CN110039249A - A kind of choosing method and trajectory planning of positioner inverse kinematics parsing solution weight - Google Patents
A kind of choosing method and trajectory planning of positioner inverse kinematics parsing solution weight Download PDFInfo
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- CN110039249A CN110039249A CN201910378182.9A CN201910378182A CN110039249A CN 110039249 A CN110039249 A CN 110039249A CN 201910378182 A CN201910378182 A CN 201910378182A CN 110039249 A CN110039249 A CN 110039249A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23K—SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- B23K37/00—Auxiliary devices or processes, not specially adapted to a procedure covered by only one of the preceding main groups
- B23K37/04—Auxiliary devices or processes, not specially adapted to a procedure covered by only one of the preceding main groups for holding or positioning work
- B23K37/047—Auxiliary devices or processes, not specially adapted to a procedure covered by only one of the preceding main groups for holding or positioning work moving work to adjust its position between soldering, welding or cutting steps
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Abstract
The invention discloses Algorithms of Selecting and positioner trajectory planning that a kind of positioner inverse kinematics parses solution weight.The nonuniqueness solved in the inverse kinematics parsing solution of positioner causes the selection that may be corresponded to multiple groups solution in a posture, therefore solve more to be that analytic solutions must solve the problems, such as.Using a kind of positioner of two degrees of freedom as research object, positioner kinematical equation is established, then, solution joint variable is carried out by analytic method.In the selection of multiple groups solution, firstly, rejecting the value for being unsatisfactory for positioner range of motion；Secondly, the processing to some special circumstances, such as the case where denominator is zero in solution procedure, finally, considering the weight in two joints, suitable objective function is designed.Suitable transient process is arranged to carry out trajectory planning on the joint variable basis solved.The present invention fast and accurate can find out the joint variable of positioner, and carry out trajectory planning by designing suitable scheduling processes.
Description
Technical field
The invention belongs to positioner kinematics fields, and in particular to positioner inverse kinematics parsing solution weight
Choosing method and positioner trajectory planning.
Background technique
Positioner is applied primarily in modern welding industry, and plays the key player of auxiliary welding.Currently, weldering
It connects positioner and has been successfully applied to automobile chassis welding, chemical pipeline welding, the industries such as welding of accurate electronic component.Weldering
Connect positioner possess treat welder's part revolution welding displacement, allow workpiece to be welded to reach ideal welding pose and guarantee to weld
In termination process the characteristics of stable speed of welding, it is widely used in modern welding industry.
The top priority for controlling positioner is inverse kinematics, by inverse kinematics, available welding
The joint variable in two joints of positioner.The method of inverse kinematics mainly has analytic method and numerical method, and analytic method is for certainly
It is relatively low more convenient by spending, numerical method is used for solving relatively high general of freedom degree.For inverse kinematics side
The advantages of method does not have general method, each method has oneself and disadvantage.The another question of inverse kinematics is
How from the multiple groups solution solved optimal solution is selected.The inverse kinematics parsing solution of positioner is since its precision is high, solves speed
Degree is fast, occupys an important position it always in many inverse kinematics methods.However, for positioner,
The nonuniqueness of analytic solutions cause the selection that may be corresponded to multiple groups solution in a posture, therefore solve more be analytic solutions must face and
It solves the problems, such as.Therefore, it is necessary to design a kind of inverse kinematics method of positioner, pass can quickly, be accurately solved
Save variable.
Track is function of the mechanical arm pose about the time.Trajectory planning is to provide a collision-free path, according to displacement
The kinematical equation of machine constrains, and finds out the time experience in path.Trajectory planning can also be in Descartes in joint space
Space carries out.In cartesian space, there is presently no the sensors that can be used for cartesian space measurement terminal position, so algorithm
It being all built upon on joint coordinates basis, is generally realized and solved by Jacobian inverse matrix, this method calculation amount is very big,
Frequently result in longer time interval.It is that the path point planned in rectangular co-ordinate may change less than joint seat there are one problem
In mark.Controlled joint variable when trajectory planning is directly with movement is carried out in joint space and carries out trajectory planning, for two
For freedom degree positioner, it is suitble to carry out trajectory planning using joint space.
Summary of the invention
The purpose of the present invention is to provide a kind of a kind of methods of positioner inverse kinematics, can be quick, quasi-
Really find out positioner joint variable.Trajectory planning is carried out on the joint variable basis of solution.
In order to achieve the above objectives, the present invention adopts the following technical scheme that.
The foundation of weld seam coordinate system, wherein the direction of welding gun is Z axis, and the direction for welding advance is Y-axis, and X-axis is according to the right hand
Rule determines.
Weldment is fixed on the disk of positioner, is needed to meet condition (1), is met downhand welding.
Wherein, T is 3 × 3 transformation matrix, and O is world coordinate system, and P is positioner coordinate system, and S is weldment coordinate system, W
It is the weld seam coordinate system established.[TOP] represent mean O coordinate system transformation to P coordinate system.
Weldment the fixed position of positioner disk be not each time it is fixed need to establish disk coordinate system C, by formula
(1) formula (2) are revised as.
Generally [TOP] it is unit matrix, formula (2) is revised as formula (3).
Wherein [TSW] it is normal vector of the solder joint under weldment coordinate system.
Formula (3) is the kinematical equation established, and needs to solve [TPC],[TCS],[TSW]。
By [the T of solutionPC],[TCS],[TSW] be brought into (3) and obtain (7).
Wherein, c represents cos function, behalf sin function.
θ3It is given value, calculating given value for convenience is 0, can find out θ according to formula (7)1,θ2。
Most suitable one group of solution is chosen from the multiple groups solution of inverse kinematics.
The θ of solution1,θ2There is certain range, according to actual needs, chooses
-120≤θ1≤120,-180≤θ2≤180。
x1=0, z1≠ 0, at this point, solving θ2When,In this case it is wrong out directly to calculate meeting
It is existing, it, can be direct in order to avoid mistake occursBy θ2(7) are brought into, can be found out:
x1≠0,z1=0, at this point, solving θ1When, it may appear that the situation similar with (2) provides at this time by direct methodIt finds out:
x1=0, z1=0, at this point it is possible to directly giveθ2It can be according to θ1Value find out.
x1≠0,z1≠ 0, at this point it is possible to be solved according to formula (7).
Since the codomain of arctan function isThis range therefore will cause less than the motion range in two joints
The phenomenon that leakage solution, is realized therefore, it is necessary to modify to the result sought by plus-minus 180 degree.
Using shortest route, the smallest one group of solution of variation is relatively selected by the joint angle with last moment as optimal
Solution.
D=ω1|θ10-θ1|+ω2|θ20-θ2| (8)
Wherein, θ1,θ2It is the joint variable of previous state；θ10,θ20The joint variable being to solve for out；ω1,ω2It is joint power
Weight.
According to the relative importance in two joints, choose:
ω2=1,
Wherein, k is proportionality coefficient, and k1 and k2 are connecting rod weight, and p1 and p2 are powers of motor.It can be with by the derivation of front
Find out joint variable.
According to the solution of front, the joint variable in two joints can be solved.Suitable transient process is chosen, makes two
Joint reaches desired value simultaneously.
The function that the transient process of design uses is as follows:
Wherein,
Two joints of positioner can be made by using the transient process of design while reaching desired location, reach track
The purpose of planning.
Detailed description of the invention
Fig. 1 is that joint variable of the invention solves flow chart.
Fig. 2 is that joint variable of the invention chooses flow chart.
Fig. 3 is that positioner welds initial pose figure.
Fig. 4 is positioner welding expected pose figure.
Fig. 5 is positioner oint motion trajectory figure.
Specific embodiment
Present invention is further described in detail below:
The foundation of weld seam coordinate system, wherein the direction of welding gun is Z axis, and the direction for welding advance is Y-axis, and X-axis is according to the right hand
Rule determines.
Weldment is fixed on the disk of positioner, is needed to meet condition (1), is met downhand welding.
Wherein, T is 3 × 3 transformation matrix, and O is world coordinate system, and P is positioner coordinate system, and S is weldment coordinate system, W
It is the weld seam coordinate system established.[TOP] represent mean O coordinate system transformation to P coordinate system.
Weldment the fixed position of positioner disk be not each time it is fixed need to establish disk coordinate system C, by formula
(1) formula (2) are revised as.
Generally [TOP] it is unit matrix, formula (2) is revised as formula (3).
Wherein [TSW] it is normal vector of the solder joint under weldment coordinate system.
Formula (3) is the kinematical equation established, and needs to solve [TPC],[TCS],[TSW]。
Solve [TCS] steps are as follows.
Coordinate system S is transformed to from coordinate system C and needs two steps, firstly, x-axis moves xw, the mobile y of y-axisw；Secondly, being rotated around z-axis
θ3。
It is solved according to above step:
Solve [TPC] steps are as follows.
Coordinate system C, which is transformed to, from coordinate system P needs four steps,
(1) along Z-direction, d1 is translated.
(2) θ is rotated around Y-axis1。
(3) θ is rotated about the z axis2。
(4) along Z-direction, d2 is translated.
It is solved according to above step:
Solve [TSW] steps are as follows.
[TSW] can directly find out, the form for being write as vector is as follows:
Formula (4) (5) (6) is brought into formula (3) and obtains kinematical equation (7).
Wherein, c represents cos function, behalf sin function.
θ3It is given value, calculating given value for convenience is 0, can find out θ according to formula (7)1,θ2。
Need to choose most suitable one group of solution from the multiple groups solution of inverse kinematics.Steps are as follows:
The θ of solution1,θ2There is certain range, according to actual needs, chooses -120≤θ1≤120,-180≤θ2≤180。
x1=0, z1≠ 0, at this point, the θ when solving2,.In this case the wrong appearance of meeting is calculated, directly in order to avoid mistake
Accidentally occur, can directly give(7) will be brought into, can be found out:
x1≠0,z1=0, at this point, solving θ1When, it may appear that the situation similar with (2) provides at this time by direct methodIt finds out:
x1=0, z1=0, at this point it is possible to directly giveθ2It can be according to θ1Value find out.
x1≠0,z1≠ 0, at this point it is possible to be solved according to formula (7).
Since the codomain of arctan function isThis range therefore will cause less than the motion range in two joints
The phenomenon that leakage solution, is realized therefore, it is necessary to modify to the result sought by plus-minus 180 degree.
Using shortest route, the smallest one group of solution of variation is relatively selected by the joint angle with last moment as optimal
Solution.
D=ω1|θ10-θ1|+ω2|θ20-θ2| (11)
Wherein, θ1, θ2It is the joint variable of previous state；θ10, θ20The joint variable being to solve for out；ω1, ω2It is joint power
Weight.
According to the relative importance in two joints, choose:
ω2=1,
Wherein, k is proportionality coefficient, and k1 and k2 are connecting rod weight, and p1 and p2 are powers of motor.It can be with by the derivation of front
Find out joint variable.
Below with reference to specific example, the invention will be described in further detail:
It can be seen that in Fig. 3
Data are brought into formula (7), can be found out: θ2={ 0 ,-π, π },
It can be found out according to the method that inverse kinematics is chosen: θ2=0,
By two joints of positioner according to such as Fig. 4 after the joint variable of solution, meet the requirements.
According to the solution of front, the joint variable in two joints can be solved.Suitable transient process is chosen, makes two
Joint reaches given value simultaneously.
The function that the transient process of design uses is as follows:
Wherein,
Reasonable transient process is designed by using function (12), the two of positioner can be made by secondly choosing suitable parameter
A joint reaches desired location simultaneously.
According to the joint variable solved in previous examples, the parameter of selection are as follows: r1=0, h1=0；r2=10, h2=
0.005。
Claims (5)
1. a kind of choosing method and trajectory planning of positioner inverse kinematics parsing solution weight, which is characterized in that include one
Lower step:
(A) transformation between coordinate system, (B) coordinate system is established, (C) chooses suitable weight method and solves optimal solution, (D) chooses
Suitable transient process carries out trajectory planning.
2. the choosing method and trajectory planning of positioner inverse kinematics parsing solution weight according to claim 1,
It is characterized in that, the step (A) needs the coordinate system established to have: world coordinate system, positioner coordinate system, weldment coordinate
System, weld seam coordinate system, positioner disk coordinate system.
3. the choosing method and trajectory planning of positioner inverse kinematics parsing solution weight according to claim 1,
It is characterized in that, the step (B) needs to establish the transformation between the coordinate system between coordinate system.Become from positioner disk coordinate system
It changes to weldment coordinate system and needs two steps, firstly, x-axis moves xw, the mobile y of y-axisw；Secondly, rotating θ around z-axis3；From positioner coordinate
System transforms to positioner disk coordinate system and needs four steps.
(1) along Z-direction, d1 is translated.
(2) θ is rotated around Y-axis1。
(3) θ is rotated about the z axis2。
(4) along Z-direction, d2 is translated.
4. the choosing method and trajectory planning of positioner inverse kinematics parsing solution weight according to claim 1,
It is characterized in that, the step (C) needs to establish suitable method, is unsatisfactory for positioner range of motion firstly, rejecting
Value；Secondly, the processing to some special circumstances, such as the case where denominator is zero in solution procedure, finally, considering two passes
The weight of section designs suitable objective function.The objective function of design is as follows:
D=ω1|θ10-θ1|+ω2|θ20-θ2| (1)
Wherein, θ1,θ2It is the joint variable of previous state；θ10,θ20The joint variable being to solve for out；ω1,ω2It is joint weight.
According to the relative importance in two joints, choose:
Wherein, k is proportionality coefficient, and k1 and k2 are connecting rod weight, and p1 and p2 are powers of motor.It can be found out by the derivation of front
Joint variable.
5. the choosing method and trajectory planning of the parsing of positioner inverse kinematics described in -4 solution weight according to claim 1,
It is characterized in that, the step (D), which needs to choose suitable transient process, carries out trajectory planning.The transient process of design is using such as
Minor function:
Wherein,
Reasonable transient process is designed by using function (3), secondly the suitable parameter of selection can make two s' of positioner
Joint reaches desired location simultaneously.
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| CN201910378182.9A CN110039249B (en) | 2019-05-08 | 2019-05-08 | Method for solving motion trail of welding positioner based on inverse kinematics analytic solution weight method of welding positioner |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111890364A (en) * | 2020-07-29 | 2020-11-06 | 库卡机器人(广东)有限公司 | Robot motion control method, device, electronic device and storage medium |
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| CN111890364A (en) * | 2020-07-29 | 2020-11-06 | 库卡机器人(广东)有限公司 | Robot motion control method, device, electronic device and storage medium |
| CN111890364B (en) * | 2020-07-29 | 2021-11-16 | 库卡机器人(广东)有限公司 | Robot motion control method, device, electronic device and storage medium |
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