpolation
X-axis vector afterwards: X (t)=O (t)-P (t), Z axis vector: Z (t)=R (t)-P (t), it is orthogonal to X-axis vector, Z axis vector units
Change processing further calculates to obtain the orthogonal X-axis unit vector of unit after interpolation, Z axis unit vector:
X-axis unit vector X after interpolationnew(t) are as follows:
Z axis unit vector Z after interpolationnew(t) are as follows:
Znew(t)=F (t) × Xnew(t)×F(t)
Wherein
According to X derived abovenew(t), Znew(t) the posture curve after interpolation is described, each trajectory interpolation curve is obtained
The corresponding posture information of upper tracing point.
According to the above scheme, in the step of step S3 one, the value of offset distance m, n are set as tracing point average headway
5~10 times.
According to the above scheme, in the step of step S3 three, the posture sectional curve after unit orthogonalization has segmentation
G2Or G3Continuity, i.e., the curve G between waypoint2Or G3Continuously, at least there is G at waypoint0Continuity.
Contemplated above technical scheme through the invention, compared with prior art, the present invention has the advantage that:
1, the continuous motion profile generation method of industrial robot proposed by the present invention can guarantee that data point tolerance chord is high
Error meets user's requirement: user can instruct specified data point tolerance chord height to miss according to processing technology demand by MOVEB
Poor threshold value, interpolation algorithm of the invention can guarantee the high error threshold of data point tolerance chord for meeting user setting, and protect
The gentle and conformal of interpolation curve is demonstrate,proved, so as to guarantee the high precision of actual job；Can be used for industrial robot welding,
The real-time continuous interpolation of motion profile in the complex jobs such as spraying, laser cutting；
2, the continuous motion profile generation method of industrial robot proposed by the present invention can guarantee the high continuity (G of tracing point2
Continuous and G3Continuously), G2Continuous track has a continuous velocity and acceleration, and G3Continuous track not only has continuously
Velocity and acceleration also has continuous acceleration, and in robot actual job, high successional track can be effective
Operating efficiency and operation quality precision are improved, acceleration can continuously reduce machine vibration, to reduce wear and tear in machines；
3, the continuous motion profile generation method of industrial robot proposed by the present invention can guarantee that the segmentation of posture is high continuous
Property (G2Continuous and G3Continuously), segmentation posture interpolation curve can guarantee posture (G between every two waypoint2Or G3) consecutive variations,
The homework precision of robot not only can be improved in the consecutive variations of robot pose, additionally it is possible to reduce robot arm and significantly put
It is dynamic, to effectively improve efficiency.
Detailed description of the invention
Fig. 1 is the instruction of ABB robot motion in the prior art；
The MOVEB movement instruction case that Fig. 2 designs for the embodiment of the present invention；
Fig. 3 is the high continuity interpolation flow chart of tracing point of the present invention；
Fig. 4 is G of the embodiment of the present invention2Bridge schematic diagram；
Fig. 5 is G of the embodiment of the present invention3Bridge schematic diagram；
Fig. 6 is tracing point of embodiment of the present invention G2(G3) interpolation conformal constraint；
Fig. 7 is tracing point of embodiment of the present invention G2(G3) interpolation iteration schematic diagram；
Fig. 8 is that Z axis of the embodiment of the present invention deviates point interpolation schematic diagram.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with attached drawing and case study on implementation,
The present invention will be described in further detail.It should be appreciated that specific implementation case described herein is only used to explain this hair
It is bright, it is not intended to limit the present invention.
The industrial robot fairing motion profile generation method of Controllable Error of the present invention, is subdivided into following four contents:
<1>generation of MOVEB movement instruction
A kind of new MOVEB movement instruction is invented, first for describing the industrial robot that off-line programming technique obtains
Motion profile, and include tracing point error threshold and action error threshold information, track can be arranged in user according to the technological requirements
Point tolerance and action error.The subsequent data content of MOVEB movement instruction includes X, Y, Z, I, J, K, U, V, W, and D, E totally ten one
Variable, wherein preceding nine data are used to describe the linear motion trajectory (tracing point and posture) of industrial robot, latter two variable
Respectively action error threshold and tracing point error threshold.As shown in Fig. 2, describe five tracing points and posture, wherein user
Specified action error threshold D=0.001mm, tracing point error threshold E=0.0001mm.
User can be by D, and E is arranged error threshold required for robot motion's trajectory interpolation, and each tracing point can be with
Identical error (the high error of track point tolerance chord) threshold value is set, different threshold values also can be set.Error threshold is by user's root
It is determined according to technique, such as action error threshold may be configured as processing franchise in robot machining, such as in numerical control processing,
The processing request of components generally in ± 0.05mm~± 0.1mm, tracing point action error can be set to 0.005mm~
0.03mm；Tracing point error threshold may be configured as numerical stability, generally 10-4~10-8mm。
MOVEB movement instruction is used to describe original motion trajectory and interpolation error, and robot control system can recognize MOVEB
Movement instruction simultaneously carries out high-order B-spline interpolation to original motion trajectory according to error threshold.The embodiment of the present invention supports there is G2
Continuous cubic Bézier curves and there is G3Continuous four B-spline interpolation respectively obtain expiring for continual curvature and curvature fairing
The fairing interpolation curve of sufficient error requirements.
<2>interpolation of robot trajectory's point
MOVEB movement instruction is imported in robot control system, obtains industrial robot motion track and error threshold
Information is parsed since different error thresholds continuous tracing point can be arranged in user in robot control system
When MOVEB movement instruction, the identical one section of continuous path of tracing point error threshold and action error threshold is formed into one group of progress
Interpolation.
As shown in figure 3, the interpolation of tracing point refers to that the motion profile point to the description of MOVEB movement instruction is missed according to tracing point
Difference and action error threshold carry out interpolation, which can realize with G2Continuous cubic Bézier curves and there is G3Continuously
Four B-spline interpolation.The main technical schemes of the interpolation of tracing point are the movement rail for importing one group of MOVEB movement instruction and indicating
Mark and error threshold (action error threshold and tracing point error threshold) then calculate the bridge joint track of iteration tracing point, then
Judge whether the error bridged between track and initial trace point meets tracing point error threshold, if meeting threshold value, interpolation terminates,
Track after export bridge joint；Otherwise it according to tracing point error update iteration tracing point and iteration action error threshold, bridges again.
In step S2, B-spline curves are bridged by construction, and constantly iteration update BridgeCurve makes track point tolerance chord
High error meets, and remembers that final bridge joint B-spline curves are interpolation curve: setting iteration tracing point and iteration action error threshold first
Value, is then bridged at each tracing point with a B-spline curves, and the track of BridgeCurve and initial trace is secondly calculated
Whether point tolerance meets user's requirement, if meeting the requirements, interpolation terminates, and exports interpolation curve；If being unsatisfactory for requiring, according to track
Point tolerance updates iteration tracing point and iteration action error, bridges again, and continuous iteration, until track, point tolerance is met the requirements,
Interpolation terminates；The interpolation of robot trajectory's point specifically comprises the following steps:
Step 1: primary iteration parameter determines, one group of robot initial trace point is obtained from MOVEB movement instructionAction error threshold D and tracing point error threshold E；The number of iterations is denoted as k=0, calculates initial change
For tracing pointWith primary iteration action error threshold
Step 2: firstly, establishing each inner track point (not including head and the tail endpoint) Pi, i=1 ... p bridge at N-1
B-spline curves are connect, in entire step 2, for convenience of describing, omit the number of iterations k, i.e.,It is equal to Pi,It is equal to
di:
The bridge joint B-spline curves share 2p+1 control point, respectively A1,i, A2,i…Ap,i,Qi,Bp,i,…B2,i,B1,i,
Knot vector is { 0,0.5,1 }, and the multiplicity of three nodes is respectively p+1, p, p+1；
Then, it is convenience of calculation, makes to bridge B-spline curves G everywhere2Or G3Continuously, it establishes in QiSymmetrical B-spline curves,
It converts the bridge joint B-spline curves to and is made of two symmetrical p Bezier curves, the control point point of two Bezier curves
It Wei not A1,i,A2,i…Ap,i,QiAnd Qi,Bp,i,…B2,i,B1,i, wherein preceding p control point is conllinear, rear p control point is conllinear, QiFor
Ap,iBp,iMidpoint, control point collinearly ensure that bridge joint B-spline curves head and the tail stitching portion G2(G3) continuity, but still need to structure
Make QiG at point2(G3) continuity.
As shown in Fig. 4~Fig. 5, dot is tracing point, and the point that five-pointed star indicates is the control point of BridgeCurve, in Fig. 4,
Cubic B-spline BridgeCurve is made of seven control points, is equivalent to two symmetrical three bezier curves.In Fig. 5, three times
B-spline BridgeCurve is made of nine control points, is equivalent to two symmetrical four Bezier curves.
Then, objective function and constraint condition: the G of two Bezier curves composition are established2And G3BridgeCurve is in intersection point Qi
Locate maximum curvature, and maximum curvature is respectivelyWithDerive most yeast
Rate and hiIt is inversely proportional, to obtain gentler BridgeCurve, it is desirable that kg2maxAnd kg3maxIt is smaller, therefore objective function is established as making
All hiAnd maximum, to obtain gentler BridgeCurve.In G2In interpolation, β can usei=0.5；In G3In interpolation, it is known that
αiIt is directly proportional to curvature extremum value, αiValue range be αi>=0.7, therefore in actually calculating, it can use αi=0.7, it is known that 0 < βi
≤ 0.5, therefore desirable βi=0.5.
Objective function is defined as solving bridge joint parameter h by the present inventioni, i=1,2 ... N-1's and greatest problem, i.e., as public
Shown in formula (1).To realize conformal constraint, as shown in Figure 6, it is desirable that coincidence part is not present in the BridgeCurve between two tracing points
Point, keep BridgeCurve conformal by establishing following three inequality (2), (3), (4)；To realize action error constraints, only need to control
P processediQiDistance meet be not more than iteration action error threshold di, establish inequality (5)；Above four formulas can turn
It turns to hiThe inequality of constraint.
BridgeCurve parameter is set to meet constraint equation (2), (3), (4), (5) constraint finally, solving optimization problem (1)
Condition solves BridgeCurve parameter to get the bridge joint track of iteration tracing point is arrived.The optimization problem is linear programming problem,
Linear search method can be used in solution procedure.h1Initial value determined by action error constraints (5) and conformal constraint (3)；hN's
Initial value is determined by action error constraints (5) and conformal constraint (4)；The N-1 for i=2 ..., first according to action error in formula (5)
Threshold value constraint takes initial valueThen judge whether initial value meets the conformal condition of formula (2), if satisfied, bridging successfully；
If not satisfied, reducing hiUntil formula (2) meet；
Step 3: the track point tolerance of bridge joint track and initial trace point is calculated, judges whether to meet tracing point error threshold
Value demand, the calculation method of track point tolerance are to calculate tracing point and two Bezier curve intersection pointsDistance:
ΔkIt is the maximum value of all track point tolerances, it is known that the BridgeCurve that the present invention constructs is symmetrical by two
Bezier curve obtains, as shown in figure 4,It is located atAngular bisector on, therefore calculating can be passed throughSize and angular bisector vector obtain.
If Δk> tracing point error threshold E illustrates that BridgeCurve does not meet tracing point error requirements, enters step four updates
Iteration tracing point and iteration action error threshold；Otherwise, interpolation success exports interpolation track；
Step 4: updating iterative parameter, and Fig. 7 demonstrates the renewal process of iteration tracing point, enables Iteration tracing point adjusted are as follows:Iteration action error threshold are as follows:Update the number of iterations: k=k+1 goes to step two.
It is high to meet data point tolerance chord by robot trajectory's point interpolation curve (interpolation track) obtained by the above method
Error, conformal and curve are gentle, have high continuity, and due to iterative solution simple and stable convergence, can use in real time
Into the Interpolation Process of robot control system.Guarantee G everywhere using B-spline Curve interpolation2Continuously, i.e. speed and acceleration
Degree is continuous；Guarantee G everywhere using four B-spline curves interpolation3Continuously, i.e., speed, acceleration is continuous and acceleration is continuous.
<3>interpolation of robot pose
The interpolation of robot motion track of the present invention not only includes the interpolation of tracing point, further includes the interpolation of posture.This hair
Bright to use the method similar with track point interpolation to posture interpolation, the interpolation of posture refers to the tool coordinates to each tracing point
The interpolation of system obtains segmentation G2(G3) continuous posture interpolation curve.Known means coordinate system can be determined that Y-axis can by Z axis and X-axis
According to Z axis and the calculating of X-axis multiplication cross.
The present invention by the interpolation of posture be converted into each tracing point tool coordinates system Z axis and X-axis interpolation, i.e. interpolation
The interpolation of offset point on Z axis and X-axis apart from tracing point fixed range.It is calculated separately in Z axis and X-axis first apart from track solid point
Then two groups of offset points of measured length are most passed through by the interpolation method similar with tracing point respectively to two groups of offset point interpolations afterwards
It crosses unitization and orthogonalization process and obtains segmentation G2(G3) continuous interpolation posture curve.Coordinate system after interpolation in order to obtain needs
The vector to form to tracing point and offset point is unitization.The Z axis after interpolation and X-axis are not necessarily orthogonal simultaneously, therefore after interpolation
It needs to do orthogonalization process.
The interpolation of robot pose specifically comprises the following steps:
Step 1: calculating offset point, and tracing point is deviated fixed range m along X-axis and Z axis respectively, and n obtains series of points,
It is denoted as X-axis offset point and Z axis offset point respectively, as shown in figure 8, black dotFor six tracing points； For six Z axis offset points, X-axis offset point can be similarly calculated；Offset distance m in the step, the value of n are not answered too small
Or it is excessive, it may be configured as 5~10 times of tracing point average headway；
Step 2: point interpolation is deviated to X-axis offset point and Z axis, using the method for track point interpolation respectively to X-axis offset point
Interpolation is carried out with Z axis offset point, obtains piecewise interpolation curve O (t), R (t), as shown in figure 8, the sectional curve after interpolation is R
(t)={ Ri(t) }, 13 i=1 ..., wherein black five-pointed star indicates waypoint, each Ri(t), i=1 ... 13 meets G2(G3)
Continuously；
Step 3: the posture of the track after calculating interpolation.In order to calculate every on interpolation track posture, need to calculate one
The X after interpolation can be obtained in the orthogonal X of group unit, Z axis vector, above-mentioned steps, Z axis vector: X (t)=O (t)-P (t), Z (t)=R
(t)-P (t), but the coordinate system that the posture of track need to be orthogonal for unit, therefore to X, Z axis vector units orthogonalization process, it obtains
The posture curve of interpolation track.Due to the presence of action error, posture curve after the unit orthogonalization appearance inside waypoint
State G2(G3) continuously, the not necessarily G at waypoint2(G3) continuous.But at least there is G0Continuously.
<4>motion profile after robot interpolation is generated
The robot pose curve that the tracing point interpolation curve and step<3>that<2>obtain through the above steps obtain is common
Motion profile after obtaining robot interpolation, motion profile fairing after interpolation, meet the high error requirements of data point tolerance chord,
It is conformal and being capable of real-time interpolation.Not only the fairing interpolation of tracing point had been realized, but also has realized the segmentation fairing interpolation of posture, so that work
Operation of the robot people along fairing interpolation stability-of-path high-quality and high-efficiency.
The present invention is not limited to the applications listed in the specification and the embodiments, and is come for those skilled in the art
It says, various corresponding changes and modification can be made according to the present invention, and all these corresponding changes and modification belong to this hair
Bright scope of protection of the claims.
Claims (7)
1. a kind of industrial robot fairing motion profile generation method of Controllable Error, which comprises the steps of:
S1, generate MOVEB movement instruction: MOVEB movement instruction is used to describe industrial robot motion track, including tracing point and
Posture and the tracing point error threshold and action error threshold of user's input；
The interpolation of S2, robot trajectory's point: the industrial robot motion track that MOVEB movement instruction is indicated imports robot control
System processed, using high-order B-spline interpolation algorithm, by high-order B-spline curves according to the track high error threshold of point tolerance chord to rail
Mark clicks through row interpolation, realizes the G of robot trajectory's point respectively2Interpolation and G3Interpolation obtains having high continuity and guarantees to meet
The interpolation track of the high error requirements of track point tolerance chord；
The interpolation of S3, robot pose: the segmentation G of robot pose is realized respectively by B-spline interpolation algorithm2And G3Interpolation, and
Unit orthogonalization process is carried out to the posture of the robot trajectory after interpolation, obtains segmentation G2And G3Continuous robot pose is bent
Line；
S4, the motion profile after robot interpolation: the tracing point interpolation curve and step S3 that S2 is obtained through the above steps is generated
The robot pose curve of acquisition obtains the motion profile after robot interpolation jointly.
2. the industrial robot fairing motion profile generation method of Controllable Error according to claim 1, which is characterized in that
The data content of MOVEB movement instruction includes X, Y, Z in the step S1, I, J, K, U, V, W, D, E totally ten one variables, wherein
The coordinate of tracing point under (X, Y, Z) representational tool coordinate system, (I, J, K) indicate the tool coordinates system established at above-mentioned tracing point
Z axis unit vector, the X-axis unit vector of (U, V, W) representational tool coordinate system, D, E respectively indicate action error threshold and rail
Mark point tolerance threshold value.
3. the industrial robot fairing motion profile generation method of Controllable Error according to claim 1, which is characterized in that
In the step S2 and step S3, when robot control system parses MOVEB movement instruction, by tracing point error threshold and action
The identical one section of continuous path of error threshold forms one group of carry out interpolation.
4. the industrial robot fairing motion profile generation method of Controllable Error according to claim 2, which is characterized in that
In the step S2, the interpolation of robot trajectory's point specifically comprises the following steps:
Step 1: primary iteration parameter determines, one group of robot initial trace point is obtained from MOVEB movement instructionN >=2, action error threshold D and tracing point error threshold E；The number of iterations is denoted as k=0, calculates primary iteration rail
Mark pointWith primary iteration action error threshold
Step 2: it specifically includes:
1. establishing each inner track pointThe bridge joint B-spline curves at place omit in entire step 2
The number of iterations k, i.e.,It is equal to Pi,It is equal to di:
The number for bridging B-spline curves is p, shares 2p+1 control point, respectively A1,i, A2,i…Ap,i,Qi,Bp,i,…B2,i,
B1,i, knot vector is { 0,0.5,1 }, and the multiplicity of three nodes is respectively p+1, p, p+1；The bridge joint B-spline curves are equivalent to
Two symmetrical p Bezier curves；
2. establishing in QiSymmetrical two p Bezier curves, the control point of two Bezier curves is respectively A1,i,A2,i…
Ap,i,QiAnd Qi,Bp,i,…B2,i,B1,i, wherein A1,i, A2,i…Ap,iWith Pi-1PiCollinearly, Bp,i,…B2,i,B1,iWith PiPi+1Collinearly,
QiFor Ap,iBp,iMidpoint；
3. dividing G2And G3Two kinds of situations of interpolation provide guarantee bridge joint B-spline curves G everywhere2Or G3Continuous control point:
If
Wherein T0,iFor Pi-1PiUnit vector；T1,iFor Ap,iBp,iUnit vector；hiFor line segment Ap,iPiLength；θiFor vector
T0,iAnd T1,iAngle；
I) in G2When interpolation, G2The control vertex of BridgeCurve meets the following conditions:
Qi=Pi-hiT0,i+hicosθiT1,i
A3,i=Qi-hicosθiT1,i
A2,i=A3,i-hiT0,i
A1,i=A2,i-βihiT0,i
Ii) in G3When interpolation, G3The control vertex of BridgeCurve meets the following conditions:
Qi=Pi-hiT0,i+hicosθiT1,i
A4,i=Qi-hicosθiT1,i
A3,i=A4,i-αihiT0,i
A1,i=A2,i-βihiT0,i
αi≥0.7,0<βi≤0.5
In G2When interpolation, hi,βiFor two BridgeCurve parameters；In G3When interpolation, hi,αi,βiFor three BridgeCurve parameters, bridge
Connect the position that parameter of curve determines BridgeCurve control point, following steps 5. in obtained by objective function optimization
It arrives, B1,i,B2,i,…,Bp,iIt is obtained by the symmetry of bridge joint B-spline curves；
4. more gently establishing optimization object function with BridgeCurve for target, and provide conformal and action control errors constraint items
Part:
The G of two Bezier curves construction2BridgeCurve and G3BridgeCurve is in intersection point QiThe maximum curvature at place, and maximum curvature
RespectivelyWithTo obtain gentler BridgeCurve, it is desirable that kg2max
And kg3maxIt is smaller, that is, require step is 3. middle to bridge parameter of curve hiIt is bigger, therefore objective function is defined as to solve BridgeCurve
Parameter hi, i=1,2 ... N-1's and greatest problem, i.e., as shown in following formula (1):
To realize conformal constraint, it is desirable that intersection is not present in the BridgeCurve between two tracing points, wherein G2Continuous and G3Even
The conformal constraint of continuous bridge joint are as follows:
|Pi-1B1,i-1|+|A1,iPi|≤|Pi-1Pi|, i=2 ... N-1 (2)
|A1,1P1|≤|P0P1| (3)
|PN-1B1,N-1|≤|PN-1PN| (4)
To realize action error constraints, P need to be only controllediQiDistance be not more than iteration action error threshold di, it may be assumed that
|PiQi|≤di (5)
5. solve optimization problem, that is, formula (1), while require BridgeCurve parameter meet constraint equation (2), (3), (4),
(5), BridgeCurve parameter is solved to get the bridge joint track of iteration tracing point is arrived；
Step 3: the tracing point max value of error Δ of bridge joint track and initial trace point is calculatedk, and judge ΔkWhether track is greater than
Point tolerance threshold value E, the calculation method of track point tolerance are to calculate tracing point and two Bezier curve intersection pointsDistance, this
In step 3 plus k subscript parameter with not plus k subscript parameter be equal, for the error-detecting for describing the secondary iteration of kth, do not saved in step 2
Slightly k:
WhereinIt is located atAngular bisector on, according to the symmetry of interpolation curve, pass through calculatingSize and angular bisector vector obtain, calculation method are as follows:
If Δk> E illustrates that BridgeCurve does not meet tracing point error requirements, enters step four update iteration tracing points and iteration string
High error threshold；Otherwise, iteration is exited in interpolation success, exports interpolation track；
Step 4: iterative parameter is updated, the adjustment vector of iteration tracing point is enabled are as follows:
Iteration tracing point adjusted are as follows:Iteration action error threshold
Value are as follows:Update the number of iterations: k=k+1 goes to step two.
5. the industrial robot fairing motion profile generation method of Controllable Error according to claim 1, which is characterized in that
In the step S3, the interpolation of robot pose specifically comprises the following steps:
Step 1: offset point, note are calculatedThe X-axis unit vector of the tool coordinates system at place is
Z axis unit vector isIt willOne section of fixed range m is deviated along X-axis, X-axis offset point is obtained and is denoted asIt willOne section of fixed range n is deviated along Z axis, Z axis offset point is obtained and is denoted as
Step 2: point interpolation is deviated to X-axis offset point and Z axis, using the method for track point interpolation respectively to X-axis offset point, Z axis
Offset pointInterpolation is carried out, piecewise interpolation curve O (t), R (t) are obtained；
Step 3: the posture of the track after calculating interpolation remembers the piecewise interpolation curve of robot trajectory's point for P (t), after interpolation
X-axis vector: X (t)=O (t)-P (t), Z axis vector: Z (t)=R (t)-P (t), at X-axis vector, Z axis vector units orthogonalization
Reason further calculates to obtain the orthogonal X-axis unit vector of unit after interpolation, Z axis unit vector:
X-axis unit vector X after interpolationnew(t) are as follows:
Z axis unit vector Z after interpolationnew(t) are as follows:
Znew(t)=F (t) × Xnew(t)×F(t)
Wherein
According to X derived abovenew(t), Znew(t) the posture curve after interpolation is described, each trajectory interpolation curve upper rail is obtained
The corresponding posture information of mark point.
6. the industrial robot fairing motion profile generation method of Controllable Error according to claim 5, which is characterized in that
In the step of step S3 one, the value of offset distance m, n are set as 5~10 times of tracing point average headway.
7. the industrial robot fairing motion profile generation method of Controllable Error according to claim 5, which is characterized in that
In the step of step S3 three, the posture sectional curve after unit orthogonalization has segmentation G2Or G3Continuity is being segmented
Curve G between point2Or G3Continuously, at least there is G at waypoint0Continuity.
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