CN107116542A - Control method and system that a kind of six joint industrial robot passes through posture singular point - Google Patents
Control method and system that a kind of six joint industrial robot passes through posture singular point Download PDFInfo
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- CN107116542A CN107116542A CN201710504635.9A CN201710504635A CN107116542A CN 107116542 A CN107116542 A CN 107116542A CN 201710504635 A CN201710504635 A CN 201710504635A CN 107116542 A CN107116542 A CN 107116542A
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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
- B25J9/02—Programme-controlled manipulators characterised by movement of the arms, e.g. cartesian coordinate type
- B25J9/04—Programme-controlled manipulators characterised by movement of the arms, e.g. cartesian coordinate type by rotating at least one arm, excluding the head movement itself, e.g. cylindrical coordinate type or polar coordinate type
- B25J9/046—Revolute coordinate type
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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
The invention belongs to industrial robot motion control field, and control method and system of a kind of six joint industrial robot by posture singular point are specifically disclosed, comprised the following steps：1) one section of track in the default path planning of industrial robot residing for interception posture singular point, obtains the positional value of track starting point and the positional value and rear three joint variable values of rear three joint variable values and terminal；2) rear three joint variable values of posture singular position are obtained with interpolation mode；3) first three corresponding joint variable value of posture singular position is asked for；4) using the corresponding rear three joint variable values of the posture singular position and first three joint variable value as industrial robot in the corresponding motion control parameter of posture singular position, the motion control of industrial robot is realized, with this so that six joint industrial robots pass through posture singular point.The present invention on the premise of original path planning is not changed so that robot passes through posture singular point, it is simple and easy to apply and operation efficiency is high.
Description
Technical field
It is logical more particularly, to a kind of six joint industrial robot the invention belongs to industrial robot motion control field
Cross the control method and system of posture singular point.
Background technology
Motion control instruction be realize instrument is moved to from a position with command speed, particular course pattern etc. it is another
What motion mode is individual specified location, need to specify using to control the motion road of arrival specified location when using movement instruction
Footpath, the type of robot motion has three kinds：Joint motions (J), linear motion (L), circular motion (C).Six joint industrial machines
Rear three joints axes of people are met at a bit, when the joint of robot the 4th and the coincidence of the 6th joints axes, and motion is cancelled out each other, machine
Device people will lose one degree of freedom, and the critical point of this joint attribute of bowing/face upward for robot, is also the unusual shape in inside of robot
Position, can be described as the posture singular point of robot.When in posture singular point, the type of sports of robot is linear motion or circular arc
Motion, now motion controller does not know the value for how choosing the 4th joint and the 6th joint, causes mechanical arm out of control and sends
Alarm, makes robot can not be according to the path of planning by posture singular point, such case often occurs in actual applications, not only
The space of robot is reduced, and very big inconvenience is brought to production.
Mainly there are following three kinds of processing methods for the posture singular point of industrial robot at present：1) posture of robot is avoided
Singular point：When running into posture singular point, change the motion path of robot to avoid Singularities；2) paths planning method：Adopt
Cause robot that by posture singular point, joint variable is obtained by interative computation with the method for carrying out path planning to posture singular point
The analytic solutions of value；3) posture method is adjusted：When in posture singular point, the 4th joint and the 6th joint it is joint variable and/or poor
For definite value, robot is caused to pass through posture singular point by the value for coordinating both.
But further investigations have shown that, the above method still has problems with：Although avoid posture method of singularities makes machine
Device people passes through from the path of posture near its singularity, avoids posture singular point, but be that it changes the original path of robot and
With blindness, it is necessary to which the posture singular point all to robot is avoided, operability is not strong, while also causing robot
Spatial dimension reduces；Paths planning method is to re-start planning to the path residing for posture singular point, is transported using complicated iteration
Calculate the analytic solutions for trying to achieve joint of robot variable, it is impossible to obtain accurate numerical solution so that robot can not accurately pass through appearance
State singular point, and calculate cumbersome, workload is larger；Although adjustment posture method can cause robot accurately strange by posture
Point, but robot is in resting state during the coordinated movement of various economic factors so that machine human efficiency is reduced, and may be caused
Movement velocity after coordination is discontinuous, is made troubles to actual production.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, pass through the invention provides a kind of six joint industrial robot
The control method and system of posture singular point, it is replaced using interpolation by the way of robot end's posture, is not changing original planning
Cause robot to pass through posture singular point on the premise of path, thus solve at present because posture singular point causes robot motion's model
Enclose limited technical problem, with simple and easy to apply, operation efficiency is high, strong applicability the features such as.
To achieve the above object, according to one aspect of the present invention, it is proposed that a kind of six joint industrial robot passes through appearance
The control method of state singular point, it comprises the following steps：
(1) one section of track in the default path planning of industrial robot residing for interception posture singular point, obtains the track and rises
The corresponding positional value of point and rear three joint variable values and the corresponding positional value of the final on trajectory and rear three joint variable values；
(2) according to rear three joint variable values of the starting point and rear three joint variable values of terminal with the side of interpolation
Formula obtains the corresponding rear three joint variable values of posture singular position；
(3) set up inverse kinematic equation and ask for first three corresponding joint variable value of posture singular position；
(4) it is used as work using the corresponding rear three joint variable values of the posture singular position and first three joint variable value
Industry robot realizes the motion control of industrial robot, with this so that six in the corresponding motion control parameter of posture singular position
Joint industrial robot passes through posture singular point.
As it is further preferred that the step (3) includes following sub-step：
(3.1) following matrix equation is initially set up：
Wherein, xt,yt,ztThree coordinate components for tool coordinates system origin relative to base coordinate system, s1=sin (θ1),
s2=sin (θ2), s23=sin (θ2+θ3), c1=cos (θ1), c2=cos (θ2), c23=cos (θ2+θ3), θ1,θ2,θ3For industry
The joint of robot first is to the joint variable in the 3rd joint, a1And a2The length of first connecting rod and second connecting rod, d are represented respectively2Table
Show the biasing between first connecting rod and second connecting rod, x3,y3,z3It is tool coordinates system origin relative to third connecting rod coordinate system
Three coordinate components；
(3.2) matrix equation two ends to foundation in step (3.1) are while premultiplication first connecting rod coordinate system is relative to pedestal
The inverse matrix of the homogeneous transform matrix of system is marked, inverse kinematic equation is set up, tries to achieve the joint values in the first joint and the 3rd joint
θ1And θ3：
Wherein, a1And a2The length of first connecting rod and second connecting rod, d are represented respectively2Represent first connecting rod, second connecting rod it
Between biasing；
(3.3) matrix equation two ends to foundation in step (3.1) are while premultiplication third connecting rod coordinate system is relative to pedestal
The inverse matrix of the homogeneous transform matrix of system is marked, inverse kinematic equation is set up, tries to achieve the joint values θ of second joint2：
Wherein, c3=cos (θ3), s3=sin (θ3)。
As it is further preferred that total points N of the interpolation is preferred to use following manner determination：
Wherein：x1,y1,z1For the positional value of track starting point, x2,y2,z2For the positional value of final on trajectory, V is interpolation rate,
T is interpolation cycle.
As it is further preferred that the interpolation rate is preferably 10mm/s, interpolation cycle is preferably 1ms.
As it is further preferred that also comprising the following steps before the step (1)：First according to six joint industrial machines
People sets up link rod coordinate system, and each joint variable that inverse kinematic obtains industrial robot is carried out to default path planning
Value, then judges whether six joint industrial robots are in posture singular point, if so, then entering step (1), if it is not, then being solved with counter
Each joint variable value of the industrial robot of acquisition realizes the motion control of industrial robot.
According to another aspect of the present invention, there is provided the control system that a kind of six joint industrial robot passes through posture singular point
System, it includes：
Data acquisition module, for intercepting one section of rail in the default path planning of industrial robot residing for posture singular point
Mark, obtains the corresponding positional value of track starting point and rear three joint variable values and the corresponding positional value of the final on trajectory with after
Three joint variable values；
Interpolation module, for the rear three joint variable values and rear three joint variable values of terminal according to the starting point
The corresponding rear three joint variable values of posture singular position are obtained in the way of interpolation；
Data processing module, for setting up inverse kinematic equation and asking for first three corresponding joint of posture singular position
Variate-value；
Motion-control module, for the corresponding rear three joint variable values of the posture singular position and first three pass
Variate-value is saved as industrial robot in the corresponding motion control parameter of posture singular position, the motion control of industrial robot is realized
System, with this so that six joint industrial robots pass through posture singular point.
As it is further preferred that the data processing module includes following submodule：
Matrix equation setting up submodule, for setting up equation below：
Wherein, xt,yt,ztThree coordinate components for tool coordinates system origin relative to base coordinate system, s1=sin (θ1),
s2=sin (θ2), s23=sin (θ2+θ3), c1=cos (θ1), c2=cos (θ2), c23=cos (θ2+θ3), θ1,θ2,θ3For industry
The joint of robot first is to the joint variable in the 3rd joint, a1And a2The length of first connecting rod and second connecting rod, d are represented respectively2Table
Show the biasing between first connecting rod and second connecting rod, x3,y3,z3It is tool coordinates system origin relative to third connecting rod coordinate system
Three coordinate components；
First joint values calculating sub module, the matrix equation two ends for being set up to matrix equation setting up submodule are simultaneously left
Multiply inverse matrix of the first connecting rod coordinate system relative to the homogeneous transform matrix of base coordinate system, set up inverse kinematic equation, try to achieve
First joint and the joint values θ in the 3rd joint1And θ3：
Second joint value calculating sub module, the matrix equation two ends for being set up to matrix equation setting up submodule are simultaneously left
Multiply inverse matrix of the third connecting rod coordinate system relative to the homogeneous transform matrix of base coordinate system, set up inverse kinematic equation, try to achieve
The joint values θ of second joint2：
Wherein, c3=cos (θ3), s3=sin (θ3)。
As it is further preferred that the total points N of interpolation when the interpolation module carries out interpolation is preferred to use following manner
It is determined that：
Wherein：x1,y1,z1For the positional value of track starting point, x2,y2,z2For the positional value of final on trajectory, V is interpolation rate,
T is interpolation cycle.
As it is further preferred that the interpolation rate is preferably 10mm/s, interpolation cycle is preferably 1ms.
As it is further preferred that the control system also includes judge module, for according to six joint industrial robots
Link rod coordinate system is set up, and to each joint variable value of default path planning progress inverse kinematic acquisition industrial robot,
Then judge whether six joint industrial robots are in posture singular point, if so, then entering step (1), if it is not, then being obtained with anti-solution
Each joint variable value of industrial robot realize the motion control of industrial robot.
In general, possess following compared with prior art, mainly by the contemplated above technical scheme of the present invention
Technological merit：
1. the present invention keeps constant using by the original position in industrial robot end, interpolation obtains industrial robot end appearance
The mode of state, so that industrial robot passes through posture singular point on the premise of original path planning is not changed, is substantially reduced
The production cost of posture singular point is tided over by external equipment, it is to avoid the complexity for using path planning mode obtaining analytic solutions changes
For computing, the numerical solution of joint position can be directly obtained, it is simple and easy to apply and operation efficiency is high, it is adaptable to which that rear three joints meet at one
The industrial robot of point.
2. the present invention is from industrial robot motion control field so that industrial robot passes through posture singular point,
Extend the motion control instruction scope of industrial robot so that the space of industrial robot is expanded, it is more clever
It is living and intelligent, it is to avoid because range of movement reduces or alarmed caused by posture singular point the problems such as, program directly can be implanted to work
In industry Robot Motion Controller so that industrial robot can pass through posture singular point without stopping, and give actual production band
Carry out convenience.
3. the present invention is also applied to the path planning of no posture singular point, operating path is not obtained by inverse kinematic
The joint values of middle series of points, and then the phenomenon that the joint variable value in the 4th joint in anti-solution preocess can not be asked for is avoided, can
Joint values are directly obtained by interpolation, it is simple and easy to apply, it is practical.
Brief description of the drawings
Fig. 1 is flow chart of the six joint industrial robots by posture singular point；
Fig. 2 (a) and (b) are the configuration pictures of the industrial robot of Central China numerical control 6012；
Fig. 3 is each link rod coordinate system of the industrial robot of Central China numerical control 6012.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below
Not constituting conflict each other can just be mutually combined.
A kind of six joint industrial robot of the present invention specifically includes following steps by the control method of posture singular point：
(1) one section of track in the default path planning of industrial robot residing for interception posture singular point, obtains the track and rises
The positional value and rear three joint variable values of the positional value of initial point and rear three joint variable values and final on trajectory；
(2) according to rear three joint variable values of the starting point and rear three joint variable values of terminal with interpolation
Mode obtains the corresponding rear three joint variable values of posture singular position；
(3) first three corresponding joint variable value of posture singular position is asked for；
(4) it is used as work using the corresponding rear three joint variable values of the posture singular position and first three joint variable value
Industry robot realizes the motion control of industrial robot, with this so that six in the corresponding motion control parameter of posture singular position
Joint industrial robot passes through posture singular point.
Asking for and calculating for the ease of each variable, needs to do following preparation before step (1)：According to six joints
Industrial robot (including six joints and six roots of sensation connecting rod, respectively the first joint, second joint, the 3rd joint, the 4th joint,
5th joint, the 6th joint, first connecting rod, second connecting rod, third connecting rod, fourth link, the 5th connecting rod, six-bar linkage) knot
Structure feature sets up link rod coordinate system, and the coordinate system can be set up using many existing modes, and the present invention sets up coordinate with D-H methods
It is illustrative exemplified by system, it is not as a limitation of the invention.
Link rod coordinate system is set up using D-H methods according to the design feature of industrial robot：Using joint i axis direction as
The z-axis z of coordinate system { i }i, using joint i and i+1 axis common vertical line direction as coordinate system { i } x-axis xi, point to by joint i
To joint i+1, the y-axis y of coordinate system { i } is provided according to right-hand rulei, xiAnd yiIntersection point as coordinate system { i } origin oi,
Basis coordinates system is arbitrarily selected, for the sake of simple and convenient, and basis coordinates system { 0 } preferably is overlapped with the coordinate system { 1 } of connecting rod 1, will
The intersection point of three joints axes is elected to be as link rod coordinate system { 4 }, the origin of { 5 } and { 6 }, so far foundation industry after industrial robot
Each link rod coordinate system of robot.
According to above-mentioned set link rod coordinate system, corresponding link parameters can be defined as follows：
ai-1=from zi-1To ziAlong xi-1The distance of measurement；
αi-1=from zi-1To ziAround xi-1The angle of rotation；
di=from xi-1To xiAlong ziThe distance of measurement；
θi=from xi-1To xiAround ziThe angle of rotation.
Corresponding link parameters are listed according to each link rod coordinate system of foundation, calculated respectively using listed link parameters
Individual connecting rod transformation matrixDerive of equal value secondly transformation matrix of the third connecting rod coordinate system relative to basis coordinates systemWith
Homogeneous transform matrix of the six-bar linkage coordinate system relative to third connecting rod coordinate system
Wherein, i=0,1..., 6, θ1,θ2,θ3For the joint variable in the first joint to the 3rd joint, { i } is represented and connecting rod i
Affixed coordinate system,Homogeneous transform matrix for industrial robot link rod coordinate system { i } relative to { i+1 }.
Specifically, as shown in figure 3, the axis in the first joint is vertical direction, as the z-axis z of coordinate system { 1 }1, it is excellent
The sensing of choosing upwards, using the first joint and the axis common vertical line direction of second joint as coordinate system { 1 } x-axis x1, point to by
First joint is to second joint, then x1And z1Intersection point be coordinate system { 1 } origin o1；Second joint and the 3rd joint
Axis is horizontal direction, respectively as coordinate system { 2 } and the z-axis z of { 3 }2And z3, and z2And z3Be parallel to each other, by second joint and
The axis common vertical line direction in the 3rd joint as coordinate system { 2 } x-axis x2, x2And z2Intersection point be coordinate system { 2 } origin
o2；Using the axis common vertical line direction in the 3rd joint and the 4th joint as coordinate system { 3 } x-axis x3, x3And z3Intersection point be sit
The origin o of mark system { 3 }3；Basis coordinates system can be with arbitrarily selected, for the sake of simple and convenient, basis coordinates system { 0 } and first preferably
The coordinate system { 1 } of connecting rod is overlapped；The axis in the 4th joint, the 5th joint and the 6th joint is met at a bit, this is clicked as even
Bar coordinate system { 4 }, the origin o of { 5 } and { 6 }4,5,6, using the axis direction in the 4th joint as coordinate system { 4 } z-axis z4, preferably
Coordinate system { 4 } x-axis x4Direction and x3Unanimously, using the axis direction in the 5th joint as coordinate system { 5 } z-axis z5, preferably
Coordinate system { 6 } z-axis z6Direction and z4Unanimously, preferably the x-axis x of coordinate system { 5 }5With the x-axis x of coordinate system { 6 }6Side
To with x4Unanimously；It is preferred that tool tip center as tool coordinates system { T } origin oT, the x of tool coordinates system { T } preferably
Axle xTDirection and x6Unanimously, preferably the z-axis z of tool coordinates system { T }TDirection and z6Unanimously.From z1To z2Along x1Distance
For a1, from x1To x2Along z2Distance be d2, from z2To z3Along x2Distance be a2, from z3To z4Along x3Distance be a3, from x3To x4
Along z4Distance be d4.Corresponding link parameters are listed according to each link rod coordinate system of foundation, listed link parameters meter is utilized
Calculate each connecting rod transformation matrixDerive of equal value secondly transformation matrix of the third connecting rod coordinate system relative to basis coordinates systemHomogeneous transform matrix with six-bar linkage coordinate system relative to third connecting rod coordinate system
Wherein, i=0,1..., 6, θiFor joint i joint variable, si=sin (θi), ci=cos (θi), s23=sin (θ2
+θ3), c23=cos (θ2+θ3), { i } is represented and coordinate system affixed connecting rod i,For industrial robot link rod coordinate system { i } phase
For the homogeneous transform matrix of { i-1 }.
Set up after link rod coordinate system, to default path planning, (path is determined that the present invention is not done by actual motion demand
Limit) each joint variable value that inverse kinematic obtains industrial robot is carried out, it is prior art, be will not be described here, normally
In the case of industrial robot moved according to default path planning, namely when being not at posture singular point, industrial robot is just
Often operation, when the joint variable value in the 4th joint can not be asked for, i.e. the joint variable in the 5th joint is zero, now industrial machine
People is in posture singular point, because the 5th joint variable is zero, it is difficult to pass through, therefore motion of the present invention to industrial robot
Pose carries out following handle：
(1) one section of track in path planning residing for interception posture singular point, in order to improve operation efficiency, track preferably is
Whole arc section or straightway where posture singular point, the positional value and rear three joints for then obtaining this track initial point become
Value, and final on trajectory positional value and rear three joint variable values；
(2) and then by the positional value of starting point and rear three joint variable values, and the positional value of final on trajectory and rear three
Individual joint variable value, which is transported in interpolator, carries out the corresponding rear three joint variable values of interpolation acquisition posture singular position, specifically
According to starting and final position be worth, interpolation rate V and interpolation cycle T can obtain wanting total points N of interpolation, the interpolation of interpolator
Speed and interpolation cycle can be given according to the actual demand of industrial robot, it is contemplated that the precision and efficiency of interpolation, preferably insert
Benefit speed is 10mm/s, and interpolation cycle is 1ms, according to the total points N of interpolation by interpolation between track starting point and final on trajectory into N
Part, namely also interpolation, into N part, obtains posture singular point between rear three joint variable values between track starting point and final on trajectory
Put corresponding rear three joint variable values；Wherein, track starting point, final on trajectory and posture singular point that interpolation is obtained positional value
It is respectively with rear three joint variable values：x1,y1,z1,θ41,θ51,θ61,x2,y2,z2,θ42,θ52,θ62,xt,yt,zt,θ4t,θ5t,
θ6t,
When in posture singular point, the type of sports of industrial robot is linear motion or circular motion, therefore is passed through
The each point that interpolator interpolation is obtained is on original path planning.
(3) first three corresponding joint variable value of posture singular position is asked for
(3.1) following matrix equation is initially set up：
Wherein, xt,yt,ztThree coordinate components for tool coordinates system origin relative to basis coordinates system, s1=sin (θ1),
s2=sin (θ2), s23=sin (θ2+θ3), c1=cos (θ1), c2=cos (θ2), c23=cos (θ2+θ3), θ1,θ2,θ3For industry
The joint of robot first is to the joint variable in the 3rd joint, a1And a2The length of first connecting rod and second connecting rod, d are represented respectively2Table
Show the biasing between first connecting rod and second connecting rod, x3,y3,z3It is tool coordinates system origin relative to third connecting rod coordinate system
Three coordinate components；
Specifically matrix equation is set up in the following way：
Homogeneous transform matrix phase by rear three connecting rod transformation matrixs and tool coordinates system relative to six-bar linkage coordinate system
Multiplying to obtain：
I.e.
Wherein,Representational tool coordinate system relative to third connecting rod coordinate system spin matrix,Representational tool coordinate system
Relative to the spin matrix of six-bar linkage coordinate system,Representational tool coordinate system is sweared relative to the position of third connecting rod coordinate system
Amount,Position vector of the representational tool coordinate system relative to six-bar linkage coordinate system；
The 4th column element correspondent equal at equation two ends is made, rear three joint variable values of posture singular point pass through interpolation
Obtain, be known on the right of equation：
First three joint of industrial robot be connected (i.e. without relative motion), it is known that tool coordinates system is relative to base
The position vector of coordinate system is：Tool coordinates system is relative to the position vector of third connecting rod coordinate system：Three joint variables are obtained by interpolation afterwards, and the kinematical equation of industrial robot is write as：
I.e.
The 4th column element correspondent equal at above-mentioned matrix equation two ends is made, equation below can be set up：
I.e.
(3.2) matrix equation two ends to foundation in step (3.1) are while premultiplication first connecting rod coordinate system is relative to pedestal
The inverse matrix of the homogeneous transform matrix of system is marked, inverse kinematic equation is set up, tries to achieve the joint values in the first joint and the 3rd joint
θ1And θ3：
Specially：The matrix equation two ends set up in step (3.1) are while premultiplication first connecting rod coordinate system is relative to base
The inverse matrix of the homogeneous transform matrix of coordinate systemSet up inverse kinematic equation as follows：
Dissolve：
In formula,Can be byInvert acquisition.
The element correspondent equal of order matrix equation (1) two ends the second row first row is obtained：
-s1xt+c1yt=-z3-d2；
IfThen obtain the joint variable value θ in the first joint1：
Selected θ1After one of solution, the member that the row of order matrix equation (1) two ends the first row the 4th and the third line the 4th are arranged
Correspondent equal is obtained element respectively：
The quadratic sum of above-mentioned two formula is：
-s3y3+c3x3=k,
IfThen obtain the joint variable value θ in the 3rd joint3：
(3.3) matrix equation two ends to foundation in step (3.1) are while premultiplication third connecting rod coordinate system is relative to pedestal
The inverse matrix of the homogeneous transform matrix of system is marked, inverse kinematic equation is set up, tries to achieve the joint values θ of second joint2：
Wherein, c3=cos (θ3), s3=sin (θ3)。
Specially：The matrix equation two ends set up in step (3.1) are while premultiplication third connecting rod coordinate system is relative to base
The inverse matrix of the homogeneous transform matrix of coordinate systemSet up inverse kinematic equation as follows：
Dissolve
In formula,Can be byInvert acquisition.
Correspondent equal is obtained the element that order matrix equation (2) two ends the first row the 4th is arranged and the second row the 4th is arranged respectively：
Both the above solving simultaneous equation is obtained into s23With：
It can be seen that s23And c23The denominator of expression formula is equal, and just, then to try to achieve the joint variable value θ of second joint2：
Wherein, s2=sin (θ2)；c2=cos (θ2)；s23=sin (θ2+θ3)；c23=cos (θ2+θ3)。
(4) it is used as work using the corresponding rear three joint variable values of the posture singular position and first three joint variable value
Industry robot realizes the motion control of industrial robot, with this so that six in the corresponding motion control parameter of posture singular position
Joint industrial robot passes through posture singular point.Also first three the joint variable value that will be obtained by above-mentioned algorithm and interpolation are obtained
To rear three joint variable values be sent in industrial robot motion controller so that six joints of industrial robot are in appearance
State singular point is respectively provided with determination numerical value, in this way, realizes that industrial robot passes through posture singular point.
Present invention also offers a kind of control system of six joint industrial robot by posture singular point, including：Data are obtained
Modulus block, for intercepting one section of track in the default path planning of industrial robot residing for posture singular point, obtains the track and rises
The corresponding positional value of point and rear three joint variable values and the corresponding positional value of the final on trajectory and rear three joint variable values；
Interpolation module, for the rear three joint variable values and rear three joint variable values of terminal according to the starting point with interpolation
Mode obtains the corresponding rear three joint variable values of posture singular position；Data processing module, for setting up inverse kinematic side
Journey simultaneously asks for first three corresponding joint variable value of posture singular position；Motion-control module, for posture singular point position
Corresponding rear three joint variable values and first three joint variable value are put as industrial robot in posture singular position correspondence
Motion control parameter, the motion control of industrial robot is realized, with this so that six joint industrial robots pass through posture
Singular point.
Specifically, the data processing module includes following submodule：
Matrix equation setting up submodule, for setting up equation below：
Wherein, xt,yt,ztRespectively tool coordinates system origin is relative to three coordinate components of base coordinate system, s1=sin
(θ1), s2=sin (θ2), s23=sin (θ2+θ3), c1=cos (θ1), c2=cos (θ2), c23=cos (θ2+θ3), θ1,θ2,θ3For
The joint of industrial robot first is to the joint variable in the 3rd joint, a1And a2The length of first connecting rod and second connecting rod is represented respectively,
d2Represent the biasing between first connecting rod and second connecting rod, x3,y3,z3Respectively tool coordinates system origin is relative to third connecting rod
Three coordinate components of coordinate system；
First joint values calculating sub module, the matrix equation two ends for being set up to matrix equation setting up submodule are simultaneously left
Multiply inverse matrix of the first connecting rod coordinate system relative to the homogeneous transform matrix of base coordinate system, set up inverse kinematic equation, try to achieve
First joint and the joint values θ in the 3rd joint1And θ3：
Second joint value calculating sub module, the matrix equation two ends for being set up to matrix equation setting up submodule are simultaneously left
Multiply inverse matrix of the third connecting rod coordinate system relative to the homogeneous transform matrix of base coordinate system, set up inverse kinematic equation, try to achieve
The joint values θ of second joint2：
Wherein, c3=cos (θ3), s3=sin (θ3)。
Specifically, the total points N of interpolation when the interpolation module carries out interpolation is preferred to use following manner determination：
Wherein：x1,y1,z1For the positional value of track starting point, x2,y2,z2For the positional value of final on trajectory, V is interpolation rate,
T is interpolation cycle.The interpolation rate is preferably 10mm/s, and interpolation cycle is preferably 1ms.
Specifically, the control system also includes judge module, sat for setting up connecting rod according to six joint industrial robots
Mark system, and each joint variable value that inverse kinematic obtains industrial robot is carried out to default path planning, then judge six
Whether joint industrial robot is in posture singular point, if so, then entering step (1), if it is not, the industrial machine then obtained with anti-solution
Each joint variable value of people realizes the motion control of industrial robot.
It is specific embodiment below：
The present embodiment is by taking the industrial robot of Central China numerical control 6012 as an example, and its configuration such as Fig. 2 (a) and (b) are shown, Central China numerical control
6012 industrial robots belong to prosthetic robot, and it is by 6 connecting rods (first connecting rod 1 as shown in Figure 2, second connecting rod 2,
Three connecting rods 3, fourth link 4, the 5th connecting rod 5, six-bar linkage 6) and 6 cradle heads (point A as shown in Figure 3, B, C, D, E,
F) composition, pedestal is fixed to be referred to as connecting rod 0, the first joint connection first connecting rod and second connecting rod, second joint connection second
Connecting rod and third connecting rod, by that analogy, instrument and connecting rod 6 are affixed.It is mainly included the following steps that by the process of posture singular point：
Step 1)：According to the design feature and D-H methods of the industrial robot of Central China numerical control 6012, the link rod coordinate system of setting
{ 0 }, { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 } and { T } are as shown in Figure 3：Basis coordinates system { 0 } is overlapped with the coordinate system { 1 } of connecting rod 1,
The z-axis z of coordinate system { 1 }1For the axis direction in the first joint, upward, the x-axis x of coordinate system { 1 } is pointed to1For first joint and 2
Axis common vertical line direction, is pointed to by the first joint to second joint, then the origin o of coordinate system { 1 }1As x1And z1Intersection point；
So far coordinate system { 1 }, which is set up, is completed, and coordinate { 2 } and { 3 } are set up by that analogy；Link rod coordinate system { 4 }, the origin of { 5 } and { 6 }
o4,5,6For the 4th joint, 5 and 6 crossing point of axes, the z-axis z of coordinate system { 4 }4For the axis direction in the 4th joint, coordinate system { 4 }
X-axis x4Direction and x3Unanimously, the z-axis z of coordinate system { 5 }5For the axis direction in the 5th joint, the z-axis z of coordinate system { 6 }6's
Direction and z4Unanimously, the x-axis x of coordinate system { 5 }5With the x-axis x of coordinate system { 6 }6Direction and x4Unanimously；Tool coordinates system { T }
Origin oTFor tool tip center, the x-axis x of tool coordinates system { T }TDirection and x6Unanimously, the z-axis z of tool coordinates system { T }T's
Direction and z6Unanimously.
Corresponding link parameters are listed according to each link rod coordinate system of foundation, as shown in table 1.
The link parameters of the industrial robot of 1 Central China numerical control of table 6012
Each connecting rod transformation matrix is calculated using listed link parameters, derives third connecting rod coordinate system relative to base
The secondly transformation matrix of equal value of coordinate system
Step 2)：Position when industrial robot is in posture singular point is：(1323.1,226.8,703.8), this posture is strange
Path where point is straight line, intercepts the whole straightway in its residing path planning, the positional value of this straightway starting point is
(999.2,450.9,532.3), the joint values of rear three joint variables are (- 108.5 °, -30.6 °, 223.8 °), the position of terminal
Value is put for (1512.3,105.6,796.4), the joint values of rear three joint variables are (36.3 °, -15.1 °, 77.1 °).
Step 3)：Starting point, the position of terminal and rear three joint variable values are transported in interpolator, interpolation rate
For 10mm/s, interpolation cycle is 1ms, total points N of interpolation：
By also interpolation, into 68 parts, obtains posture singular point position between track starting point and rear three joint variable values of final on trajectory
Put corresponding rear three joint variable values：(-11.9°,-20.2°,119.3°).
Step 4)：Known means coordinate system is relative to the position vector of six-bar linkage coordinate system：The rear three joint variable values θ that will be obtained by interpolation4, θ5, θ6Substitution formula (2)：
Therefore tool coordinates system is relative to the position vector of third connecting rod coordinate systemFor：
First three joint of industrial robot is connected, in posture singular point, it is known that tool coordinates system is relative to pedestal
Marking the position vector for being is：Three joint variable θ afterwards4, θ5, θ6Obtained by interpolation
, the kinematical equation of industrial robot is write as：
The 4th column element correspondent equal at order matrix equation (4) two ends, can set up equation below：
Premultiplication first connecting rod coordinate system is inverse relative to the homogeneous transform matrix of base coordinate system simultaneously at matrix equation (5) two ends
MatrixSet up inverse kinematic equation as follows：
The element correspondent equal of order matrix equation (6) two ends the second row first row is obtained：-1332.1s1+226.8c1=-
346.8(7)；Solve the joint variable value in the first joint：θ1=174.8 ° or θ1=24.5 °.
Selected θ1After one of solution, the member that the row of order matrix equation (6) two ends the first row the 4th and the third line the 4th are arranged
Correspondent equal is obtained element respectively：
The quadratic sum of above-mentioned two formula is：-(-1254)s3+(-42.1)c3=k (9)；
Wherein,
Solve proper θ1The joint variable value in the 3rd joint at=174.8 °：θ3=-343.5 ° or θ3=-192.6 °；Work as θ1=
The joint variable value in the 3rd joint at 24.5 °：θ3=-9.8 ° or θ3=-166.4 °.
Premultiplication third connecting rod coordinate system is inverse relative to the homogeneous transform matrix of base coordinate system simultaneously on matrix equation (5) both sides
MatrixSet up inverse kinematic equation as follows：
Correspondent equal is obtained the element that order matrix equation (10) two ends the first row the 4th is arranged and the second row the 4th is arranged respectively：
Both the above solving simultaneous equation is obtained into s23And c23,
Solve：θ23=-141 °, θ23=-86.1 °, θ23=88.8 °, θ23=158.5 °.
Therefore the joint variable value of second joint is：θ2=202.5 °, θ2=106.5 °, θ2=98.6 °, θ2=324,9 °.Before
Anti- solution one has four groups of solutions to three joint variables, as shown in table 2：
The anti-solution value of industrial robot first three joint variable of 2 Central China numerical control of table 6012
| θ1 | θ2 | θ3 | |
| First group | 174.8° | 202.5° | -343.5° |
| Second group | 174.8° | 106.5° | -192.6° |
| 3rd group | 24.5° | 98.6° | -9.8° |
| 4th group | 24.5° | 324.9° | -166.4° |
Only the 3rd group solution meets the range of movement in the given joint of table 1, i.e. first three joint variable is respectively：θ1=
24.5 °, θ2=98.6 °, θ3=-9.8 °.
Step 5)：Rear three joint variable values that first three the joint variable value obtained by above-mentioned algorithm and interpolation are obtained
It is sent in industrial robot motion controller so that six joints of industrial robot are respectively provided with determination number in posture singular point
Value；In this way, realize that industrial robot passes through posture singular point.
This example is according to above-mentioned position and inverse kinematic equation, first three pass when trying to achieve robot positioned at posture singular point
Variable is saved, and the joint variable in rear three joints is obtained by interpolation, obtained robot end is checked by forward kinematics solution
Position and actual end position consistency.
The invention provides a kind of control method of six joint industrial robot by posture singular point, do not changing original rule
Cause robot to pass through posture singular point on the premise of drawing path, greatly reduce and posture singular point is tided over by external equipment
Production cost, it is to avoid complicated interative computation of the path planning mode to analytic solutions, can directly obtaining robot, to be in posture strange
The numerical solution of joint position during point, simple and easy to apply and operation efficiency is high, and the present invention realizes motion planning and robot control instruction in addition
Program, can directly be implanted in Robot Motion Controller, convenience is brought to actual production by the extension of scope.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, it is not used to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the invention etc., it all should include
Within protection scope of the present invention.
Claims (10)
1. a kind of six joint industrial robot passes through the control method of posture singular point, it is characterised in that comprise the following steps：
(1) one section of track in the default path planning of industrial robot residing for interception posture singular point, obtains the track starting point pair
The positional value answered and rear three joint variable values and the corresponding positional value of the final on trajectory and rear three joint variable values；
(2) obtained according to rear three joint variable values of rear three joint variable values of the starting point and terminal in the way of interpolation
Obtain the corresponding rear three joint variable values of posture singular position；
(3) set up inverse kinematic equation and ask for first three corresponding joint variable value of posture singular position；
(4) it is used as industrial machine using the corresponding rear three joint variable values of the posture singular position and first three joint variable value
Device people realizes the motion control of industrial robot in the corresponding motion control parameter of posture singular position, with this so that six joints
Industrial robot passes through posture singular point.
2. six joint as claimed in claim 1 industrial robot passes through the control method of posture singular point, it is characterised in that described
Step (3) includes following sub-step：
(3.1) following matrix equation is initially set up：
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Wherein, xt,yt,ztThree coordinate components for tool coordinates system origin relative to base coordinate system, s1=sin (θ1), s2=
sin(θ2), s23=sin (θ2+θ3), c1=cos (θ1), c2=cos (θ2), c23=cos (θ2+θ3), θ1,θ2,θ3For industrial machine
The joint of people first is to the joint variable in the 3rd joint, a1And a2The length of first connecting rod and second connecting rod, d are represented respectively2Represent the
Biasing between one connecting rod and second connecting rod, x3,y3,z3Three for tool coordinates system origin relative to third connecting rod coordinate system
Coordinate components；
(3.2) matrix equation two ends to foundation in step (3.1) are while premultiplication first connecting rod coordinate system is relative to base coordinate system
Homogeneous transform matrix inverse matrix, set up inverse kinematic equation, try to achieve the joint values θ in the first joint and the 3rd joint1With
θ3：
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(3.3) matrix equation two ends to foundation in step (3.1) are while premultiplication third connecting rod coordinate system is relative to base coordinate system
Homogeneous transform matrix inverse matrix, set up inverse kinematic equation, try to achieve the joint values θ of second joint2：
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Wherein, c3=cos (θ3), s3=sin (θ3)。
3. six joint as claimed in claim 1 or 2 industrial robot passes through the control method of posture singular point, it is characterised in that
Total points N of the interpolation is preferred to use following manner determination：
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Wherein：x1,y1,z1For the positional value of track starting point, x2,y2,z2For the positional value of final on trajectory, V is interpolation rate, and T is
Interpolation cycle.
4. six joint as claimed in claim 3 industrial robot passes through the control method of posture singular point, it is characterised in that described
Interpolation rate is preferably 10mm/s, and interpolation cycle is preferably 1ms.
5. the six joint industrial robots as described in claim any one of 1-4 pass through the control method of posture singular point, its feature
It is, also comprises the following steps before the step (1)：Link rod coordinate system is set up according to six joint industrial robots first, and
Each joint variable value that inverse kinematic obtains industrial robot is carried out to default path planning, the industry of six joints is then judged
Whether robot is in posture singular point, if so, then entering step (1), if it is not, each pass of the industrial robot then obtained with anti-solution
Section variate-value realizes the motion control of industrial robot.
6. a kind of six joint industrial robot passes through the control system of posture singular point, it is characterised in that including：
Data acquisition module, for intercepting one section of track in the default path planning of industrial robot residing for posture singular point, is obtained
Take the corresponding positional value of track starting point and rear three joint variable values and the corresponding positional value of the final on trajectory and latter three
Joint variable value；
Interpolation module, for the rear three joint variable values and rear three joint variable values of terminal according to the starting point with slotting
The mode of benefit obtains the corresponding rear three joint variable values of posture singular position；
Data processing module, for setting up inverse kinematic equation and asking for first three corresponding joint variable of posture singular position
Value；
Motion-control module, for being become with the corresponding rear three joint variable values of the posture singular position and first three joint
Value, in the corresponding motion control parameter of posture singular position, realizes the motion control of industrial robot as industrial robot,
With this so that six joint industrial robots pass through posture singular point.
7. six joint as claimed in claim 6 industrial robot passes through the control system of posture singular point, it is characterised in that described
Data processing module includes following submodule：
Matrix equation setting up submodule, for setting up equation below：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mi>t</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mi>t</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>z</mi>
<mi>t</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>c</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>d</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>c</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>d</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>s</mi>
<mn>23</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>c</mi>
<mn>23</mn>
</msub>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>s</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mn>3</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mn>3</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>z</mi>
<mn>3</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
Wherein, xt,yt,ztThree coordinate components for tool coordinates system origin relative to base coordinate system, s1=sin (θ1), s2=
sin(θ2), s23=sin (θ2+θ3), c1=cos (θ1), c2=cos (θ2), c23=cos (θ2+θ3), θ1,θ2,θ3For industrial machine
The joint of people first is to the joint variable in the 3rd joint, a1And a2The length of first connecting rod and second connecting rod, d are represented respectively2Represent the
Biasing between one connecting rod and second connecting rod, x3,y3,z3Three for tool coordinates system origin relative to third connecting rod coordinate system
Coordinate components；
First joint values calculating sub module, for the matrix equation two ends set up to matrix equation setting up submodule premultiplication the simultaneously
One link rod coordinate system sets up inverse kinematic equation, tries to achieve first relative to the inverse matrix of the homogeneous transform matrix of base coordinate system
Joint and the joint values θ in the 3rd joint1And θ3：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<mn>1</mn>
</msub>
<mo>=</mo>
<mi>A</mi>
<mi>tan</mi>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>t</mi>
</msub>
<mo>,</mo>
<msub>
<mi>x</mi>
<mi>t</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>A</mi>
<mi>tan</mi>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mo>-</mo>
<msub>
<mi>z</mi>
<mn>3</mn>
</msub>
<mo>-</mo>
<msub>
<mi>d</mi>
<mn>2</mn>
</msub>
<mo>,</mo>
<mo>&PlusMinus;</mo>
<msqrt>
<mrow>
<msubsup>
<mi>x</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mn>3</mn>
</msub>
<mo>+</mo>
<msub>
<mi>d</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<mn>3</mn>
</msub>
<mo>=</mo>
<mi>A</mi>
<mi>tan</mi>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>3</mn>
</msub>
<mo>,</mo>
<msub>
<mi>y</mi>
<mn>3</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>A</mi>
<mi>tan</mi>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>,</mo>
<mo>&PlusMinus;</mo>
<msqrt>
<mrow>
<msubsup>
<mi>x</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msup>
<mi>k</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>x</mi>
<mi>t</mi>
</msub>
<mo>+</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>y</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msubsup>
<mi>z</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mn>3</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>a</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>2</mn>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
Second joint value calculating sub module, for the matrix equation two ends set up to matrix equation setting up submodule premultiplication the simultaneously
Three link rod coordinate systems set up inverse kinematic equation, try to achieve second relative to the inverse matrix of the homogeneous transform matrix of base coordinate system
The joint values θ in joint2：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mi>&theta;</mi>
<mn>23</mn>
</msub>
<mo>=</mo>
<mi>A</mi>
<mi>t</mi>
<mi>a</mi>
<mi>n</mi>
<mn>2</mn>
<mo>&lsqb;</mo>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>3</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>c</mi>
<mn>3</mn>
</msub>
<mo>)</mo>
<msub>
<mi>z</mi>
<mi>t</mi>
</msub>
<mo>+</mo>
<mo>(</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>x</mi>
<mi>t</mi>
</msub>
<mo>+</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>y</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>s</mi>
<mn>3</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>3</mn>
</msub>
<mo>)</mo>
<mo>,</mo>
<mo>(</mo>
<msub>
<mi>y</mi>
<mn>3</mn>
</msub>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>s</mi>
<mn>3</mn>
</msub>
<mo>)</mo>
<msub>
<mi>z</mi>
<mi>t</mi>
</msub>
<mo>+</mo>
<mo>(</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msub>
<mi>x</mi>
<mi>t</mi>
</msub>
<mo>+</mo>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<msub>
<mi>y</mi>
<mi>t</mi>
</msub>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>2</mn>
</msub>
<msub>
<mi>c</mi>
<mn>3</mn>
</msub>
<mo>+</mo>
<msub>
<mi>x</mi>
<mn>3</mn>
</msub>
<mo>)</mo>
<mo>&rsqb;</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&theta;</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<msub>
<mi>&theta;</mi>
<mn>23</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mn>3</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
Wherein, c3=cos (θ3), s3=sin (θ3)。
8. the control system that six joint industrial robots as claimed in claims 6 or 7 pass through posture singular point, it is characterised in that
The total points N of interpolation when the interpolation module carries out interpolation is preferred to use following manner determination：
<mrow>
<mi>N</mi>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
<mo>/</mo>
<mi>V</mi>
<mi>T</mi>
<mo>;</mo>
</mrow>
Wherein：x1,y1,z1For the positional value of track starting point, x2,y2,z2For the positional value of final on trajectory, V is interpolation rate, and T is
Interpolation cycle.
9. six joint as claimed in claim 8 industrial robot passes through the control system of posture singular point, it is characterised in that described
Interpolation rate is preferably 10mm/s, and interpolation cycle is preferably 1ms.
10. six joint as claimed in claim 6 industrial robot passes through the control system of posture singular point, it is characterised in that institute
Stating control system also includes judge module, for setting up link rod coordinate system according to six joint industrial robots, and to default rule
Draw path and carry out each joint variable value that inverse kinematic obtains industrial robot, whether then judge six joint industrial robots
In posture singular point, if so, then entering step (1), if it is not, each joint variable value of the industrial robot then obtained with anti-solution is real
The motion control of existing industrial robot.
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| CN108268013A (en) * | 2017-12-29 | 2018-07-10 | 北京航空航天大学 | A kind of high speed and super precision interpolation system and beeline interpolation algorithm based on FPGA |
| CN108724191A (en) * | 2018-06-27 | 2018-11-02 | 芜湖市越泽机器人科技有限公司 | A kind of robot motion's method for controlling trajectory |
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| CN108227492A (en) * | 2018-01-03 | 2018-06-29 | 华中科技大学 | A kind of discrimination method of six degree of freedom serial manipulator end load kinetic parameter |
| CN108724191A (en) * | 2018-06-27 | 2018-11-02 | 芜湖市越泽机器人科技有限公司 | A kind of robot motion's method for controlling trajectory |
| CN109483551B (en) * | 2018-12-26 | 2020-08-11 | 合肥欣奕华智能机器有限公司 | Method, device and system for controlling multi-axis motion of robot |
| CN109483551A (en) * | 2018-12-26 | 2019-03-19 | 合肥欣奕华智能机器有限公司 | A kind of method, apparatus and system controlling robot multiaxial motion |
| CN110850807A (en) * | 2019-12-04 | 2020-02-28 | 广东博智林机器人有限公司 | Singular point avoiding method, device, equipment and medium |
| CN110850807B (en) * | 2019-12-04 | 2021-04-27 | 广东博智林机器人有限公司 | Singular point avoiding method, device, equipment and medium |
| CN111958602A (en) * | 2020-08-20 | 2020-11-20 | 华中科技大学 | Real-time inverse solution method for wrist offset type 6-axis robot |
| CN111958602B (en) * | 2020-08-20 | 2022-05-20 | 华中科技大学 | Real-time inverse solution method for wrist offset type 6-axis robot |
| CN112405525A (en) * | 2020-10-21 | 2021-02-26 | 深圳市汇川技术股份有限公司 | Singular position avoiding method, system, equipment and computer readable storage medium |
| CN114378830A (en) * | 2022-02-18 | 2022-04-22 | 深圳市大族机器人有限公司 | Robot wrist joint singularity avoidance method and system |
| CN114378830B (en) * | 2022-02-18 | 2024-02-20 | 深圳市大族机器人有限公司 | Robot wrist joint singular avoidance method and system |
| CN116277039A (en) * | 2023-05-23 | 2023-06-23 | 极限人工智能(北京)有限公司 | Method, system, equipment and medium for planning track of robot arm passing wrist singular point |
| CN116277039B (en) * | 2023-05-23 | 2024-04-05 | 极限人工智能(北京)有限公司 | Method, system, equipment and medium for planning track of robot arm passing wrist singular point |
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