CN106650917A - Mechanical arm inverse kinematics solving method based on chaotic and parallelized artificial bee colony algorithm - Google Patents
Mechanical arm inverse kinematics solving method based on chaotic and parallelized artificial bee colony algorithm Download PDFInfo
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Abstract
The invention discloses a mechanical arm inverse kinematics solving method based on a chaotic and parallelized artificial bee colony algorithm. The method comprises the steps of 1), in an initialization phase, initializing a food source group through chaotic mapping and dividing the whole group into a plurality of mutually independent subgroups for parallel evolution; 2), in an employing bee phase, introducing control parameters to adjust search pace and parameter modification frequency when employing bees search new food sources; 3), calculating a selected probability of each food source based on a fitness value; 4), in an observation bee phase, selecting one food source for tracking by observation bees according to a roulette method; 5), in a detection bee phase, searching new food sources by detection bees and replacing the food sources with scanty nectar; and 6), in an information communication phase, replacing the relatively poor food source of one subgroup by the relatively good food source of the other subgroup. According to the method provided by the invention, the performance of the basic artificial bee colony algorithm in solving a mechanical arm inverse kinematics problem is improved, and the relatively fast convergence rate and relatively high global search capability are achieved.
Description
Technical field
The present invention relates to the technical field of Robotic inverse kinematics, refers in particular to a kind of based on parallelization chaos ant colony algorithm
Mechanical arm inverse kinematics method.
Background technology
The expected pose of known mechanical arm end effector, it is desirable to calculate and meet the joint angle for expecting to require, it is this kind of to ask
Topic is referred to as the Inverse Kinematics Problem of mechanical arm.The method for solving mechanical arm inverse kinematics is divided into two big class：Closing solution sum
Value solution.Closing solution solving speed is fast, in this way it is easy to determine be possible to solution, but the scope of application is little, and only structural parameters are very special
Mechanical arm just exist closing solution (analytic solutions).Numerical solution is applied widely, but its iterative nature causes solving speed slow, nothing
Method meets the requirement of real-time control.So finding a kind of general, efficient numerical solution for solving Inverse Kinematics Problem has weight
The practical significance wanted.In recent years, swarm intelligence algorithm is widely used in Inverse Kinematics Problem, for example particle cluster algorithm, harmony
Algorithm, artificial bee colony algorithm etc., these algorithms can within reasonable time draw preferable numerical solution.
Artificial bee colony algorithm (Artificial Bee Colony Algorithm, ABC) is 2005 by Karaboga etc.
A kind of novel heuristic search algorithm for putting forward, is a concrete application of swarm intelligence.It imitates the row that bee colony is looked for food
By the individual local optimal searching behavior of people worker bee, finally to protrude in colony global optimum and coming, with receiving faster
Hold back speed.The algorithm because control parameter is less, be easily achieved receive publicity with excellent solution performance and be widely used in it is each
In planting actual optimization problem.
In ABC algorithms, the frequency that parameter is changed when searching for New food source is constant, i.e., only change current foodstuff source one
Parameter produces New food source, causes algorithm the convergence speed slower.Meanwhile, search paces are also constant, i.e., parameter is only in fixed range
Inside it is altered, algorithm cannot be adjusted flexibly paces according to ruuning situation, easily be absorbed in local optimum.For this purpose, Karaboga et al. is carried
Gone out a kind of improved artificial bee colony algorithm, the algorithm introduce more probability MR (modified Rate (Modified Rate) and
Zoom factor SF (scaling factor) exerts one's influence to the frequency and search paces of parameter change.Initial food source colony
Be distributed to the searching algorithm based on colony it is critical that, without in the case of any priori, being randomly generated just
Beginning, colony was a kind of most common method, but the method can not assist search, algorithm efficiently obtains domain knowledge, causes
Ability of searching optimum is not good.For this purpose, Sharma etc. proposes that a kind of use Halton point sets generate the new algorithm in initial food source, claim
For H-ABC.Inspired by chaos system, Alatas etc. proposes a kind of the artificial of use chaotic maps optimization initial food source distribution
Ant colony algorithm, referred to as CABC (Chaotic ABC).In order to reduce the time of artificial bee colony algorithm solving complexity optimization problem, carry
Rise convergence rate, Luo etc. the thought of parallelization calculating is incorporated in ABC algorithms and the exchange mechanism between a seed group is proposed.
The above improves artificial bee colony algorithm and although improves ABC convergences of algorithm speed and ability of searching optimum, but
Other swarm intelligence algorithms are compared, such as particle cluster algorithm still has gap in convergence rate or ability of searching optimum, it is impossible to full
The requirement of sufficient mechanical arm real-time control.
The content of the invention
It is an object of the invention to overcome the deficiencies in the prior art, there is provided a kind of machine based on parallelization chaos ant colony algorithm
Tool arm inverse kinematics method CPABC (Chaotic and Parallelized Artificial Bee Colony), should
Method considers the requirement with very fast convergence rate and stronger ability of searching optimum when Inverse Kinematics Problem is solved, and overcomes
ABC algorithms and its innovatory algorithm can not well meet mechanical arm real-time control and try to achieve the problem of more excellent inverse solution.
For achieving the above object, technical scheme provided by the present invention is：It is a kind of based on parallelization chaos ant colony algorithm
Mechanical arm inverse kinematics method, comprises the following steps：
1) initial phase：Food source colony is initialized using chaotic maps and be divided into whole colony multiple mutually only
Vertical subgroup parallel evolutionary；
2) the honeybee stage is employed：Introducing control parameter adjusts search paces when employing honeybee search New food source and parameter change
Frequency；
3) selected probability of each food source is gone out based on fitness value calculation；
4) observe the honeybee stage：Observation honeybee selects a food source to be tracked with roulette method；
5) investigate the honeybee stage：Investigation honeybee searches for new food source and replaces the deficient food source of nectar；
6) the information interchange stage：The poor food source of one subgroup is substituted for the more excellent food source of another subgroup.
In step 1) in, described initial phase is specific as follows：
Chaos is peculiar and generally existing a kind of phenomenon in nonlinear system, and seeming confusion but has the inherent knot of exquisiteness
Structure.Randomness, ergodic and regularity are the most typical features of chaos so as to can be according to a certain rule of itself not repeatedly time
The all states gone through in given range.Chaos thought is incorporated in artificial bee colony algorithm, algorithm can be to a certain extent prevented
It is absorbed in local optimum and accelerates convergence rate.Wherein, using following 1 dimensional Logistic Map initialization food source：
Xn+1=μ Xn(1-Xn) n=0,1 ..., K
In formula, Xn(0,1), μ is Logistic parameters to ∈, and K is the iterations of chaos sequence.Generate i-th initial food
Thing source miProcess it is as follows：
A) the iterations K of chaos sequence is set.
B) the random initial vector ch for generating chaos sequence0=(ch01,ch02,...,ch0D), wherein D is the ginseng of food source
Number quantity (dimension of solution space).
C) according to chaos equation loop iteration K time, chaos vector ch is producedK=(chK1,chK2,...,chKD)。
D) initial food source m is producedi=(mi1,mi2,...,miD), wherein：
mij=mj min+chKj(mj max-mj min), i=1,2 ..., SN j=1,2 ... D
Wherein, mijRepresent j-th parameter of i-th food source, mj maxAnd mj minRepresent respectively the maximum of j-th parameter with
Minimum of a value, SN represents food source quantity, and D represents the dimension of solution space.Meanwhile, each food source has one to be initialized to
0 counter trial represents the number of times for attempting search.Initial food source can be employed honeybee, observation honeybee, investigation in the subsequent stage
Explore on honeybee loop iteration ground, until it reaches maximum iteration time MCN simultaneously obtains best foods source.Each food source can only be by one
It is individual to employ honeybee or observation honeybee to be responsible for collection, that is, employ the quantity of honeybee, observation honeybee and food source three equal.
Initial food source colony is divided into into P subgroup, each subgroup individually develops.Each subgroup is per iteration R time with regard to phase
Mutual exchange of information.After all subgroups all develop to be finished, contrast in each subgroup best foods source and obtain the optimal of whole colony
Food source.
In step 2) in, described employs the honeybee stage, specific as follows：
New algorithm introduces control parameter more probability MR (modified rate), employs honeybee to surround food source miThe new food of search
Thing source viWhen, for miJ-th parameter generate random number Rij∈ (0,1), RijGenerate v after comparing with MR as the following formulaij：
In formula, mkIt is the individual food source of randomly selected kth (k is not equal to i), ФijThe change frequency of parameter is represented, in ABC
In be random number between interval [- 1,1], and in new algorithm be the random number between interval [- SF, SF].Zoom factor SF
(scaling factor) is another control parameter that new algorithm is introduced, and it sets and searching for before algorithm operation
According to Rechenberg1/5 mutation rule adjust automaticallies in journey, the adjustment formula according to the rule settings is as follows：
In formula, ФmThe quantity ratio of the more excellent food source after m iterative search and total foodstuff source is represented, if ФmIt is less than
1/5, SF reduction improves the development ability of algorithm.If ФmThe search capability of algorithm is improved more than 1/5, SF increases.
Employ honeybee according to cost function to New food source viQuality evaluated, if viQuality be higher than mi, then viTake
For mi, trial is reset as 0.If viQuality be less than or equal to mi, trial cumulative 1.If vijJ-th parameter is exceeded
Span, then reset vijFor the virtual value in zone of reasonableness.Then, New food source v is drawn according to equation belowiIt is suitable
Answer angle value fitnessi：
In formula, costiRepresent the quality of i-th food source.
In step 3) in, the described selected probability for going out each food source based on fitness value calculation is specific as follows：
Employ honeybee that the fitness value of food source is taken back into honeycomb to share with observation honeybee.Algorithm goes out based on fitness value calculation
Selected probability p of i food sourcei, formula is as follows：
In step 4) in, it is the described observation honeybee stage, specific as follows：
Observation honeybee is according to selected probability piMore excellent food source is tracked with roulette wheel selection, is observed during tracking
Honeybee performs and employs honeybee stage identical task.After all observation honeybees are finished, fitness under current iteration number of times is recorded
Value highest food source.
In step 5) in, it is the described investigation honeybee stage, specific as follows：
Investigation honeybee checks the Counter Value trial of each food source, if trial is more than threshold value limit, shows food
Source and its periphery nectar are deficient and are abandoned, and new food source is searched for according to the mode of initial phase by investigation honeybee.If
There is the trial of multiple food sources more than limit, just abandon wherein trial maximum food source.
In step 6) in, it is the described information interchange stage, specific as follows：
All subgroups, with regard to mutual exchange of information, allow subgroup group per iteration R timeiMiddle nectar is most abundant, and (fitness value is most
It is high) k food source replace subgroup group(i+1)mod PK most deficient food source of middle nectar, wherein i represents that subgroup is compiled
Number, p represents subgroup quantity.After the completion of information interchange, each subgroup is from step 2) start to continue independently to develop parallel.
The present invention compared with prior art, has the advantage that and beneficial effect：
1st, using chaotic maps initialization food source colony, chaotic maps have extreme sensitivity to the present invention to primary condition
Dependence, even if chaos sequence initial vector ch0In D parameter between it is very close, in dimensional Logistic chaotic maps
Iteration effect under, final vector chkIn each parameter all may separate, this undoubtedly improves the various of initial food source colony
Property, algorithm is avoided to a certain extent is absorbed in local optimum, and accelerate convergence of algorithm speed.
2nd, present invention introduces paces and parameter change frequency are searched in control parameter adjustment, because ABC, CABC and PABC-RC
Algorithm the change frequency of parameter and search paces when New food source is searched for all immobilize, i.e., only change in fixed range and work as
One parameter of front food source produces New food source, is employing honeybee and is observing the distribution of New food source of honeybee effect stepwise, causes
Global exploring ability is not good, is easily trapped into local optimum.And CPABC cause each parameter in current foodstuff source have the opportunity to by
Change, while change amplitude can suitably be adjusted according to the solution performance of current algorithm, so global exploring ability with locally
Development ability reaches the state of a dynamic equilibrium, and algorithm can well play this two classes ability, can find in solution space
More excellent solution.
3rd, the bee colony of search food source is divided into multiple independent subgroup parallel evolutionaries by the present invention, and CPABC is substantially
The multiple ABC algorithms of executed in parallel on multiprocessor, the solving speed for making algorithm is improved.Exchange mechanism between subgroup simultaneously
Poor solution is allowed to be abandoned, only the excellent solution around this subgroup and other subgroups is continued search for, and improves the global convergence speed of algorithm.
Description of the drawings
Fig. 1 a are one of kinematics model of PUMA560 in the present embodiment.
Fig. 1 b are two of the kinematics model of PUMA560 in the present embodiment.
Fig. 2 is the simple process figure that single subgroup develops in the present embodiment.
Fig. 3 is that average optimal cost function value changes when 5 kinds of algorithms solve respectively Inverse Kinematics Problem 30 times in the present embodiment
For the comparison curves of process.
Specific embodiment
With reference to specific embodiment, the invention will be further described.
By taking typical sixdegree-of-freedom simulation PUMA560 as an example.PUMA560 mechanical arms have six-freedom degree and own
Joint is cradle head.First three joint mainly affects the position of end effector, and afterwards three joints determine end effector
Attitude.Using D-H methods PUMA560 mechanical arms are indicated and are modeled, and derive forward kinematics equation.Fig. 1 a, 1b
The distribution situation of link rod coordinate system when showing that all joint angles are zero-bit, wherein Fig. 1 b represent mechanical brachiocubital distribution feelings
Condition.Table 1 below then gives the D-H parameters of PUMA560：
The D-H parameters of the PUMA560 of table 1
| Joint angle | αi-1(degree) | ai-1(rice) | di(rice) | θi(degree) | Scope (degree) |
| 1 | 0 | 0 | 0 | θ1 | - 160～160 |
| 2 | -90 | 0 | 0 | θ2 | - 245～45 |
| 3 | 0 | 0.4318 | 0.1491 | θ3 | - 45～225 |
| 4 | -90 | -0.0203 | 0.4331 | θ4 | - 110～170 |
| 5 | 90 | 0 | 0 | θ5 | - 100～100 |
| 6 | -90 | 0 | 0 | θ6 | - 266～266 |
Coordinate system i is as follows relative to the transformation matrix of coordinate system i-1：
Transformation matrix between all adjacent links coordinate systems is obtained according to the D-H parameters of PUMA560 mechanical arms0 1T(θ1)、1 2T
(θ2)、2 3T(θ3)、3 4T(θ4)、4 5T(θ5) and5 6T(θ6), finally obtain the product of 6 transformation matrixs：
In formula,0 6T(θ6) forward kinematics equation of PUMA560 is constituted, it describes end effector (link rod coordinate system
6) relative to the pose of basis coordinates system (link rod coordinate system 0).
Value (the θ of all joint angles of given mechanical arm1,θ2,θ3,θ4,θ5,θ6), end can be performed by positive kinematics
Cartesian coordinate (x of the device in tool coordinates systemT,yT,zT) be converted to cartesian coordinate (x in basis coordinates systemB,yB,zB).This
It is exactly to find out one group of optimum joint angle value using the method that inventive method solves sixdegree-of-freedom simulation Inverse Kinematics Problem, is made
Obtain (xB,yB,zB) with expectation coordinate (x, y, z) of the end effector in basis coordinates system as close possible to wherein optimal joint angle
Value (θ1,θ2,θ3,θ4,θ5,θ6) be exactly the inventive method optimum food source.For this reason, it may be necessary to define a cost function go to weigh
(xB,yB,zB) with degree of approximation between (x, y, z), be used herein as this point-to-point transmission Euclidean distance square as in of the invention
Cost function, formula is as follows：
Cost=(x-xB)2+(y-yB)2+(z-zB)2
The mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm that the present embodiment is provided, concrete bag
Include following steps：
1) initial phase
Using following 1 dimensional Logistic Map initialization food source：
Xn+1=μ Xn(1-Xn) n=0,1 ..., K
In formula, Xn(0,1), Logistic parameter μs are set as 4 to ∈.Generate i-th initial food source miProcess it is as follows：
A) the iterations K=1000 of chaos sequence is set.
B) the random initial vector ch for generating chaos sequence0=(ch01,ch02,...,ch0D), wherein D=6.
C) according to chaos equation loop iteration K time, chaos vector ch is producedK=(chK1,chK2,...,chKD)。
D) initial food source m is producedi=(mi1,mi2,...,miD), wherein：
mij=mj min+chKj(mj max-mj min), i=1,2 ..., SN j=1,2 ... D
Wherein, mijRepresent j-th parameter of i-th food source, mj maxAnd mj minRepresent respectively the maximum of j-th parameter with
Minimum of a value, corresponds in the present embodiment the maximal and minmal value of j-th joint angle in table 1.Food source quantity SN=40, solution space
Dimension D=6, in the present embodiment correspondence D joint angle.Meanwhile, each food source has a counting for being initialized to 0
Device trial represents the number of times for attempting search.Initial food source can be employed honeybee, observation honeybee, investigation honeybee circulation in the subsequent stage
Iteratively explore, until it reaches maximum iteration time MCN obtains best foods source, MCN is set as 500.Each food source is only
By one honeybee or observation honeybee can be employed to be responsible for collection, that is, employ the quantity of honeybee, observation honeybee and food source three equal.
Initial food source colony is divided into into P subgroup, wherein P is 4, and each subgroup individually develops.Each subgroup often changes
For R time with regard to mutual exchange of information, R=50 in the present embodiment.After all subgroups all develop to be finished, contrast and most preferably eaten in each subgroup
Thing source simultaneously obtains the best foods source of whole colony.
2) the honeybee stage is employed
Arrange parameter more probability MR is 0.3, employs honeybee to surround food source miSearch New food source viWhen, for miJ-th
Parameter generates random number Rij∈ (0,1), RijGenerate v after comparing with MR as the following formulaij：
In formula, mkIt is the individual food source of randomly selected kth (k is not equal to i), ФijThe change frequency of parameter is represented, in ABC
In be random number between interval [- 1,1], and in new algorithm be the random number between interval [- SF, SF].Zoom factor SF
Be new algorithm introduce another control parameter, algorithm operation before be set as 0.6 and in search procedure according to
Rechenberg1/5 mutation rule adjust automaticallies, adjustment formula is as follows：
In formula, ФmThe quantity ratio of the more excellent food source after m search and total foodstuff source is represented, if ФmLess than 1/5,
SF reduces improves the development ability of algorithm.If ФmThe search capability of algorithm is improved more than 1/5, SF increases.
Employ honeybee according to cost function cost to New food source viQuality evaluated, if viQuality be higher than mi, then
viReplace mi, trial is reset as 0.If viQuality be less than or equal to mi, trial cumulative 1.If vijJ-th ginseng is exceeded
Several spans, then reset vijFor the virtual value in zone of reasonableness.Then, New food source v is drawn according to equation belowi
Fitness value fitnessi：
In formula, costiRepresent the quality of i-th food source.
3) selected probability of each food source is gone out based on fitness value calculation
Employ honeybee that the fitness value of food source is taken back into honeycomb to share with observation honeybee.Algorithm goes out based on fitness value calculation
Selected probability p of i food sourcei, formula is as follows：
4) observe the honeybee stage
Observation honeybee is according to selected probability piMore excellent food source is tracked in the way of roulette, is observed during tracking
Honeybee performs and employs honeybee stage identical task.After all observation honeybees are finished, fitness under current iteration number of times is recorded
Value highest food source.
5) investigate the honeybee stage
Investigation honeybee contrasts the Counter Value trial of each food source and threshold value limit, limit=in the present embodiment
150, if trial is more than limit, shows food source and its periphery nectar scarcity and abandoned, by investigation honeybee according to initial
The mode in change stage searches for new food source.If multiple food sources trial be more than limit, just will wherein trial it is maximum
Food source abandon.
6) the information interchange stage
All subgroups, with regard to mutual exchange of information, allow subgroup group per iteration R timeiMiddle nectar is most abundant, and (fitness value is most
It is high) k food source replace subgroup group(i+1)mod PK most deficient food source of middle nectar, wherein i represents that subgroup is compiled
Number, p represents subgroup quantity, and k is set as 5.After the completion of information interchange, each subgroup is from step 2) start to continue independently to drill parallel
Change.
The process that single subgroup develops refers to Fig. 2.
Inverse Kinematics Problem except solving PUMA560 using the inventive method, also in identical parameter in the present embodiment
Setting is lower to be solved using ABC algorithms and its 3 kinds of innovatory algorithms.Table 2 below is that 5 kinds of algorithms are solved respectively after Inverse Kinematics Problem 30 times
The statistics of optimal cost functional value.
2-5 kinds of algorithms of table solve respectively the statistics of optimal cost functional value after Inverse Kinematics Problem 30 times
| It is best | It is worst | Averagely | Variance | |
| ABC | 1.072511e-03 | 3.150317e-02 | 1.316312e-02 | 6.638365e-05 |
| CABC | 2.970008e-05 | 1.440834e-03 | 3.158536e-04 | 7.998854e-08 |
| PABC-RC | 3.585916e-05 | 1.363282e-02 | 5.690389e-03 | 1.036634e-05 |
| MABC | 1.278826e-17 | 1.074712e-16 | 5.859731e-17 | 7.762848e-34 |
| CPABC | 1.498140e-18 | 5.243530e-17 | 1.983738e-17 | 1.555608e-34 |
As can be seen from the table：A) because ABC algorithms are easily trapped into local optimum, resulting optimization in solution procedure
As a result there is relatively large deviation compared with other four kinds of algorithms.B) in 30 operation results, optimum and worst optimization that CPABC draws
Xie Jun is better than the respective value of other four kinds of algorithms, illustrates that the introducing of two control parameters of more probability MR and zoom factor SF causes to calculate
The ability of searching optimum of method is improved.C) the optimization solution variance that CPABC operations are obtained for 30 times will be less than other four kinds of algorithms
Respective value, illustrates that the solution quality of the algorithm is relatively stable.
Fig. 3 is the ratio of average optimal cost function value iterative process when 5 kinds of algorithms solve respectively Inverse Kinematics Problem 30 times
Compared with curve.It can be seen that：A) because the change frequency of ABC, CABC and PABC-RC algorithm parameter when New food source is searched for
All immobilize with search paces, i.e., the parameter that current foodstuff source is only changed in fixed range produces New food source,
Employ honeybee and observe the distribution of New food source of honeybee effect stepwise, cause global exploring ability not good, be easily trapped into local optimum.
And MABC and CPABC cause each parameter in current foodstuff source to have the opportunity to be modified, while the amplitude of change can be according to current
The solution performance of algorithm is suitably adjusted, and so global exploring ability reaches the shape of a dynamic equilibrium with local development ability
State, algorithm can well play this two classes ability, and more excellent solution can be found in solution space.So it is observed from fig. 3 that MABC
With the iterativecurve rapid advance of CPABC in transverse axis, global exploring ability is compared other 3 kinds of algorithms and is significantly increased.b)CABC
Compare ABC and PABC-RC, CPABC compare MABC, the final optimization pass solution that the former algorithm is obtained will be better than the latter, this is because
CABC and CPABC have used Logistic chaotic maps to produce initial food source colony.Chaotic maps have pole to primary condition
The sensitive dependence in end, even if chaos sequence initial vector ch0In D parameter between it is very close, Logistic mapping
Iteration effect under, final vector chkIn each parameter all may separate, this undoubtedly improves the various of initial food source colony
Property, algorithm is avoided to a certain extent is absorbed in local optimum, and accelerate convergence of algorithm speed.C) due to existing in CPABC
Multiple subgroup parallel evolutionaries, the exchange mechanism between subgroup allows excellent solution of each subgroup around itself other subgroup to continue search for, and
MABC can only abandon worst solution.Therefore the optimal cost functional value of CPABC can be observed from Fig. 3 in most of iterationses
Will be also such case better than MABC, PABC-RC and ABC.
Table 3 is given on the premise of same computer and parameter setting, and 5 kinds of Algorithm for Solving Inverse Kinematics Problems draw most
Eventually optimization solution is average time-consuming, and as can be seen from the table the average CPU of CPABC is time-consuming more compared with other algorithms, is only below CABC.
But it is relevant to mention many factors such as written in code skill with computer hardware configuration, operating system, programming language because CPU is time-consuming,
Algorithm is more concerned with setting the quality of solution in identical parameters. from this view set forth herein CPABC algorithms have more preferably
Solution performance.
3-5 kinds of algorithms of table show that the average CPU of final optimization pass solution takes
| Algorithm | It is average time-consuming |
| ABC | 0.043267 |
| CABC | 0.087467 |
| MABC | 0.049133 |
| PABC-RC | 0.060500 |
| CPABC | 0.075567 |
In sum, Mechanical transmission test is solved using the inventive method and compares ABC algorithms and its derivative algorithm tool against solution
There are convergence rate faster and stronger ability of searching optimum, be worthy to be popularized.
Embodiment described above is only the preferred embodiments of the invention, not limits the practical range of the present invention with this, therefore
The change that all shapes according to the present invention, principle are made, all should cover within the scope of the present invention.
Claims (7)
1. a kind of mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm, it is characterised in that including following
Step：
1) initial phase：Food source colony is initialized using chaotic maps and be divided into whole colony multiple separate
Subgroup parallel evolutionary；
2) the honeybee stage is employed：Introduce control parameter adjustment and employ search paces during honeybee search New food source with parameter change frequently
Rate；
3) selected probability of each food source is gone out based on fitness value calculation；
4) observe the honeybee stage：Observation honeybee selects a food source to be tracked with roulette method；
5) investigate the honeybee stage：Investigation honeybee searches for new food source and replaces the deficient food source of nectar；
6) the information interchange stage：The poor food source of one subgroup is substituted for the more excellent food source of another subgroup.
2. a kind of mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm according to claim 1,
Characterized in that, in step 1) in, described initial phase is specific as follows：
Chaos is peculiar and generally existing a kind of phenomenon in nonlinear system, and seeming confusion but has the immanent structure of exquisiteness；With
Machine, ergodic and regularity are the most typical features of chaos so as to can according to a certain rule of itself not repeatedly travel through to
Determine all states in scope；Chaos thought is incorporated in artificial bee colony algorithm, can to a certain extent prevent algorithm to be absorbed in
Local optimum simultaneously accelerates convergence rate；Wherein, using following 1 dimensional Logistic Map initialization food source：
Xn+1=μ Xn(1-Xn) n=0,1 ..., K
In formula, Xn(0,1), μ is Logistic parameters to ∈, and K is the iterations of chaos sequence；Generate i-th initial food source mi
Process it is as follows：
A) the iterations K of chaos sequence is set；
B) the random initial vector ch for generating chaos sequence0=(ch01,ch02,...,ch0D), wherein D is the parameter number of food source
Amount is the dimension of solution space；
C) according to chaos equation loop iteration K time, chaos vector ch is producedK=(chK1,chK2,...,chKD)；
D) initial food source m is producedi=(mi1,mi2,...,miD), wherein：
mij=mj min+chKj(mj max-mj min), i=1,2 ..., SN j=1,2 ... D
Wherein, mijRepresent j-th parameter of i-th food source, mj maxAnd mj minThe maximum and minimum of j-th parameter are represented respectively
Value, SN represents food source quantity, and D represents the dimension of solution space；Meanwhile, each food source has one to be initialized to 0
Counter trial represents the number of times for attempting search；Initial food source can be employed honeybee, observation honeybee, investigation honeybee in the subsequent stage
Explore on loop iteration ground, until it reaches maximum iteration time MCN simultaneously obtains best foods source；Each food source can only be by one
Employ honeybee or observation honeybee to be responsible for collection, that is, employ the quantity of honeybee, observation honeybee and food source three equal；
Initial food source colony is divided into into P subgroup, each subgroup individually develops；Each subgroup is per R just mutually friendship of iteration
Stream information；After all subgroups all develop to be finished, contrast best foods source in each subgroup and obtain the best foods of whole colony
Source.
3. a kind of mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm according to claim 1,
Characterized in that, in step 2) in, described employs the honeybee stage, specific as follows：
New algorithm introduces control parameter more probability MR, employs honeybee to surround food source miSearch New food source viWhen, for miJth
Individual parameter generates random number Rij∈ (0,1), RijGenerate v after comparing with MR as the following formulaij：
In formula, mkIt is randomly selected k-th food source, k is not equal to i, ФijThe change frequency of parameter is represented, in ABC Zhong Shi areas
Between random number between [- 1,1], and in new algorithm be the random number between interval [- SF, SF]；Zoom factor SF is new calculation
Another control parameter that method is introduced, it sets and in search procedure according to Rechenberg1/5 before algorithm operation
Mutation rule adjust automatically, the adjustment formula according to the rule settings is as follows：
In formula, ФmThe quantity ratio of the more excellent food source after m iterative search and total foodstuff source is represented, if ФmLess than 1/5,
SF reduces improves the development ability of algorithm；If ФmThe search capability of algorithm is improved more than 1/5, SF increases；
Employ honeybee according to cost function to New food source viQuality evaluated, if viQuality be higher than mi, then viReplace mi,
Trial is reset as 0；If viQuality be less than or equal to mi, trial cumulative 1；If vijThe value of j-th parameter is exceeded
Scope, then reset vijFor the virtual value in zone of reasonableness；Then, New food source v is drawn according to equation belowiFitness
Value fitnessi：
In formula, costiRepresent the quality of i-th food source.
4. a kind of mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm according to claim 1,
It is characterized in that：In step 3) in, the described selected probability for going out each food source based on fitness value calculation is specific as follows：
Employ honeybee that the fitness value of food source is taken back into honeycomb to share with observation honeybee；Algorithm goes out i-th based on fitness value calculation
Selected probability p of food sourcei, formula is as follows：
5. a kind of mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm according to claim 1,
It is characterized in that：In step 4) in, it is the described observation honeybee stage, specific as follows：
Observation honeybee is according to selected probability piMore excellent food source is tracked with roulette wheel selection, honeybee is observed during tracking and is held
Go and employ honeybee stage identical task；After all observation honeybees are finished, fitness value is recorded under current iteration number of times most
High food source.
6. a kind of mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm according to claim 1,
It is characterized in that：In step 5) in, it is the described investigation honeybee stage, specific as follows：
Investigation honeybee checks the Counter Value trial of each food source, if trial is more than threshold value limit, show food source and
Its periphery nectar is deficient and is abandoned, and new food source is searched for according to the mode of initial phase by investigation honeybee；If many
The trial of individual food source is more than limit, just abandons wherein trial maximum food source.
7. a kind of mechanical arm inverse kinematics method based on parallelization chaos ant colony algorithm according to claim 1,
It is characterized in that：In step 6) in, it is the described information interchange stage, specific as follows：
All subgroups, with regard to mutual exchange of information, allow subgroup group per iteration R timeiMost abundant i.e. fitness value highest k of middle nectar
Individual food source replaces subgroup group(i+1)mod PK most deficient food source of middle nectar, wherein i represents that subgroup is numbered, and p is represented
Subgroup quantity；After the completion of information interchange, each subgroup is from step 2) start to continue independently to develop parallel.
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