CN109664303A - A kind of four smooth orbit generation methods of shaft industrial robot B-spline transition type that error is controllable - Google Patents
A kind of four smooth orbit generation methods of shaft industrial robot B-spline transition type that error is controllable Download PDFInfo
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Abstract
A kind of four smooth orbit generation methods of shaft industrial robot B-spline transition type that error is controllable, include the following steps: (1) the pretreatment of four shaft industrial robot tracks: track, which is divided into, to be needed smooth orbit segment and is not required to smooth orbit segment, and four axis postures are pre-processed, guarantee to walk minor arc track between two tracing points；Step 2, four track shaft B-splines are smooth: the smooth orbit segment of need that traversal step 1 generates, and are required according to tracing point error threshold, location point action error threshold and continuity each orbit segment to generate the smooth track of B-spline transition type using geometric iteration.The smooth track of B-spline transition type of the present invention is made of linear track and B-spline track, G1 the or G2 continuity that whole track has position synchronous with posture, meet the position action error between track point tolerance and tracing point, and it is smooth using the track that batten track can be realized four shaft industrial robot complicated applications, and then improve the operating efficiency and quality of four shaft industrial robots.
Description
Technical field
The invention belongs to industrial robot track optimizing fields, and in particular to a kind of four shaft industrial robots that error is controllable
The smooth orbit generation method of B-spline transition type.
Background technique
Four shaft industrial robots, also known as plane articulation (SCARA) robot, there are three tools rotary shaft and a translation shaft,
It is widely used in the operations such as carrying, assembly and gluing.
The movement instruction of four shaft industrial robots is mostly consistent with six-shaft industrial robot, including linear instruction, circular arc refer to
It enables and axis joint movement instruction.Every instruction simultaneously, which can specify, to be accurate to a little or seamlessly transits.Being accurate to an instruction can
Meet path accuracy requirement, but reach tracing point must reduction of speed be zero, cause operating efficiency to reduce；It smoothly can be at tracing point
Reduction of speed does not seamlessly transit in the case where being zero, but results in the reduction of tracing point precision.
The track of robot complicated applications mostly uses linear instruction or circular arc instruction description, individual machine people producer in order to
It is improving successional while improving precision, increasing free curve or batten movement instruction.As the MOVS of An Chuan robot refers to
It enables, using free curve interpolation, track is the parabola by three points.KUKA robot is established using the concept of batten group to be connected
Continuous straight line, circular arc or batten section.Compared with regular motion, it is easier to keep the speed of programming setting；But two tracing points it
Between trajectory error can not be by user's control, in fact it could happen that track is deviateed the excessive situation of initial trace and is occurred, so as to cause work
The reduction of industry quality.
Position point tolerance and action can be controlled simultaneously by having accepted Patent Application Publication 201710097192.6 and proposing one kind
The industrial robot smooth movement orbit generation method of error, easement curve therein provide cubic B-spline and four B-splines
Two kinds of curves, but smoothly posture is not necessarily continuous at straightway and the tie point of batten section for double track.Patent application text is accepted
It offers 201811468150.X and proposes a kind of smooth method of the three-dimensional track locus of points that error is controllable, this method is only applicable to three-dimensional
The track that is continuous, conformal and meeting precision of location point is smooth.
In track (position and posture, the abbreviation pose) expression of existing four shaft industrial robot, without meeting height simultaneously
Continuity (pose synchronizes continuously) and high-precision (meeting the position action error between track point tolerance and tracing point) it is smooth
Track expression.
Summary of the invention
The technical problem to be solved by the present invention is to, for existing four shaft industrial robot track expression it is existing it is above-mentioned not
Foot provides a kind of four smooth orbit generation methods of shaft industrial robot B-spline transition type that error is controllable, provides the continuous sample of G1
Item and G2 two kinds of smooth methods of continuous batten, the generation of smooth batten calculate simple；It can reach what whole track pose synchronized
G1 is continuous and G2 is continuous；Can satisfy the tracing point (position and posture) of four shaft industrial robots error and tracing point it
Between location point action error；And on the basis of robot existing tracing point definition can not be changed inside robot controller
Increase batten instruction.
Used technical solution is the present invention to solve above-mentioned technical problem:
A kind of four smooth orbit generation methods of shaft industrial robot B-spline transition type that error is controllable, include the following steps:
Step 1, the pretreatment of four shaft industrial robot tracks: linear track is divided into according to positional distance and angle to be needed smoothly
Orbit segment and it is not required to smooth orbit segment；And posture is pre-processed；
Step 2 needs smooth orbit segment smooth: the smooth orbit segment of need that traversal step 1 generates, to each section of smooth track of need
Section requires to generate G1 or G2 company using geometric iteration according to tracing point error threshold, location point action error threshold and continuity
The continuous smooth track of B-spline transition type.
According to the above scheme, the step 1 specifically comprises the following steps:
Step 1.1, according to fragmentation threshold computation segmented index set, input the orbit segment of continuous two tracing points or more,
Export segmented index；If the track point set of four shaft industrial robots of input isTracing point number N
>=2, wherein each tracing point Pi(xi,yi,zi,θi) it is position (xi,yi,zi) and the angle, θ that rotates about the z axis of postureiComposition
Four dimensional vectors, location segment condition is with positional distance threshold value δdWith position angle threshold value δaAs index；
It traverses tracing point and indexes i=1,2 ... N-1, judge to index whether i meets location segment condition respectively:
Orbit segment P is calculated firsti-1PiAnd PiPi+1Two sections of positional distance di-1And diIf di-1Or diLess than positional distance
Threshold value δd, then it is assumed that index i meets location segment condition；Otherwise, orbit segment P is calculatedi-1PiAnd PiPi+1Position angle aiIf
sin aiLess than position angle threshold value δa, then it is assumed that index i meets location segment condition；Otherwise it is assumed that index i is unsatisfactory for position point
Section condition；Segmented index set is added in the index i for meeting location segment condition, segmentation rope is added in 0, N of head and the tail index by default
Draw the head and the tail of set；
Step 1.2 is segmented according to segmented index set, and one whole section of orbit segment is divided into several rails according to segmented index set
Mark section, wherein tracing point number is denoted as greater than 2 orbit segment and needs smooth orbit segment in orbit segment, and the track for next step is flat
It is suitable；Otherwise it is denoted as and is not required to smooth orbit segment, in the track after being output to smoothly according to linear track；
Step 1.3, posture pretreatment index i=1 according to minor arc preferential principle traversal tracing point between two tracks,
2 ... N, if two neighboring tracing point Pi-1,PiPosture angle distance oi-1Greater than 180 °, oi-1=| θi-θi-1|, then modify Pi
Fourth dimension attitude angle: if θi> 0, then it is revised as Pi(xi,yi,zi,θi-360°)；Otherwise it is revised as Pi(xi,yi,zi,θi+
360°)。
According to the above scheme, the method that the step 2 generates the smooth track of B-spline transition type to the smooth orbit segment of each section of need
It is specific as follows:
Step 2.1, primary iteration parameter setting, if the 4 D trajectory point of current linear track section is
It is denoted as initial trace point, if the positional distance error threshold that the track after smooth need to meet is εmax, position action error threshold note
For δmax, posture point angle error threshold value omax, the number of iterations threshold value kmax, setting current iteration number is k=0, iteration tracing point
It is denoted as
Step 2.2, traversal index i=1,2 ... N-1, according to location point action error constraints, G1 or G2 continuity constraint
Iteration tracing point is generated respectively with conformal constraintThe transition B-spline track at place
It calculates separately firstWithPositional distance di-1And diAnd location point angle βi, and calculate
di-1And diSmaller value dmin=min (di-1,di)；
Then it is calculated according to location point action error constraints and conformal constraintThe transition ratio r of front-rear position pointi-1And ri, first
The transition length for first calculating front-rear position point, for G1 transition B-spline, transition length are as follows:
For G2 transition B-spline, transition length isThen two transition ratios are calculated:Wherein 0 < α < 1 is conformal parameter, and the linear track section represented between two sections of transition B-splines accounts for entirely
The distance proportion of orbit segment；C > 1 is the proportionality coefficient for determining control point；Batten continuous for G1, whenWhen,
The preceding three-dimensional of transition batten constitutes plane PH batten；Batten continuous for G2, takes c=1.5；
The control point that four-dimensional batten is finally calculated according to G1 the or G2 condition of continuity and two transition ratios, meets G1 continuous strip
There are four control points for the transition batten tool of part；Meet the transition batten tool of the G2 condition of continuity there are five control point, each control point
Calculation method it is as follows:
G1 batten:G2 batten:
Step 2.3, traversal index i=1,2 ... N-1, calculate i-th transition B-splineWith initial trace point Qi's
Track point tolerance constructs four-dimensional B-spline according to the control point in step 2.2 firstUsing the B sample of uniform node three times
Curve:Wherein [0,1] t ∈；For G1 batten, M=3；For G2 batten, M=4.Bj,3
(t) it is B-spline basic function, is calculated according to knot vector；
Then the parameter midpoint of four-dimensional B-spline track is calculated as track point tolerance maximum point:
Finally calculate transition B-splineWith initial trace point QiTrack point tolerance, track point tolerance include position away from
From error and posture point angle error, according toThree-dimensional position distance and posture angle distance obtain；
Step 2.4, the maximum position range error for calculating all transition B-splines and initial trace pointWith maximum posture
Point angle errorIfLess than positional distance error threshold εmax, andLess than posture point angle error threshold value omax, or
Person current iteration number k is greater than the number of iterations threshold value kmax, terminate iteration and export the smooth track of B-splineTurn step
Rapid 2.6；Otherwise, 2.5 are gone to step；
Step 2.5, traversal i=1 ... N-1, according to initial trace point QiWith track point tolerance maximum pointCalculate offset
VectorAnd update iteration tracing point:
K=k+1 is enabled, goes to step 2.2；
Step 2.6, the smooth track exported to step 2.4 are arranged and are exported, it is smooth after track by N item four-dimension line
Property track and the smooth track combination of (N-1) item four-dimension B-spline form, be successively in order: linear trackSmooth B
Batten trackLinear trackSmooth B-spline trackSmooth B-spline track
Linear track
Contemplated above technical scheme through the invention, compared with prior art, the present invention has the advantage that:
1, according to the smooth orbit generation method of circular arc transition type of four shaft industrial robots, position can be generated and posture is same
The B-spline track that the thinking is generalized to four shaft industrial robots is generated, can be generated a kind of high by the continuous smooth track the G1 of step
Continuity (G1 or G2 are continuous), the conformal and smooth track of high-precision four shaft industrial robots B-spline transition type, smooth track by
Linear track and B-spline track composition, can satisfy the position precision between tracing point precision and tracing point, reach position and appearance
The continuous smooth track state synchronous G1 or G2；
2, it is instructed relative to the existing linear track of four shaft industrial robots, smoothing function and batten or free curve, this hair
Open-birth at the smooth track of B-spline transition type not only there is higher continuity, but also can guarantee successional while keep higher
Execution precision, position and the posture of desired guiding trajectory can be reached, and guarantee to meet the position precision between tracing point, thus
Homework precision is improved while improving four shaft industrial robot operating efficiencies；
3, the continuously smooth track the synchronous G1 of pose can not only be generated, the synchronous continuous rail of G2 of pose can be also generated
Mark, and B-spline track can generate the smaller smooth track of curvature relative to arc track, relative to the smooth rail of circular arc transition type
Mark B-spline track of the present invention has better flexibility and continuity.
Detailed description of the invention
Fig. 1 is the four smooth flow chart of shaft industrial robot B-spline an iteration of the embodiment of the present invention；
Fig. 2 is that the embodiment of the present invention constructs the continuous batten schematic diagram of G1；
Fig. 3 is that the embodiment of the present invention constructs the continuous batten schematic diagram of G2；
Fig. 4 is position of the embodiment of the present invention continuous schematic diagram synchronous with posture.
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 four controllable smooth orbit generation methods of shaft industrial robot B-spline transition type of a kind of error of the present invention, including such as
Lower step:
Step 1, the pretreatment of four shaft industrial robot tracks: linear track is divided into according to positional distance and angle to be needed smoothly
Orbit segment and it is not required to smooth orbit segment；All tracing points of whole track are traversed, according to the positional distance and folder of track
Angle is segmented, and whole track is divided into several segments orbit segment set；And four axis postures are pre-processed:
Step 1.1, according to fragmentation threshold computation segmented index set, input the orbit segment of continuous two tracing points or more,
Segmented index is exported, if the track point set of four shaft industrial robots of input is(tracing point number
N >=2), two of them tracing point Pi-1,PiBetween positional distance calculation method beIf adjacent three tracing point Pi-1,Pi,Pi+1Preceding three-dimensional
The location point of composition is respectively pi-1,pi,pi+1；If di-1di≠ 0, the angle of three location points is
Location segment condition is with positional distance threshold value δdWith adjacent position angle threshold value δaAs index, according to location segment
It is consistent with the three-dimensional point segmentation method for having accepted patent application (201811468150.X), traversal tracing point index i=1,2 ...
N-1 judges to index whether i meets location segment condition respectively；If di-1<δdOr di<δd, then it is assumed that index i meets location segment
Condition, if otherwise sinai<δa, then think that indexing i meets location segment condition；The index i for meeting location segment condition is added
The head and the tail of segmented index set are added in 0, N of head and the tail index by segmented index set, default；
Step 1.2 is segmented according to segmented index set, and one whole section of orbit segment is divided into several rails according to segmented index set
Mark section, wherein tracing point number is denoted as greater than 2 orbit segment and needs smooth orbit segment in orbit segment, and the track for next step is flat
It is suitable；Otherwise it is denoted as and is not required to smooth orbit segment, in the track after being output to smoothly according to linear track；
Step 1.3 pre-processes posture according to minor arc preferential principle between two tracks, and traversal tracing point indexes i=
1,2 ... N, two neighboring tracing point Pi-1,PiPosture angle distance calculation method be oi-1=| θi-θi-1|, if oi-1It is greater than
180 °, then modify PiFourth dimension attitude angle: if θi> 0, then it is revised as Pi(xi,yi,zi,θi-360°)；Otherwise it is revised as Pi(xi,
yi,zi,θi+360°)。
The smooth orbit segment of need that step 2, traversal step 1 generate, to each section of smooth orbit segment of need according to track point tolerance
Threshold value, location point action error threshold and continuity require to generate the smooth track of B-spline transition type using geometric iteration, generate
The thinking of smooth track is consistent with the smooth thinking of circular arc, and the main distinction is to meet the structure of precision and successional B-spline curves
The step of making, the geometric iteration construction smooth track of B-spline transition type introduced with one section of need smooth orbit segment below:
Step 2.1, primary iteration parameter setting, if the 4 D trajectory point of current linear track section is
It is denoted as initial trace point, if the positional distance error threshold that the track after smooth need to meet is εmax, position action error threshold note
For δmax, posture point angle error threshold value omax, the number of iterations threshold value kmax, setting current iteration number is k=0, iteration tracing point
It is denoted asWork as kmaxWhen=1, such as similar transition batten of existing smoothing function will be generated, such as Fig. 1 institute
Show, dotted line is the location point line of linear track, and solid line is the easement curve that maximum number of iterations is 1, which can
The precision for reaching continuous effect, but not can guarantee location point meets high-precision demand, therefore raw using following step
At not only meeting precision but also meet the synchronous B-spline transition track of successional pose；
Step 2.2, traversal index i=1,2 ... N-1, according to location point action error constraints, G1 or G2 continuity constraint
Iteration tracing point is generated respectively with conformal constraintThe transition B-spline track at place
It calculates separately firstWithPositional distance di-1And diAnd location point angle βi, position away from
From the preceding three-dimensional that the calculation method with location point angle needs first to take out four dimensional vectors, three-dimensional distance and three-dimensional position point folder are calculated
Angle, and calculate di-1And diSmaller value dmin=min (di-1,di)；
Then it is calculated according to location point action error constraints and conformal constraintThe transition ratio r of front-rear position pointi-1With
ri, the transition length of front-rear position point is calculated first, is derived according to the property of B-spline, continuity, required precision and conformal requirement
Out, for G1 transition B-spline, transition length are as follows:For G2 transition B-spline, transition
Length are as follows:The length refers to the transition length of three-dimensional position point, the of transition length
A part indicates the transition length for meeting action error threshold, and second part indicates the transition length for meeting conformal requirement；
Then two transition ratios are calculated:Wherein 0 < α < 1 is conformal parameter, represents two sections of mistakes
The linear track section crossed between B-spline accounts for the distance proportion of entire orbit segment；C > 1 is the proportionality coefficient for determining control point；For
The continuous batten of G1, whenWhen, the preceding three-dimensional of transition batten constitutes the plane that property is calculated with good arc length
PH batten, the batten can simply be calculated the arc length of B-spline by analytic method, provide convenience for speed planning very much.It is right
In the continuous batten of G2, without loss of generality, c=1.5. can use
The control point that four-dimensional batten is finally calculated according to G1 the or G2 condition of continuity and two transition ratios, as shown in Fig. 2, full
There are four control point (white dot), bilateral symmetries for the transition batten tool of the sufficient G1 condition of continuity；As shown in figure 3, it is continuous to meet G2
There are five control point (white dot), the first two and latter two bilateral symmetry, intermediate point and transition points for the transition batten tool of condition
It is overlapped, the calculation method at each control point is following (operation rule of four dimensional vectors is identical as three-dimensional):
G1 batten:G2 batten:
Step 2.3, traversal index i=1,2 ... N-1, calculate i-th transition B-splineWith initial trace point Qi's
Track point tolerance constructs four-dimensional B-spline according to the control point in step 2.2 firstUsing the B sample of uniform node three times
Curve:Wherein [0,1] t ∈；For G1 batten, M=3；For G2 batten, M=4；Bj,3
(t) it is B-spline basic function, is calculated according to knot vector；Wherein the knot vector of the continuous batten of G1 be [0,0,0,0,1,1,
1,1]；The knot vector of the continuous batten of G2 is [0,0,0,0,0.5,1,1,1,1]；
Then the parameter midpoint of four-dimensional B-spline track is calculated as track point tolerance maximum point: As shown in the asterism in Fig. 2 and Fig. 3；
Finally calculate transition B-splineWith initial trace point QiTrack point tolerance, track point tolerance include position away from
From error and posture point angle error, according toThree-dimensional position distance and posture angle distance obtain；
Step 2.4, the maximum position range error for calculating all transition B-splines and initial trace pointWith maximum posture
Point angle errorMaximum position three-dimensional position of the distance for all transition B-splines and iteration tracing point between in most
Big value, the maximum value of posture angle of the maximum posture point angle error between all transition B-splines and iteration tracing point will most
Big positional distance and maximum posture point angle and threshold value comparison, ifLess than positional distance error threshold εmax, andIt is less than
Posture point angle error threshold value omaxOr current iteration number k is greater than the number of iterations threshold value kmax, terminate iteration and export B sample
The smooth track of transition typeGo to step 2.6；Otherwise, 2.5 are gone to step；
Step 2.5, traversal i=1 ... N-1, according to initial trace point QiWith track point tolerance maximum pointCalculate offset
VectorAnd update iteration tracing point:
K=k+1 is enabled, goes to step 2.2；
Step 2.6, the smooth track exported to step 2.4 are arranged and are exported, it is smooth after track by N item four-dimension line
Property track and the smooth track combination of (N-1) item four-dimension B-spline form, be successively in order: linear trackSmooth B
Batten trackLinear trackSmooth B-spline trackSmooth B-spline trackLinear track
Smooth track derived above can guarantee that position is synchronous with posture continuous, i.e., not only guarantee that smooth track is taken up an official post
The position p of meaning tracing pointi(xi,yi,zi) G1 or G2 it is continuous, and guarantee arbitrary point qi=pi+RZ(θi) v G1 or G2 it is continuous
Property.Wherein v is Arbitrary 3 D vector, RZ(θi) for around the spin matrix of z-axis.As shown in figure 4, solid line is smooth preceding tool in figure
The linear position track of central point (TCP)；Dotted line be it is smooth after straight line and batten composition smooth track (such as above formula of location point
Location point piTrack), overstriking dotted line is believed that location track (such as above formula position that certain is put in the X-axis of tool coordinates system in figure
Point qiTrack), it can be seen that it is synchronous with posture continuous that the track after smooth can reach position.
Claims (3)
1. the four controllable smooth orbit generation methods of shaft industrial robot B-spline transition type of a kind of error, which is characterized in that including
Following steps:
Step 1, the pretreatment of four shaft industrial robot tracks: linear track is divided into according to positional distance and angle needs smooth track
Section and be not required to smooth orbit segment；And posture is pre-processed；
Step 2 needs smooth orbit segment smooth: the smooth orbit segment of need that traversal step 1 generates presses each section of smooth orbit segment of need
It is required according to tracing point error threshold, location point action error threshold and continuity continuous using geometric iteration generation G1 or G2
The smooth track of B-spline transition type.
2. the four controllable smooth orbit generation methods of shaft industrial robot B-spline transition type of error according to claim 1,
It is characterized in that, the step 1 specifically comprises the following steps:
Step 1.1, according to fragmentation threshold computation segmented index set, input the orbit segment of continuous two tracing points or more, output
Segmented index；If the track point set of four shaft industrial robots of input isTracing point number N >=2,
Wherein each tracing point Pi(xi, yi, zi, θi) it is position (xi, yi, zi) and the angle, θ that rotates about the z axis of postureiThe four-dimension of composition
Vector, location segment condition is with positional distance threshold value δdWith position angle threshold value δaAs index；
Traverse tracing point index i=1,2 ... N-1, judge respectively index i whether meet location segment condition:
Orbit segment P is calculated firsti-1PiAnd PiPi+1Two sections of positional distance di-1And diIf di-1Or diLess than positional distance threshold value
δd, then it is assumed that index i meets location segment condition；Otherwise, orbit segment P is calculatedi-1PiAnd PiPi+1Position angle aiIf sin ai
Less than position angle threshold value δa, then it is assumed that index i meets location segment condition；Otherwise it is assumed that index i is unsatisfactory for location segment item
Part；Segmented index set is added in the index i for meeting location segment condition, segmented index collection is added in 0, N of head and the tail index by default
The head and the tail of conjunction；
Step 1.2 is segmented according to segmented index set, and one whole section of orbit segment is divided into several tracks according to segmented index set
Section, wherein tracing point number is denoted as greater than 2 orbit segment and needs smooth orbit segment in orbit segment, and the track for next step is flat
It is suitable；Otherwise it is denoted as and is not required to smooth orbit segment, in the track after being output to smoothly according to linear track；
Step 1.3, posture pretreatment, according between two tracks minor arc preferential principle traversal tracing point index i=1,2,
... N, if two neighboring tracing point Pi-1, PiPosture angle distance oi-1Greater than 180 °, Oi-1=| θi-θi-1|, then modify Pi
Fourth dimension attitude angle: if θi> 0, then be revised as Pi(xi, yi, zi, θi-360°)；Otherwise it is revised as Pi(xi, yi, zi, θi+
360°)。
3. the four controllable smooth orbit generation methods of shaft industrial robot B-spline transition type of error according to claim 1,
It is characterized in that, the step 2 generates the method for the smooth track of B-spline transition type specifically such as to the smooth orbit segment of each section of need
Under:
Step 2.1, primary iteration parameter setting, if the 4 D trajectory point of current linear track section isIt is denoted as
Initial trace point, if the positional distance error threshold that the track after smooth need to meet is εmax, position action error threshold is denoted as
δmax, posture point angle error threshold value Omax, the number of iterations threshold value kmax, setting current iteration number is k=0, iteration tracing point note
For
Step 2.2, traversal index i=1,2 ... N-1, according to location point action error constraints, G1 or G2 continuity constraint and guarantor
Shape constraint generates iteration tracing point respectivelyThe transition B-spline track at place
It calculates separately firstWithPositional distance di-1And diAnd location point angle βi, and calculate di-1
And diSmaller value dmin=min (di-1, di)；
Then it is calculated according to location point action error constraints and conformal constraintThe transition ratio r of front-rear position pointi-1And ri, first
The transition length for calculating front-rear position point, for G1 transition B-spline, transition length are as follows:
For G2 transition B-spline, transition length isThen two transition ratios are calculated:Wherein 0 < α < 1 be conformal parameter, represent the linear track section between two sections of transition B-splines account for it is whole
The distance proportion of a orbit segment；C > 1 is the proportionality coefficient for determining control point；Batten continuous for G1, when
When, the preceding three-dimensional of transition batten constitutes plane PH batten；Batten continuous for G2, takes c=1.5；
The control point that four-dimensional batten is finally calculated according to G1 the or G2 condition of continuity and two transition ratios, meets the G1 condition of continuity
There are four control points for transition batten tool；Meet the transition batten tool of the G2 condition of continuity there are five control point, the meter at each control point
Calculation method is as follows:
G1 batten:G2 batten:
Step 2.3, traversal index i=1,2 ... N-1 calculates i-th transition B-splineWith initial trace point QiTrack
Point tolerance constructs four-dimensional B-spline according to the control point in step 2.2 firstIt is bent using the B-spline of uniform node three times
Line:Wherein die ∈ [0,1]；For G1 batten, M=3；For G2 batten, M=4.BJ, 3(t)
For B-spline basic function, it is calculated according to knot vector；
Then the parameter midpoint of four-dimensional B-spline track is calculated as track point tolerance maximum point:
Finally calculate transition B-splineWith initial trace point QiTrack point tolerance, track point tolerance include positional distance miss
Difference and posture point angle error, according toThree-dimensional position distance and posture angle distance obtain；
Step 2.4, the maximum position range error for calculating all transition B-splines and initial trace pointIt is pressed from both sides with maximum posture point
Angle errorIfLess than positional distance error threshold Emax, andLess than posture point angle error threshold value omax, or work as
Preceding the number of iterations k is greater than the number of iterations threshold value kmax, terminate iteration and export the smooth track of B-splineIt goes to step
2.6；Otherwise, 2.5 are gone to step；
Step 2.5, traversal i=1 ... N-1, according to initial trace point QiWith track point tolerance maximum pointCalculate offset vectorAnd update iteration tracing point:Enable k
=k+1, goes to step 2.2；
Step 2.6, the smooth track exported to step 2.4 are arranged and are exported, it is smooth after track by N item four-dimension linear rails
Mark and the smooth track combination of (N-1) item four-dimension B-spline form, and are successively in order: linear trackSmooth B-spline
TrackLinear trackSmooth B-spline trackSmooth B-spline trackLinearly
Track
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| CN201910151081.8A CN109664303B (en) | 2019-02-28 | 2019-02-28 | Error-controllable B-spline transition type smooth trajectory generation method for four-axis industrial robot |
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| CN112356032A (en) * | 2020-11-05 | 2021-02-12 | 哈工大机器人（合肥）国际创新研究院 | Posture smooth transition method and system |
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| CN114488941A (en) * | 2020-11-11 | 2022-05-13 | 沈机（上海）智能***研发设计有限公司 | Trace fairing method and medium for micro line segments and machine tool numerical control equipment |
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| CN113276116B (en) * | 2021-05-21 | 2022-01-18 | 武汉瀚迈科技有限公司 | Error-controllable robot track synchronous transition method |
| CN113276116A (en) * | 2021-05-21 | 2021-08-20 | 武汉瀚迈科技有限公司 | Error-controllable robot track synchronous transition method |
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| CN115958597A (en) * | 2022-12-16 | 2023-04-14 | 广州数控设备有限公司 | Industrial robot continuous attitude path fairing method and system |
| CN115958597B (en) * | 2022-12-16 | 2023-09-15 | 广州数控设备有限公司 | Industrial robot continuous attitude path fairing method and system |
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