CN110216673A - The non-dominant neighborhood immune genetic Multipurpose Optimal Method of electro-hydraulic joint of robot track - Google Patents
The non-dominant neighborhood immune genetic Multipurpose Optimal Method of electro-hydraulic joint of robot track Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
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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
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Abstract
The present invention proposes a kind of optimization method of joint of robot track based on non-dominant neighborhood immune genetic multi-objective Algorithm.First according to the successional requirement of joint of robot smooth trajectory, the planning of joint of robot track is carried out using 5 B-spline curves；Then on the basis of joint trajectories and robot kinematics constrain, emphasis considers machine task efficiency and service life, energy consumption and elliptical gear, proposes three targets of robot multiple-objective track optimizing: the time is most short, energetic optimum and impact are minimum；Finally based on multiple target feature and Pareto optimal solution set meaning, the non-dominant neighborhood immune genetic multi-objective Algorithm of three track targets of optimization is proposed；The algorithm can handle the relationship between three time, energy and impact targets well, when guaranteeing that one of target is more excellent, other two target is unlikely to deteriorate, joint trajectories runing time after robot optimization is shorter, and energy consumption is lower, and elliptical gear is smaller, joint of robot starts smaller with impact when stopping, and the speed, acceleration and acceleration track continuity of joint of robot are preferable, and flatness is more excellent, and the joint of robot path effect after optimization is ideal reliable.
Description
Technical field
The present invention relates to robots, are particularly suitable for the joint trajectories for the robot that executing agency is made of hydraulic motor
Multiple-objection optimization is realized the determination of joint of robot track scheme using intelligent multi-objective optimization algorithm, belongs to robot motion
Trajectory planning field.
Background technique
Robot has become one of most important role of current robot field, the various machines using novel hydraulic technology
People is widely applied in various related fieldss, and the correlative study work for robot is come into being.Due to trajectory planning
It is the premise controlled robot, therefore the trajectory planning of robot is the key area of its research, robot is to belong to
The research method of one kind of industrial robot, trajectory planning is similar with ordinary robot, and the movement being also based between joint is closed
What system was studied.
Trajectory planning be according to task requirement specify beginning and end, using interpolation curve seek a starting point and
Then path between terminal converts path in the joint space in each joint of robot, final to determine each joint of robot
Position, speed, acceleration and acceleration track.Effectively reliable trajectory planning scheme can be improved the work effect of robot
Rate and service life.
Robot in practical applications, will comprehensively consider the problems such as working efficiency is with service life, energy consumption, stationarity,
The trajectory planning scheme that better robot can be obtained determines the objective functions such as most short time, energetic optimum and impact minimum, benefit
It is optimized with joint trajectories of the multi-objective Algorithm to robot, the reliable trajectory planning scheme of final performance.
Summary of the invention
In view of above-mentioned knowledge, the purpose of the present invention is to provide one kind to be based on non-dominant neighborhood immune genetic multi-objective Algorithm
Joint of robot track optimization method, this method one improve machine task efficiency, reduce energy consumption and reduce fortune
Dynamic impact is that objective function carries out multiple-objection optimization, various factors is comprehensively considered, to make each joint of robot in motion process
In reach the objectives equilibrium, extend the service life of robot.
To achieve the above object, the invention adopts the following technical scheme:
The optimization method of joint of robot track based on non-dominant neighborhood immune genetic multi-objective Algorithm, feature exist
In: the following steps are included:
1): based on specification B-spline basic function, using 5 B-spline curves functions to the path of joint of robot track
Row interpolation is clicked through, i-th section of 5 B-spline curves interpolation track in n-th of joint of robot can be described as:
Wherein n=1,2 ..., N, N=6 are joint of robot number；npiIt (x) is i-th section 5 of n-th of joint of robot
Secondary B-spline curves interpolation track；X is the node of 5 B-spline curves；Bj,5It (x) is 5 B-spline basic functions；najFor robot
J-th of B-spline curves control point in n-th joint；M+1 is the number of joint path point；
2): determining the optimization object function of joint of robot track are as follows:
Wherein, S1For run duration index, machine task efficiency is measured；ΔtiFor robot runing time section interval,
tiFor robot to the runing time of i-th of joint path point, S2For the acceleration index in joint, robot energy consumption is measured
Size；TtotThe total run time of object pose is moved to from initial pose for robot；S3For the acceleration index in joint,
Measure robot trajectory's flatness and impact；nαi,njerkiThe respectively acceleration and acceleration in n-th of joint of robot；
3): the convex-hull property based on 5 B-spline curves, by the fortune such as the speed, acceleration of robot and acceleration constraint
The dynamic control point constraint learned constraint and be converted into 5 B-spline curves, constraint conversion may be expressed as:
Wherein,WithThe respectively speed, acceleration in n-th of joint of robot and acceleration B-spline is bent
J-th of control point on line,nωmax,nαmax,njerkmaxRespectively the position in n-th of joint of robot, speed, acceleration and
Acceleration tolerance limit；
4): according to the 5 of robot B-spline curves interpolation tracks, optimization object function and kinematical constraint condition are used
The immune genetic multi-objective optimization algorithm of non-dominant neighborhood, corresponding Pareto optimal solution set after being optimized.
2. the joint of robot track according to claim 1 based on non-dominant neighborhood immune genetic multi-objective Algorithm
Optimization method, which is characterized in that the step 4) includes the following steps:
S1: the relevant parameter of non-dominant neighborhood immune genetic multi-objective Algorithm initialization is set, initial antibodies population is given
Scale, it is random to generate initial antibodies population；
S2: the advantage antibody population in initial antibodies population is determined according to Pareto optimal solution criterion, and is further calculated
The crowding distance of each antibody, crowding distance are expressed as follows in advantage antibody population:
Wherein, d is the antibody in advantage antibody population；D is advantage antibody population；I (d, D) is antibody d in advantage antibody
Crowding distance in population D；K is expectation target number, K=3；fi maxAnd fi minRespectively i-th of target in advantage antibody population
Maximum value and minimum value；Ii(d, D) is expressed as follows:
S3: according to the crowding distance of antibody each in advantage antibody population, ratio clone operations is executed to antibody, remove trimming
Clone's ratio of each antibody after boundary's antibody is expressed as follows:
Wherein, qiTo clone ratio；ncFor the desired value of clonal antibody population scale；| D | for the big of advantage antibody population
It is small；
Clone's ratio of boundary antibody is 2 times of above-mentioned clone's ratio maximum value；
S4: according to the crossover probability and mutation probability in algorithm, intersection and mutation operation is executed to clonal antibody population, produced
It changes xenoantibody population；
S5: the scale of advantage antibody population is determined according to Pareto optimal solution criterion to antibody variants population, and is calculated excellent
It is larger to retain crowding distance if the scale of advantage antibody population is more than desired value for the crowding distance of antibody in gesture antibody population
Antibody；
S6: judging whether algorithm meets termination condition, if satisfied, thening follow the steps S7, otherwise jumps to step S3；
S7: the corresponding Pareto optimal solution set of the objective function is exported；
S8: final trajectory planning scheme is selected from Pareto optimal solution set described in step S7.
3. the joint of robot track according to claim 2 based on non-dominant neighborhood immune genetic multi-objective Algorithm
Optimization method, it is characterised in that:
The method of the Pareto optimal solution determined from initial antibodies population or updated antibody population is foundation
In the advantage antibody population that Pareto optimal solution criterion obtains through clone, intersect with after mutation operation again depending on Pareto most
The Pareto optimal solution that excellent solution criterion obtains.
4. the joint of robot according to claim 1 or 3 based on non-dominant neighborhood immune genetic multi-objective Algorithm
The optimization method of track, which is characterized in that this method further include:
After obtaining the corresponding Pareto optimal solution set of optimization object function, according to runing time, path acceleration and track
The smaller principle of acceleration selects optimal trajectory planning scheme from the Pareto optimal solution set.
The present invention has the advantages that
The present invention comprehensively considers the kinematical constraint condition in each joint of robot, according to the time of proposition is most short, energy most
The excellent and the smallest objective function of impact, the effective movenent performance for improving joint of robot utilize the immune something lost of non-dominant neighborhood
Passing multiple target, scaling method has obtained reliable robot trajectory planning's scheme again.
Detailed description of the invention
Fig. 1: the joint trajectory planning flow chart of robot
Fig. 2: non-dominant neighborhood immune genetic multi-objective Algorithm flow chart
Fig. 3: being the forward position the Pareto distribution map that benefit is obtained by the present invention in a specific embodiment
Fig. 4: being the position curve figure that robot finally chooses in each joint programme in a specific embodiment
Fig. 5: being the speed curve diagram that robot finally chooses in each joint programme in a specific embodiment
Fig. 6: being the acceleration plots that robot finally chooses in each joint programme in a specific embodiment
Fig. 7: being the jerk curve figure that robot finally chooses in each joint programme in a specific embodiment
Specific embodiment
Below in conjunction with drawings and examples to the invention will be further described.
It is the joint trajectory planning process of robot with reference to attached drawing 1, robot need to utilize the system before execution task
Trajectory planning is carried out to each joint for mission requirements, carries out the nodes of locations that path setting generates joint according to mission requirements,
A joint in robot must be under the conditions of meeting kinematical constraint, successively by each path node to complete task.
Setting robot complete task have to by joint position node are as follows:
nΘ=[nθ0 nθ1 … nθm]T (1)
Wherein,nθiFor i-th of position in n-th of joint of robot, i=0,1,2 ..., m；N=1,2 ..., N, N=6
For joint of robot number；M+1 is the number of joint path point.
Timing node corresponding with joint position node are as follows:
T=[t0 t1 … tm] (2)
Time interval sequence between joint position node are as follows:
Δ T=[Δ t0,Δt1,…,Δtm-1] (3)
Wherein, Δ ti=ti+1-ti, i=0,1,2 ..., m-1
The total run time of robot completion task are as follows:
Ttot=tm-t0 (4)
Based on specification B-spline basic function, each joint of robot is generated from fortune using 5 B-spline curves interpolating functions
The track for each path node that dynamic origin-to-destination passes through；I-th section of 5 B-spline curves interpolation rail in n-th of joint of robot
Mark can be described as:
Wherein n=1,2 ..., N, N=6 are joint of robot number；npiIt (x) is i-th section 5 of n-th of joint of robot
Secondary B-spline curves interpolation track；X is the node of 5 B-spline curves；Bj,5It (x) is 5 B-spline basic functions；najFor robot
J-th of B-spline curves control point in n-th joint；M+1 is the number of joint path point；The node of B-spline interpolation curve is sweared
Measure X=[x0,x1,…,xm+2k]；Two end node multiplicities are k+1, i.e. x0=x1=...=xk=0, xm+1=xm+2=...=
xm+k+1=1, to timing node T standardization, obtain the sequence node X unknown node of the B-spline interpolation curve in joint really
Cut value；This will provide basis for subsequent solution joint position, velocity and acceleration track.B-spline interpolation curve unknown node
Value are as follows:
By spline curve domain [xk,xm+k] in nodal value successively substitute into formula (8), obtain m+1 equation:
There is m+k control point to need to find out in the B-spline interpolation curve of joint of robot track, could finally determine machine
The geometric locus in each joint of people, therefore k-1 equation should be also resettled, homogeneous equation group could be constituted, n-th of joint trajectories is set
Start-stop speednωs,nωeAnd accelerationnαs,nαe, specify the start-stop joint velocity of the robot of this research and acceleration equal
It is zero, then equation are as follows:
The total m+k equation in joint type (7)-(11), can be write as matrix form:
nCM nAM=nΘ* (12)
In formula,nCMFor the coefficient matrix of n-th of joint trajectories equation；
nAMFor the unknown control point vector of n-th of joint trajectories equation；
nΘMThe vector formed for the interpolation path point and Boundary motion condition of n-th of joint trajectories.
Control point value can be obtained in solution formula (12) solution, and control point value substitution formula (5) can be obtained by the joint of robot
Location track, to its derivation, then speed, acceleration and acceleration geometric locus can be found out.
Most short according to the time, energetic optimum and impact are minimum, determine robot optimization object function are as follows:
Wherein, S1For run duration index, machine task efficiency is measured；ΔtiFor robot runing time section interval,
tiFor robot to the runing time of i-th of joint path point, S2For the acceleration index in joint, robot energy consumption is measured
Size；TtotThe total run time of object pose is moved to from initial pose for robot；S3For the acceleration index in joint,
Measure robot trajectory's flatness and impact；nαi,njerkiThe respectively acceleration and acceleration in n-th of joint of robot；
Based on the convex-hull property of 5 B-spline curves, by the movement such as the speed, acceleration of robot and acceleration constraint
The control point constraint that constraint is converted into 5 B-spline curves is learned, constraint conversion may be expressed as:
Wherein,WithThe respectively speed, acceleration in n-th of joint of robot and acceleration B-spline is bent
J-th of control point on line,nωmax,nαmax,njerkmaxRespectively the position in n-th of joint of robot, speed, acceleration and
Acceleration tolerance limit；
It is non-dominant neighborhood immune genetic multi-objective Algorithm process with reference to attached drawing 2, according to the 5 of robot B-spline curves
Interpolation track, optimization object function and kinematical constraint condition, using the immune genetic multi-objective optimization algorithm of non-dominant neighborhood,
Corresponding Pareto optimal solution set after being optimized.
Specific step is as follows:
S1: the relevant parameter of non-dominant neighborhood immune genetic multi-objective Algorithm initialization is set, initial antibodies population is given
Scale generates initial antibodies population according to the range of variable in algorithm at random,
S2: the advantage antibody population in initial antibodies population is determined according to Pareto optimal solution criterion, and is further calculated
The crowding distance of each antibody in advantage antibody population, the crowding distance of each antibody are expressed as follows:
Wherein, I (d, D) is crowding distance of the antibody d in advantage antibody population D；D is anti-in advantage antibody population
Body；D is advantage antibody population；K is expectation target number, K=3；fi maxAnd fi minRespectively i-th of mesh in advantage antibody population
Target maximum value and minimum value；Ii(d, D) is expressed as follows:
S3: according to the crowding distance of antibody each in advantage antibody population, ratio clone operations is executed to antibody, remove trimming
Clone's ratio of each antibody after boundary's antibody is expressed as follows:
Wherein, qiTo clone ratio；I(di, D) and it is antibody body diCrowding distance；ncFor the phase of clonal antibody population scale
Prestige value；
Clone's ratio of boundary antibody is 2 times of above-mentioned clone's ratio maximum value；
S4: according to the crossover probability and mutation probability in algorithm, intersection and mutation operation is executed to clonal antibody population, produced
It changes xenoantibody population；
S5: the scale of advantage antibody population is determined according to Pareto optimal solution criterion to antibody variants population, and is calculated excellent
It is larger to retain crowding distance if the scale of advantage antibody population is more than desired value for the crowding distance of antibody in gesture antibody population
Antibody；
S6: judging whether algorithm meets termination condition, if satisfied, thening follow the steps S7, otherwise jumps to step S3；
S7: the corresponding Pareto optimal solution set of the objective function is exported；
S8: optimal trajectory planning scheme is selected from Pareto optimal solution set described in step S7.
The optimization method of joint of robot track based on non-dominant neighborhood immune genetic multi-objective Algorithm, feature exist
In:
The method of the Pareto optimal solution determined from initial antibodies population or updated antibody population is foundation
In the advantage antibody population that Pareto optimal solution criterion obtains through clone, intersect with after mutation operation again depending on Pareto most
The Pareto optimal solution that excellent solution criterion obtains.
The optimization method of joint of robot track based on non-dominant neighborhood immune genetic multi-objective Algorithm, feature exist
In this method further include:
After obtaining the corresponding Pareto optimal solution set of optimization object function, according to runing time, path acceleration and track
The smaller principle of acceleration selects optimal trajectory planning scheme from the Pareto optimal solution set.
In a particular embodiment, trajectory planning is carried out to the electro-hydraulic robot that one includes six joints, and according to target
Function optimizes；The kinematical constraint in each joint when electro-hydraulic robot trajectory planning are as follows:
Table one
Data in table one indicate the speed, acceleration in each joint of electro-hydraulic machine device people and the constraint condition of acceleration.
Give the joint position node in six joints of electro-hydraulic robot are as follows:
Table two
Data in table two indicate: when electro-hydraulic robot completes task from start to stopping the road to be passed through of each joint motions
Diameter point.
Under given constraint and joint path condition, using method of the invention, emulated by Matlab software
It studies, the initial parameter in algorithm are as follows:
Table three
The data that three kinds of table indicate the initial relevant parameter of non-dominant neighborhood immune genetic multi-objective Algorithm.
It is the forward position the Pareto distribution map obtained after emulation experiment with reference to attached drawing 3, as shown, target S1Optimal value be
6.00s, target S2Optimal value be 3.41 °/s2, target S3Optimal value be 3.91 °/s3；It is optimal close to A point time performance, but
Energy and impact are larger；It is optimal close to C point energy and impact, but runing time is longer；B point indicates time, energy and impact three
A target is relatively good.
It with reference to attached drawing 4 to Fig. 7 is chosen with reference to the B point in attached drawing 3 as electro-hydraulic robot trajectory after emulation experiment respectively
The scheme of planning, position, speed, acceleration and the jerk curve schematic diagram in corresponding six joints.As shown, six
Joint reaches final position by defined joint path node, and speed, acceleration curve is continuous, and all kinematical constraints
In restriction range, the scheme of trajectory planning is more reliable.
The above content is further detailed description of the invention in conjunction with specific embodiments, and it cannot be said that of the invention
Specific implementation is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, without departing substantially from this
Under the premise of inventive concept, any equivalent transformation based on the basis of technical solution of the present invention, simple deduction or replace etc. it is aobvious and
The change being clear to, all shall be regarded as belonging within protection scope of the present invention.
Claims (4)
1. the optimization method of the joint of robot track based on non-dominant neighborhood immune genetic multi-objective Algorithm, it is characterised in that:
The following steps are included:
1): based on specification B-spline basic function, being clicked through using path of 5 B-spline curves functions to joint of robot track
I-th section of 5 B-spline curves interpolation track of row interpolation, n-th of joint of robot can be described as:
Wherein n=1,2 ..., N, N=6 are joint of robot number；npiIt (x) is i-th section of 5 B in n-th of joint of robot
Spline curve interpolation track；X is the node of 5 B-spline curves；Bj,5It (x) is 5 B-spline basic functions；najIt is the n-th of robot
J-th of B-spline curves control point in a joint；M+1 is the number of joint path point；
2): determining the optimization object function of joint of robot track are as follows:
Wherein, S1For run duration index, machine task efficiency is measured；ΔtiFor robot runing time section interval, tiFor
Runing time of the robot to i-th of joint path point, S2For the acceleration index in joint, it is big to measure robot energy consumption
It is small；TtotThe total run time of object pose is moved to from initial pose for robot；S3For the acceleration index in joint, weighing apparatus
Measure robot trajectory's flatness and impact；nαi,njerkiThe respectively acceleration and acceleration in n-th of joint of robot；
3): the convex-hull property based on 5 B-spline curves, by the kinematics such as the speed, acceleration of robot and acceleration constraint
Constraint is converted into the control point constraint of 5 B-spline curves, and constraint conversion may be expressed as:
Wherein,WithRespectively in the speed, acceleration and acceleration B-spline curves in n-th of joint of robot
J-th of control point,nωmax,nαmax,njerkmaxRespectively position, speed, acceleration and the Jia Jia in n-th of joint of robot
Speed tolerance limit；
4): according to the 5 of robot B-spline curves interpolation tracks, optimization object function and kinematical constraint condition, using non-branch
Immune genetic multi-objective optimization algorithm with neighborhood, corresponding Pareto optimal solution set after being optimized.
2. the joint of robot track according to claim 1 based on non-dominant neighborhood immune genetic multi-objective Algorithm is excellent
Change method, which is characterized in that the step 4) includes the following steps:
S1: being arranged the relevant parameter of non-dominant neighborhood immune genetic multi-objective Algorithm initialization, give initial antibodies population scale,
It is random to generate initial antibodies population；
S2: the advantage antibody population in initial antibodies population is determined according to Pareto optimal solution criterion, and further calculates advantage
The crowding distance of each antibody, crowding distance are expressed as follows in antibody population:
Wherein, d is the antibody in advantage antibody population；D is advantage antibody population；I (d, D) is antibody d in advantage antibody population D
In crowding distance；K is expectation target number, K=3；fi maxAnd fi minI-th of target be most respectively in advantage antibody population
Big value and minimum value；Ii(d, D) is expressed as follows:
S3: according to the crowding distance of antibody each in advantage antibody population, ratio clone operations is executed to antibody, it is anti-to remove boundary
Clone's ratio of each antibody after body is expressed as follows:
Wherein, qiTo clone ratio；ncFor the desired value of clonal antibody population scale；| D | it is the size of advantage antibody population；
Clone's ratio of boundary antibody is 2 times of above-mentioned clone's ratio maximum value；
S4: according to the crossover probability and mutation probability in algorithm, intersection and mutation operation is executed to clonal antibody population, generate change
Xenoantibody population；
S5: the scale of advantage antibody population is determined according to Pareto optimal solution criterion to antibody variants population, and it is anti-to calculate advantage
It is biggish anti-to retain crowding distance if the scale of advantage antibody population is more than desired value for the crowding distance of antibody in body population
Body；
S6: judging whether algorithm meets termination condition, if satisfied, thening follow the steps S7, otherwise jumps to step S3；
S7: the corresponding Pareto optimal solution set of the objective function is exported；
S8: final trajectory planning scheme is selected from Pareto optimal solution set described in step S7.
3. the joint of robot track according to claim 2 based on non-dominant neighborhood immune genetic multi-objective Algorithm is excellent
Change method, it is characterised in that:
From initial antibodies population or updated antibody population determine Pareto optimal solution method be according to Pareto most
In the excellent obtained advantage antibody population of solution criterion through clone, intersect with after mutation operation again depending on Pareto optimal solution criterion
Obtained Pareto optimal solution.
4. the joint of robot track according to claim 1 or 3 based on non-dominant neighborhood immune genetic multi-objective Algorithm
Optimization method, which is characterized in that this method further include:
After obtaining the corresponding Pareto optimal solution set of optimization object function, according to runing time, path acceleration and track add
Speed selects optimal trajectory planning scheme compared with small column from the Pareto optimal solution set.
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