CN105511266B - The Delta method for planning track of robot of particle cluster algorithm is searched for based on gravitation - Google Patents
The Delta method for planning track of robot of particle cluster algorithm is searched for based on gravitation Download PDFInfo
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Abstract
The present invention provides a kind of Delta method for planning track of robot for searching for particle cluster algorithm based on gravitation, and Delta robots main belt working region is divided into M × N number of grid by the way of mesh generation and determines standard point coordinates；It builds cartesian space "door" type and captures track, derive the Inverse Kinematics Solution of each driving shaft angle and end effector position；Particle cluster algorithm is searched for using gravitation, using time optimal as fitness function, under conditions of meeting joint velocity, acceleration, pulsation continuously smooth and limits value specified no more than servo motor, 7 non-uniform rational B-spline functions are constructed, the angle timing node sequence of offline interpolation joint space is obtained；After Delta robots online recognition goes out coordinate of ground point, the angle discrete series of joint space are calculated, data of the inquiry offline storage in three-dimensional array obtain timing node sequence, set movement is completed in programming movement track.
Description
Technical field
The present invention relates to Delta robot trajectory plannings fields, in particular to a kind of gravitation that is based on to search for particle cluster algorithm
Delta method for planning track of robot.
Background technology
In industry spot, the Origin And Destination of robot motion need to be only given, robot can complete corresponding actions.For
Ensure the compliance acted between robot terminal, reduces the abrasion of mechanical structure, and meeting servo motor indices
Under the premise of quick acting, need to carry out trajectory planning to the action process in each joint of robot.
Currently, difference of the trajectory planning scheme according to optimization aim, can be divided into energetic optimum, time optimal, minimal ripple
Etc. types.Wherein, time optimal and the trajectory planning of minimal ripple disclosure satisfy that industry spot to production efficiency and extend machine
The demand of tool service life, application are relatively broad.Time optimal trajectory planning will mainly seek timing node be converted into it is non-linear
Optimization problem currently proposes many solutions both at home and abroad for non-linear optimization problem, such as particle swarm optimization algorithm, letter
Rely domain algorithm, adaptive harmonic search algorithm and quadratic programming etc..Due to the complexity and at this stage of above-mentioned optimization algorithm
The constraint of hardware calculating speed, real-time become the bottleneck that the algorithm is applied to industrial robot.
Invention content
Each joint start and stop are without friction when the present invention is in order to reach different location object on Delta robots crawl main belt
And the shortest purpose of run time, provide it is a kind of meet industrial requirement of real-time particle cluster algorithm is searched for based on gravitation
Delta robots time optimal trajectory planning method.
For this purpose, the present invention is achieved through the following technical solutions：
A. use the mode of mesh generation by Delta robots main belt working region be divided into M × N number of length of side for
dcm(0<D≤2) square, each square is known as grid, and selections grid element center point is standard point；
B. in cartesian space, to the standard point and fixed placement point Q in the step A6Using straight line and circular interpolation
Mode, obtain the position discrete series { Q of cartesian space "door" type track0,Q1,…Q6}；
C. according to Delta robot architecture's models, each driving shaft angle, θ is found out1,θ2,θ3With end effector position E0's
Inverse Kinematics Solution；
D. according to the Inverse Kinematics Solution in the step C by the position of cartesian space "door" type track in the step B
Discrete series { Q0,Q1,…Q6It is converted into the angle discrete series { P of Delta robotic joint spaces0,P1,…P6}；
E. the timing node sequence { t of w group joint spaces is initialized0,t1,…t6, the timing node sequence of every group of joint space
Row are consistent using standard point as the timing node sequence corresponding to the "door" type track of starting point with cartesian space, said for simplification
It is bright, hereafter referred to collectively as " timing node sequence ", and interval { the Δ t of every group of timing node sequence0,Δt1,…Δt5Be 1s with
Interior random number；
F. by the angle discrete series { P of joint space in the step D0,P1,…P6With the step E in any one group
Timing node sequence { t0,t1,…t6Corresponding, form angle-timing node sequence { P of joint spacei, ti, i=0,1 ...
6, and angle-timing node sequence of 7 non-uniform rational B-spline function interpolation joint spaces is constructed, control each joint
Movement；
G. build time adaptive optimal control degree function is meeting joint velocity, acceleration, pulsation continuously smooth and no more than watching
Under conditions of taking Rated motor limits value, particle cluster algorithm is searched for using gravitation, to w group timing node sequences { t0,t1,…t6}
Off-line optimization exports one group of optimal time sequence node until meeting maximum iteration；
H. it uses offline mode to M × N number of standard point in the step A, repeats step B~G described above, obtain M × N
Group is using standard point as the optimal time sequence node { t corresponding to the "door" type track of starting point0,t1,…t6And it is stored in three dimensions
In group A and B；
I. industrial intelligent camera identifies the central point of object on main belt, which is known as target point, using looking into online
Inquiry mode is obtained using mesh standard point where target point as one group of optimal time node sequence corresponding to the "door" type track of starting point
Arrange { t0,t1,…t6, while the target point is used into the method similar to standard point, it repeats the above step B~D and quickly advises
Robot motion track is drawn, set movement is completed.
The beneficial effects of the invention are as follows：Provide the Delta robots time optimal that particle cluster algorithm is searched for based on gravitation
Method for planning track.Delta robots main belt working region is divided into M × N number of grid by the way of mesh generation
And determine standard point coordinates；It builds cartesian space "door" type and captures track, derive each driving shaft angle and end effector
The Inverse Kinematics Solution of position；Particle cluster algorithm is searched for using gravitation, using time optimal as fitness function, is meeting joint speed
Degree, acceleration, pulsation continuously smooth and no more than under conditions of the specified limits value of servo motor, construct 7 non-uniform rational B samples
Function, obtains angle-timing node sequence of offline interpolation joint space；Delta robots online recognition goes out target point seat
After mark, the angle discrete series of joint space are calculated, data of the inquiry offline storage in three-dimensional array obtain timing node sequence
Row, set movement is completed in programming movement track.
Description of the drawings
Attached drawing is used to provide further understanding of the present invention, and a part for constitution instruction, the reality with the present invention
It applies example to be used to explain the present invention together, not be construed as limiting the invention.In the accompanying drawings：
Fig. 1 is off-line algorithm flow；
Fig. 2 is on-line Algorithm flow；
Fig. 3 is gridding main belt working region；
Fig. 4 is cartesian space "door" type crawl track；
Fig. 5 is Delta robot kinematics' models；
Fig. 6 is standard point and target point in grid.
Specific implementation mode
To make the objectives, technical solutions, and advantages of the present invention clearer with reference to specific embodiments and reference
Attached drawing, invention is further described in detail.
General object of the present invention is with the artificial platform of Delta machines, to different location object on crawl main belt
Action carries out trajectory planning, under conditions of meeting robot servo motors specified limits value, hunting time optimal motion track.
Entire algorithm flow is broadly divided into target positioning, off-line optimization goes out optimal time sequence node, online query optimal time node
Sequence, as shown in Figure 1 and Figure 2.
Further, specific implementation step is：
A. Delta robots main belt working region is divided into M × N number of square by the way of mesh generation,
Each square is known as grid, and its side length is dcm, the numerical value of d no more than 2 and generally takes 1 or 2, and the value of M is generally even number, choosing
It is standard point to take grid element center point.Such as Fig. 3, M ' × N number of grid is distributed in first quartile, and remaining M ' × N number of grid is distributed in
Two quadrant, and they are symmetrical about Y-axis, wherein M '=M/2.
B. in cartesian space, to the standard point and fixed placement point Q in step A6By straight line and circular interpolation, generate
7 discrete position sequences capture path to build "door" type in cartesian space, as shown in Figure 4.7 discrete position sequences
Coordinate is：
Q0=(x0,y0,z0),
Q1=(x0,y0,z0+H),
Q5=(x6,y6,z6+H),
Q6=(x6,y6,z6) (1)
In formula, Q0(x0,y0,z0) it is standard point, Q6(x6,y6,z6) it is fixed placement point, position hoisting depth is Hcm, number
Value can be set according to the requirement of the practical crawl object of Delta robots；Circular interpolation radius is Rcm, and numerical value can be according to standard point
Q0To fixed placement point Q6Distance finely tune, with eliminate due in cartesian space interpolation point choose it is very few caused by " door "
The size of the phenomenon that type arc locus transition portion distorts, R values can be determined according to formula (2)：
In formula,For current grasping movement when cartesian space get the bid
Q on schedule0With fixed placement point Q6Between line segment length, RmaxWith RminThe respectively maximum value of arc transition radius R and minimum
Value, setting value are：
In formula, LmaxWith LminRespectively fixed placement point Q6The longest formed with M on main belt × N number of mesh standard point
Line segment length and line of shortest length segment length, numerical value can be obtained according to Delta robot work region off-line measurements.
C. Fig. 5 is the structural model of Delta robots, and base is established in the center of Delta robots fixed platform
Mark system O-XYZ and solution coordinate system O-XiYiZ, it is contemplated that three branches of Delta robots are identical, can be used and rotate about the z axis
The mode of coordinate system simplifies solution, obtains each driving shaft angle, θ of Delta robots1,θ2,θ3With end effector position E0Fortune
It is dynamic to learn inverse solution：
Wherein,
Set θiIt being rotated down as positive direction, rotates up as negative direction, a, b, c are intermediate variable, e=A ' B '=
B ' C '=C ' A ' are the length of side of mobile platform triangle, and f=AB=BC=CA is the length of side of fixed platform triangle,
re=J1E1For the length of slave arm, rf=F1J1For the length of master arm,For i-th branch master arm with it is driven
The intersection point J of armiIn solving model coordinate system O-XiYiThe Y axis coordinate of Z and Z axis coordinate, E0(x0,y0,z0) held for robot end
Coordinate of the row device in basis coordinates system, E10(x10,y10,z10)、E20(x20,y20,z20)、E30(x30,y30,z30) it is respectively i=1,
2,3 time point E0(x0,y0,z0) solving coordinate system O-XiYiCoordinate under Z, specially：
D. according to the Inverse Kinematics Solution in step C by the position discrete series of cartesian space "door" type track in step B
{Q0,Q1,…Q6It is converted into the angle discrete series { P of Delta robotic joint spaces0,P1,…P6}；
E. the timing node sequence { t of w group joint spaces is initialized0,t1,…t6, the timing node sequence of every group of joint space
Row are consistent using standard point as the timing node sequence corresponding to the "door" type track of starting point with cartesian space, said for simplification
It is bright, hereafter referred to collectively as " timing node sequence ", meanwhile, define the interval of delta t of every group of timing node sequenceiFor：
Δti=ti+1-ti(i=0,1 ..., 5) (7)
In formula, Δ tiIt is servo motor by angle PiTurn to Pi+1Time interval, and Δ tiIt is random within 1s
Number；tiP is turned to for servo motoriAt the time of corresponding and tiFor non-decreasing series.
F. by the angle discrete series { P of the joint space in step D0,P1,…P6With step E in any one group when segmentum intercalaris
Point sequence { t0,t1,…t6Corresponding, form angle-timing node sequence { P of joint spacei, ti, i=0,1 ... 6；Construction
Angle-timing node sequence of 7 non-uniform rational B-spline function interpolation joint spaces, controls the forms of motion in each joint.
It is described to be specially：
For angle-timing node sequence { P of joint spacei, ti, i=0,1 ... 6, wherein Pi=[P1i,P2i,P3i
]T, the angle in the joint 1,2,3 of i-th of discrete series is corresponded to respectively.Continuous path of pulsing requires each joint trajectories curvilinear function Pm
=fm(t) at least three rank geometry continuums, and angle-timing node sequence, i.e. P of joint space is crossed in trackmi=fm(ti), m=1,
2,3 correspond to 3 joints of Delta robots.
K times non-homogeneous B spline curve Unify legislation is：
In formula, dj∈R3×1Vertex vector in order to control, j=0,1 ... n；For
Knot vector；P(u)∈R3×1For the joint angles vector at the u moment；Nj,k(u) it is the basic function of k non-uniform rational B-spline,
And：
The r order derivatives P of k non-homogeneous B spline curver(u), r=1,2,3, it can be calculated by De Buer recurrence formula：
Pass through angle-timing node sequence of joint space, 7 non-uniform rational B-spline songs of reverse according to joint trajectories
Line traffic control vertex sequence.Using accumulative Chord Length Parameterization method to timing node sequence { t0,t1,…t6Normalization, determine node
Vectorial u ∈ [u0,u1,…,u6+2×7]：
u0=u1=...=u7,
u6+7=u6+7+1=...=u6+2×7. (12)
Corresponding 7 equations of angle-timing node sequence constraints of joint space can be listed：
In formula, i=0,1 ..., 6, djFor 13 control vertex vectors of B-spline geometric locus, j=0,1 ..., 12.Cause
This, it is also necessary to 6 equations are increased by boundary condition.The numerical value of setting joint start and stop speed, acceleration and pulsation, obtains 13 sides
Journey：
V in formulas, as, jsJoint starting velocity, acceleration and pulsation vector, v are indicated respectivelye, ae, jeRespectively joint is whole
Only speed, acceleration, pulsation vector, P ' (u), P " (u), P " ' (u) are respectively joint velocity, acceleration, pulsation geometric locus.
Above formula is described as to the form of matrix equation：
Cmdm=Pm (15)
Wherein, Cm∈R13×13For coefficient matrix and dm=[dm0,dm1,…,dm12]T,Pm=[Pm0,Pm1,…,Pm6,vms,
vme,ams,
ame,jms,jme]T, it is possible thereby to find out the control vertex vector of 7 non-uniform rational B-spline tracks：
dm=Cm -1Pm (16)
The C of joint m can be found out according to control vertex vector sum timing node vector6Continuous 7 non-uniform rationals B samples
Joint trajectories.
G. build time adaptive optimal control degree function is meeting joint velocity, acceleration, pulsation continuously smooth and no more than watching
Under conditions of taking Rated motor limits value, particle cluster algorithm is searched for using gravitation, to w group timing node sequences { t0,t1,…t6}
Off-line optimization exports one group of optimal time sequence node until meeting maximum iteration.The specific steps are：
Under the premise of Delta robots operate steadily, it is desirable that movement total time is most short, and construction object function is：
In formula, VCj,ACj,JCjSpeed, acceleration and the specified limits value of pulsation of robot servo motors are indicated respectively.
θ′mj(t)、θ″mj(t)、θ″′mj(t) it is respectively each joint velocity, acceleration, pulsation, can be obtained by formula (10)~(11)：
Particle cluster algorithm is searched for using gravitation, under conditions of meeting formula (17)~(18), to w group timing node sequences
{t0,t1,…t6Off-line optimization is carried out, optimizing expression formula is：
In formula, ω is the weight coefficient between 0-1；rand1With rand2It is equally distributed random between 0-1
Function；c′1Indicate influence degree of the acceleration to subsequent time particle rapidity of last moment particle itself；c′2To adjust particle
Fly to the step-length of global history optimal location；gbestd(t) optimal solution that the cut-off entire population of t moment is found is indicated；D is indicated
Dimension, value 0,1 ... 5；Indicate that the numerical value in i-th of particle d dimension of t moment corresponds respectively to timing node sequence
Interval of delta ti6 numerical value.
Optimizing algorithm meets maximum iteration, then exports one group of optimal time sequence node { t0,t1,…t6}。
H. it uses offline mode to M in step A × N number of standard point, repeats above step B~G, obtain M × N groups with standard
Point is the optimal time sequence node { t corresponding to the "door" type track of starting point0,t1,…t6And it is stored in three-dimensional array A and B
In.It is as follows：
For the distribution situation foundation three-dimensional for the first quartile mesh standard point that X-axis positive direction and Y-axis positive direction are formed
Array A, the first dimension number of elements is consistent with the standard point quantity being distributed along X-axis positive direction uniline, as M '；Two-dimensional element number
Measure, as N consistent with the standard point quantity being distributed along Y-axis positive direction uniline；Third dimension number of elements and each group of timing node
The quantity of sequence is consistent, and as 7, therefore call number is respectively 0- (M'-1), 0- (N-1), 0-6；Similarly, for X-axis negative direction
Three-dimensional array B, dimension and call number and three-dimensional are established with the distribution situation of the second quadrant mesh standard point of Y-axis positive direction composition
Array A is identical.
Under offline mode, to M in step A × N number of standard point, above step B~G is repeated, when acquisition M × N groups are optimal
Segmentum intercalaris point sequence { t0,t1,…t6}。
According to position of each standard point on main belt, determine using the standard point as corresponding to the "door" type track of starting point
One group of optimal time sequence node { t0,t1,…t6Call number in three-dimensional array.As the abscissa x >=0 of standard point,
Then store this group of optimal time sequence node { t0,t1,…t6Corresponding position in three-dimensional array A；Conversely, being then stored in three
Corresponding position in dimension group B is prepared for robot on-line operation.
I. when industrial intelligent camera identifies object central point on main belt, which is also referred to as target point, passes through coordinate
Shift conversion is the coordinate position of robot working space, grid mark where determining the object by the value of abscissa and ordinate
Position on schedule is calculated using the standard point as one group of optimal time sequence node { t corresponding to the "door" type track of starting point0,
t1,…t6Call number in three-dimensional array, the three-dimensional array A established in step H in the way of online query obtained with B
This group of optimal time sequence node { t0,t1,…t6, while the target point being used to the method for being similar to standard point, it is more than repetition
The quick planning robot's movement locus of step B~D, completes set movement, and online query flow is as shown in Fig. 2, target point and mark
Relationship on schedule is as shown in Figure 6.
It the foregoing is merely embodiments of the present invention are illustrated, is not intended to restrict the invention, for the technology of this field
For personnel, all within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in
Within protection scope of the present invention.
Claims (1)
1. a kind of Delta method for planning track of robot for searching for particle cluster algorithm based on gravitation, which is characterized in that comprising following
Step：
A. Delta robots main belt working region is divided into M × N number of square by the way of mesh generation, each
Square is known as grid, and its side length is dcm, the numerical value of d is 1 or 2, and the value of M is even number, and selection grid element center point is standard point；M′
× N number of grid is distributed in first quartile, and remaining M ' × N number of grid is distributed in the second quadrant, and they are symmetrical about Y-axis, wherein
M '=M/2；
B. in cartesian space, to the standard point and fixed placement point Q in step A6By straight line and circular interpolation, flute card is generated
7 discrete position sequences capture path to build "door" type in your space, and 7 discrete position sequence coordinates are：
Q0=(x0,y0,z0),
Q1=(x0,y0,z0+H),
Q5=(x6,y6,z6+H),
Q6=(x6,y6,z6) (1)
In formula, Q0(x0,y0,z0) it is standard point, Q6(x6,y6,z6) it is fixed placement point, position hoisting depth is Hcm, numerical value according to
The requirement setting of the practical crawl object of Delta robots；Circular interpolation radius is Rcm, numerical value is according to standard point Q0To fixed placement
Point Q6Distance finely tune, with eliminate due in cartesian space interpolation point choose it is very few caused by "door" type arc locus mistake
The phenomenon that part is distorted is crossed, the size of R values is determined according to formula (2)：
In formula,For current grasping movement when cartesian space acceptance of the bid on schedule
Q0With fixed placement point Q6Between line segment length, RmaxWith RminThe respectively maxima and minima of arc transition radius R, number
Value is set as：
In formula, LmaxWith LminRespectively fixed placement point Q6The longest line segment formed with M on main belt × N number of mesh standard point
Length and line of shortest length segment length, numerical value are obtained according to Delta robot work region off-line measurements；
C. it establishes basis coordinates system O-XYZ in the center of Delta robots fixed platform and solves coordinate system O-XiYiZ considers
It is identical to three branches of Delta robots, simplify solution by the way of rotating coordinate system about the z axis, obtains Delta machines
Each driving shaft angle, θ of people1,θ2,θ3With end effector position E0Inverse Kinematics Solution：
Wherein,
Set θiIt being rotated down as positive direction, rotates up as negative direction, a, b, c are intermediate variable, e=A ' B '=
B ' C '=C ' A ' are the length of side of mobile platform triangle, and f=AB=BC=CA is the length of side of fixed platform triangle, re=
J1E1For the length of slave arm, rf=F1J1For the length of master arm,For the master arm and slave arm of i-th branch
Intersection point JiIn solving model coordinate system O-XiYiThe Y axis coordinate of Z and Z axis coordinate, E0(x0,y0,z0) it is end effector of robot
Coordinate in basis coordinates system, E10(x10,y10,z10)、E20(x20,y20,z20)、E30(x30,y30,z30) when being respectively i=1,2,3
Point E0(x0,y0,z0) solving coordinate system O-XiYiCoordinate under Z, specially：
D. according to the Inverse Kinematics Solution in step C by the position discrete series { Q of cartesian space "door" type track in step B0,
Q1,…Q6It is converted into the angle discrete series { P of Delta robotic joint spaces0,P1,…P6}；
E. the timing node sequence { t of w group joint spaces is initialized0,t1,…t6, the timing node sequence of every group of joint space with
It is consistent using standard point as the timing node sequence corresponding to the "door" type track of starting point in cartesian space, illustrate to simplify,
Hereafter referred to collectively as " timing node sequence ", meanwhile, define the interval of delta t of every group of timing node sequenceiFor：
Δti=ti+1-ti(i=0,1 ..., 5) (7)
In formula, Δ tiIt is servo motor by angle PiTurn to Pi+1Time interval, and Δ tiIt is the random number within 1s, ti
P is turned to for servo motoriAt the time of corresponding and tiFor non-decreasing series；
F. by the angle discrete series { P of the joint space in step D0,P1,…P6With step E in any one group of timing node sequence
Arrange { t0,t1,…t6Corresponding, form angle-timing node sequence { P of joint spacei, ti, i=0,1 ... 6, it constructs 7 times
The angle of the non-uniform rational B-spline function interpolation joint space-timing node sequence controls the forms of motion in each joint, institute
It states specially：
For angle-timing node sequence { P of joint spacei, ti, i=0,1 ... 6, wherein Pi=[P1i,P2i,P3i]T, respectively
The angle in the joint 1,2,3 of corresponding i-th of discrete series, pulsation continuous path require each joint trajectories curvilinear function Pm=fm(t)
At least three rank geometry continuums, and angle-timing node sequence, i.e. P of joint space is crossed in trackmi=fm(ti), m=1,2,3 pairs
It should be in 3 joints of Delta robots；
K times non-homogeneous B spline curve Unify legislation is：
In formula, dj∈R3×1Vertex vector in order to control, j=0,1 ... n,For node
Vector, P (u) ∈ R3×1For the joint angles vector at the u moment, Nj,k(u) it is the basic function of k non-uniform rational B-spline, and：
The r order derivatives P of k non-homogeneous B spline curver(u), r=1,2,3, it is calculated by De Buer recurrence formula：
Pass through angle-timing node sequence of joint space, 7 non-homogeneous B spline curve controls of reverse according to joint trajectories
Vertex sequence processed, using accumulative Chord Length Parameterization method to timing node sequence { t0,t1,…t6Normalization, determine knot vector
u∈[u0,u1,…,u6+2×7]：
u0=u1=...=u7,
u6+7=u6+7+1=...=u6+2×7. (12)
List corresponding 7 equations of angle-timing node sequence constraints of joint space：
In formula, i=0,1 ..., 6, djFor 13 control vertex vectors of B-spline geometric locus, j=0,1 ..., 12, therefore, also
Need to increase by 6 equations by boundary condition, setting joint start and stop speed, acceleration and pulsation numerical value, obtain 13 equations：
V in formulas, as, jsJoint starting velocity, acceleration and pulsation vector, v are indicated respectivelye, ae, jeRespectively joint terminates speed
Degree, acceleration, pulsation vector, P ' (u), P " (u), P " ' (u) are respectively joint velocity, acceleration, pulsation geometric locus；
Above formula is described as to the form of matrix equation：
Cmdm=Pm (15)
Wherein, Cm∈R13×13For coefficient matrix and dm=[dm0,dm1,…,dm12]T,Pm=[Pm0,Pm1,…,Pm6,vms,vme,ams,
ame,jms,jme]T, thus find out the control vertex vector of 7 non-uniform rational B-spline tracks：
dm=Cm -1Pm (16)
The C of joint m can be found out according to control vertex vector sum timing node vector6Continuous 7 non-uniform rational B-splines close
Save track；
G. build time adaptive optimal control degree function is meeting joint velocity, acceleration, pulsation continuously smooth and is being no more than servo electricity
Under conditions of the specified limits value of machine, particle cluster algorithm is searched for using gravitation, to w group timing node sequences { t0,t1,…t6Offline
Optimizing exports one group of optimal time sequence node until meeting maximum iteration, the specific steps are：
Under the premise of Delta robots operate steadily, it is desirable that movement total time is most short, and construction object function is：
In formula, VCj,ACj,JCjSpeed, acceleration and the specified limits value of pulsation of robot servo motors, θ ' are indicated respectivelymj
(t)、θ″mj(t)、θ″′mj(t) it is respectively each joint velocity, acceleration, pulsation, is obtained by formula (10)~(11)：
Particle cluster algorithm is searched for using gravitation, under conditions of meeting formula (17)~(18), to w group timing node sequences { t0,
t1,…t6Off-line optimization is carried out, optimizing expression formula is：
In formula, ω is the weight coefficient between 0-1, rand1With rand2It is the equally distributed random letter between 0-1
Number, c'1Indicate the acceleration of last moment particle itself to the influence degree of subsequent time particle rapidity, c'2Fly to adjust particle
To the step-length of global history optimal location, gbestd(t) indicate that the optimal solution that the cut-off entire population of t moment is found, d indicate dimension
Degree, value 0,1 ... 5,Indicate that the numerical value in i-th of particle d dimension of t moment corresponds respectively to timing node sequence
Interval of delta ti6 numerical value；
Optimizing algorithm meets maximum iteration, then exports one group of optimal time sequence node { t0,t1,…t6}；
H. it uses offline mode to M in step A × N number of standard point, repeats above step B~G, obtain M × N groups is with standard point
Optimal time sequence node { t corresponding to the "door" type track of starting point0,t1,…t6And be stored in three-dimensional array A and B, tool
Steps are as follows for body：
The distribution situation of the first quartile mesh standard point formed for X-axis positive direction and Y-axis positive direction establishes three-dimensional array
A, first dimension number of elements it is consistent with standard point quantity be distributed along X-axis positive direction uniline, as M ', second tie up number of elements and
Standard point quantity along the distribution of Y-axis positive direction uniline is consistent, as N, third dimension number of elements and each group of timing node sequence
Quantity it is consistent, as 7, therefore call number is respectively 0- (M'-1), 0- (N-1), 0-6, similarly, for X-axis negative direction and Y-axis
The distribution situation of second quadrant mesh standard point of positive direction composition establishes three-dimensional array B, dimension and call number and three-dimensional array A
It is identical；
Under offline mode, to M in step A × N number of standard point, above step B~G is repeated, obtains M × N group optimal time sections
Point sequence { t0,t1,…t6}；
According to position of each standard point on main belt, determine using the standard point as one corresponding to the "door" type track of starting point
Group optimal time sequence node { t0,t1,…t6Call number in three-dimensional array；As the abscissa x >=0 of standard point, then deposit
Store up this group of optimal time sequence node { t0,t1,…t6Corresponding position in three-dimensional array A；Conversely, being then stored in three dimensions
Corresponding position in group B, prepares for robot on-line operation；
I. when industrial intelligent camera identifies object central point on main belt, which is also referred to as target point, passes through coordinate transform
It is converted into the coordinate position of robot working space, mesh standard point where determining the object by the value of abscissa and ordinate
Position, calculate using the standard point as one group of optimal time sequence node { t corresponding to the "door" type track of starting point0,t1,…
t6Call number in three-dimensional array, in the way of online query the group is obtained in the three-dimensional array A that step H is established and B
Optimal time sequence node { t0,t1,…t6, while the target point is used into the method similar to standard point, repeat above step
The quick planning robot's movement locus of B~D, completes set movement.
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| CN109108983A (en) * | 2018-10-12 | 2019-01-01 | 中国航天空气动力技术研究院 | Manipulator method for planning track based on sort process |
| CN110196590B (en) * | 2019-04-23 | 2021-12-14 | 华南理工大学 | Time optimal trajectory planning method for robot path tracking |
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| CN111897216B (en) * | 2020-07-16 | 2021-07-02 | 华中科技大学 | Multi-motion-segment speed planning and interpolation method |
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