CN106844827B - Six-degree-of-freedom parallel mechanism optimization method - Google Patents
Six-degree-of-freedom parallel mechanism optimization method Download PDFInfo
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Abstract
The invention relates to a six-degree-of-freedom parallel mechanism optimization method, which comprises the steps of establishing a six-degree-of-freedom parallel mechanism model in ADAMS; compiling a six-degree-of-freedom parallel mechanism genetic algorithm according to structure optimization parameters and a target function in the six-degree-of-freedom parallel mechanism model; adding a six-degree-of-freedom parallel mechanism genetic algorithm into the ADAMS by utilizing a dynamic link library technology, and selecting a motion mode, an optimized objective function, optimized parameters and constraint conditions in an optimized design dialog box of the ADAMS; and calling a genetic algorithm of the six-degree-of-freedom parallel mechanism in the optimization algorithm so as to complete the optimization of the six-degree-of-freedom parallel mechanism. The method utilizes the advantages of flexibility, high efficiency and accurate and convenient dynamics analysis of ADAMS parametric modeling, simultaneously comprehensively utilizes the advantages of strong global optimization capability, strong robustness and parallel processing of a genetic algorithm, realizes the combination of an artificial intelligence algorithm and mechanical optimization, and can efficiently complete the structural optimization design of the six-degree-of-freedom parallel mechanism.
Description
Technical Field
The invention relates to a six-degree-of-freedom parallel mechanism optimization method, and belongs to the field of structural design and optimization.
Background
The prior optimization design method of the six-degree-of-freedom parallel mechanism can be divided into two types: one is based on ADAMS mechanical simulation software, and utilizes traditional optimization algorithms provided in ADAMS to optimize the mechanism parameters, i.e. OPTDES-GRG and OPTDES-SQP. Both algorithms are OPTDES codes provided by Design Synthesis, and both require a certain range of variation of Design variables and a certain range of operation of the objective function. The defects are that the traditional algorithms are difficult to achieve ideal effects in actual work, are easy to fall into local optimal solutions, and are easy to generate software error prompts when the number of variables is more than 4.
The second type is based on C language or MAT L AB programming, and uses different optimization algorithms to carry out optimization calculation of the six-degree-of-freedom parallel mechanism, the optimization algorithms can be flexibly selected, traditional optimization algorithms are eliminated, and bionic optimization algorithms based on a simulated biological system, such as genetic algorithms and ant colony algorithms, a standard Stewart parallel mechanism structure parameter design meeting local optimal dynamic isotropy is given by considering the load characteristics of the parallel mechanism in a standard six-degree-of-freedom parallel mechanism global optimization design method provided by patent CN 201310626619.9.
The invention content is as follows:
the technical problem solved by the invention is as follows: the method is characterized in that the defects in the background technology are overcome, a six-degree-of-freedom parallel mechanism optimization method is provided, the load characteristics, the working space, the positioning precision, the envelope size and the economic technical scheme of a parallel mechanism are comprehensively considered, the advantages of flexibility, high efficiency and accuracy and convenience of dynamic analysis of ADAMS parametric modeling are combined, the advantages of strong global optimization capability, strong robustness and parallel processing of a genetic algorithm are combined, a user interface of the optimization algorithm is provided for ADAMS software, the genetic algorithm is added into the ADAMS by utilizing a dynamic link library technology, a parallel mechanism parametric model is established in the ADAMS, and the link between the ADAMS and a target function is established. Therefore, the structural parameters of the six-freedom-degree parallel mechanism are optimally designed.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a six-degree-of-freedom parallel mechanism optimization method comprises the following steps:
(1) establishing a six-degree-of-freedom parallel mechanism model in ADAMS;
(2) compiling a six-degree-of-freedom parallel mechanism genetic algorithm according to structure optimization parameters and a target function in the six-degree-of-freedom parallel mechanism model;
(3) adding a six-degree-of-freedom parallel mechanism genetic algorithm into an ADAMS by utilizing a dynamic link library technology, and selecting a motion mode, an optimization objective function, an optimization parameter and a constraint condition in an optimization design dialog box in the ADAMS; and calling a genetic algorithm of the six-degree-of-freedom parallel mechanism in the optimization algorithm so as to complete the optimization of the six-degree-of-freedom parallel mechanism.
In the step (1), a six-degree-of-freedom parallel mechanism simulation model is established in ADAMS as follows:
selecting structural optimization parameters including an upper hinge point distribution circular radius, an upper hinge point distribution angle, a lower hinge point distribution circular radius, a lower hinge point distribution angle and a middle position time strut length, and determining upper and lower limits of the structural optimization parameters; in the ADMAS, the characteristics of the six-degree-of-freedom parallel mechanism in different directions are obtained according to the stroke change of the support rod when the structural optimization parameters are changed, an optimization objective function is determined to be the minimum value of the maximum extension value of the support rod based on the characteristics, the simulated motion form is sinusoidal motion along the Z axis, and finally a constraint condition function is established.
In the step (3), a program of a six-degree-of-freedom parallel mechanism genetic algorithm is generated, an obj file is compiled through ADAMS software to generate a dynamic link library file dll, and a link between ADAMS/View and an objective function is established by utilizing a dynamic link library technology, so that a user-defined algorithm, namely the genetic algorithm, is successfully operated during optimization design.
Compared with the prior art, the invention has the following advantages:
(1) the dynamic simulation method is based on ADAMS mechanical system dynamics simulation software, a dynamic model of a mechanical system can be conveniently established on a platform of the software, the dynamic process of the mechanical system can be directly and clearly demonstrated, and a completely parameterized mechanical system geometric model can be established. The method can simplify modeling steps to a great extent, improve modeling speed, combine kinematics dynamics and optimization, and improve simulation analysis efficiency.
(2) The genetic algorithm used by the invention is a calculation model for simulating the biological evolution process. The genetic algorithm is used as a new global optimization search algorithm and has the remarkable characteristics of simplicity, universality, strong robustness, suitability for parallel processing, wide application range and the like.
(3) The method utilizes the advantages of flexibility, high efficiency and accurate and convenient dynamics analysis of ADAMS parametric modeling, simultaneously comprehensively utilizes the advantages of strong global optimization capability, strong robustness and parallel processing of a genetic algorithm, realizes the combination of an artificial intelligence algorithm and mechanical optimization, and can efficiently complete the structural optimization design of the six-degree-of-freedom parallel mechanism.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a parameterized model of an ADAMS six-degree-of-freedom parallel mechanism in the invention;
FIG. 3 is a flow chart of a genetic algorithm in the present invention;
FIG. 4 is a design block for ADAMS optimization design;
FIG. 5 is a setup box for the ADAMS optimization algorithm.
The specific implementation mode is as follows:
the invention is further described with reference to the following figures and embodiments.
As shown in FIG. 1, the invention relates to an optimization method for a six-degree-of-freedom parallel mechanism based on ADAMS simulation software and genetic algorithm, which comprises the following steps:
firstly, establishing a correct simulation model in ADAMS (automatic dynamic analysis system), as shown in figure 2, simplifying the whole six-degree-of-freedom parallel mechanism system into a movable platform, a static platform, 12 struts, 6 spherical hinges and 6 hooke hinges, firstly clicking a cylindrical button in an ADAMS modeling tool bar to respectively establish the movable platform, the static platform and 12 struts, wherein the movable platform, the static platform and the 12 struts comprise 6 upper struts and 6 lower struts, in order to simulate the motion of the parallel mechanism, correct constraints are required to be added between the components, a fixed pair constraint is adopted between the static platform and the ground to fix the static platform to the ground, a hooke hinge constraint is adopted between the lower strut and the static platform to ensure that only 2 rotational degrees of freedom are provided between the lower strut and the static platform, a hinged spherical constraint is adopted between the upper strut and the movable platform to ensure that only 3 rotational degrees of freedom are provided between the upper strut and the movable platform, a movable pair constraint is adopted between the upper strut and the lower strut to ensure that only 1 translational degree of freedom is provided between the upper strut and the static platform, the lower strut and the static platform, the dynamic platform are provided with only 1 translational degree of freedom, the upper and lower hinge point distribution radius, the middle hinge point of the parametric distribution, and the upper hinge point of the upper hinge, the upper hinge point, the upper hinge distribution radius of the middle hinge point of the upper hinge, the dynamic platform, the upper hinge point of the lower hinge point of the dynamic platform, the upper hinge point of the lower hinge, the upper hinge point of the lower hinge, the lower hinge.
And step two, selecting the radius R of the upper hinge point distribution circle, the distribution angle α of the upper hinge point, the radius R of the lower hinge point distribution circle, the distribution angle β of the lower hinge point and the length L of the middle position time support rod as optimization parameters, and determining the corresponding upper and lower limits thereof.
The platform moves in a translational mode along the direction of X, Y, Z with each single degree of freedom by the same displacement to compare the stroke change of each supporting rod, and then the platform rotates around X, Y, Z shafts with each single degree of freedom by the same angle to compare the stroke change of each supporting rod, so that a supporting rod stroke change curve is obtained. The maximum change of the stroke of the supporting rod during the Z-direction translation can be obtained by combining the motion range and the stroke change curve of the supporting rod. Therefore, when the parallel mechanism parameter optimization problem is determined to be researched, the stroke of any supporting rod can be researched only when the parallel mechanism moves along the Z axis in a single degree of freedom. Therefore, the movement mode is determined to be sinusoidal along the Z axis, the study object is any strut, and the strut 1 is not taken. This can greatly simplify the calculation process and reduce the amount of calculation.
When the maximum stroke of the supporting rod is minimum, the dynamic force of the parallel mechanism, the static force of the limit pose and the Jacobian matrix can obtain reasonable values, so that the optimal objective function established in the ADAMS is the minimum maximum value of the absolute value of the telescopic quantity of the supporting rod, namely the maximum value is the minimum value
f(x)＝min(max|L(x)-L(0)|)
x is an independent variable and is composed of design variables R, R, α, β, L, and x is [ R R α β L ]]＝[x1x2x3x4x5]L (0) represents the length of the first strut in the neutral position, L (x) represents the length of the first strut when the upper platform is displaced Z along the Z axis, and defines xmin＝[rminRminαminβminLmin]And xmax＝[rmaxRmaxαmaxβmaxLmax]。
And establishing constraint functions in the ADAMS, wherein the constraint functions comprise upper and lower platform size constraints of the strut, strut length constraints, upper and lower hinge rotation angle range constraints and the like.
And step three, designing a genetic optimization algorithm, including encoding and generating an initial population, evaluating and detecting fitness values, selecting, crossing, mutating and terminating, wherein the process is shown as a figure 3.
(1) Firstly, expressing solution space variables, namely five optimization parameters R, R, α, β and L of a six-degree-of-freedom parallel mechanism as genotype floating point numbers of a genetic space in a real value coding mode, then randomly generating a plurality of chromosomes to be uniformly distributed in the solution space, and constructing an initial population of a genetic algorithm, wherein the size of the population is N-100, N is the size of the population, the space of the chromosomes is consistent with the solution space and is a continuous real number interval [ L, U](L＝xminAnd U ═ xmax)。
(2) And evaluating and detecting the fitness value. The genetic algorithm is a maximization optimization of the fitness function, thus transforming the minimization objective function into a maximization fitness function, i.e., f (x) 1/f (x).
(3) Selection, crossover, and mutation. Selecting: the selection operation is realized by adopting a gambling wheel selection method, and for an individual xiHas a fitness value of F (x)iI is the serial number of the individual, then the individual xiIs selected probability piIs composed of
Cumulative probability
Rotating the wheel N times, randomly generating a random number t between 0 and 1 when PP rotatesk-1≤t≤PPkThen, individual x is selectedkK is the serial number of the selected individual as the genetic parent; and (3) crossing: randomly generating a probability, the probability being less than the cross probability pcThen, calculate the crossover operator x'k＝axk+(1-a)xlAs new generation of individual x'kElse x'k＝xkWherein a is a constant over (0,1), xlIs another parent randomly selected, and l is the serial number thereof; mutation: randomly generating a probability, the probability being less than the mutation probability pmThen, a binary random number q (q ∈ {0,1}) is generated with equal probability, and then a new individual is obtained by mutation according to the following formula
Otherwise x "k＝x'kWhere Δ (n, y) ═ yr (1-n/T)bR is [0,1 ]]And (3) uniformly distributing random numbers, wherein y is a variable, n is a current iterative algebra, T is a maximum iterative algebra, and b is a preset constant.
(4) And when the iteration times reach the maximum iteration algebra T, the operation is terminated, and the solution corresponding to the maximum fitness function value obtained in the genetic process is output as the optimal solution, namely the final optimized structural parameters R, R, α, β and L.
C language is used for writing related programs such as genetic optimization algorithm, optimization algorithm calling interface and the like in vc _ init _ usr.c and mdi _ c.h in the ADAMS installation directory \ aview \ user _ subs, and the related programs are added into corresponding functions.
And modifying the program VC _ ini _ usr.c with the genetic optimization algorithm by using VC + +6.0 to generate a VC _ ini _ usr.obj file. And copying the file to an ADAMS installation directory \ common. And inputting mdi.bataview cr-u n vc _ init _ usr.obj-n vc _ init _ usr.dll on the cmd interface to generate a dynamic link library file vc _ init _ usr.dll. Then, after mdi.bat average ru-u i vc _ init _ usr.dll is input into cmd, carriage return is carried out, and the genetic algorithm can be called from ADAMS/View.
And fourthly, writing an interface function of the ADAMS and the calling program, determining that an interface is any one of the interfaces from user1 to user3, and importing corresponding data. And opening a design box of the ADAMS optimization design, and selecting the motion mode determined in the step 2, and the established objective function, design variable and constraint function as shown in FIG. 4. Clicking on "optimizer" appears the set up box for the optimization algorithm, as shown in FIG. 5. The User1, the User2 and the User3 are User-defined algorithms, and can call a genetic optimization algorithm compiled before, and then the genetic algorithm can be called for optimization by clicking a Start key in fig. 3.
In a word, a parallel mechanism parameterized model is established in ADAMS, the relation between the motion mode and the mechanism performance of the parallel mechanism is researched by applying ADMAS, the characteristics of the mechanism in different directions are obtained, and optimization parameters are selected and an objective function and constraint conditions thereof are determined. And compiling a six-degree-of-freedom parallel mechanism genetic algorithm, then combining an artificial intelligence genetic algorithm with the ADAMS, namely, generating a dynamic link library by genetic algorithm optimization codes, adding the dynamic link library into the ADAMS/View, and calling the compiled genetic algorithm to complete the optimization of the six-degree-of-freedom parallel mechanism in an ADAMS optimization design module. The method utilizes the advantages of high ADAMS modeling efficiency, parameterization and accurate and convenient dynamics analysis, simultaneously comprehensively utilizes the advantages of strong global optimization capability, strong robustness and parallel processing of a genetic algorithm, realizes the combination of an artificial intelligence algorithm and mechanical optimization, and can efficiently complete the structure optimization design of the six-degree-of-freedom parallel mechanism.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (2)
1. A six-degree-of-freedom parallel mechanism optimization method is characterized by comprising the following steps:
(1) establishing a six-degree-of-freedom parallel mechanism model in ADAMS;
the six-freedom parallel mechanism model includes: the device comprises a movable platform, a static platform, 12 supporting rods, 6 spherical hinges and 6 hooke hinges; a fixed pair constraint is adopted between the static platform and the ground, so that the static platform is fixed on the ground; the lower support rod and the static platform are constrained by a Hooke hinge, so that only 2 rotational degrees of freedom are formed between the lower support rod and the static platform; the upper support rod and the movable platform are constrained by a spherical hinge, so that only 3 rotational degrees of freedom are formed between the upper support rod and the movable platform; the upper support rod and the lower support rod are constrained by a sliding pair, so that only 1 translational degree of freedom is formed between the upper support rod and the lower support rod, and the extension and retraction of the support rods are realized;
parameterizing the upper and lower hinge point distribution circle radius, the upper and lower hinge point distribution angles and the middle position time support rod length to respectively obtain corresponding parameters, namely an upper hinge point distribution circle radius R, a lower hinge point distribution circle radius R, an upper hinge point distribution angle α, a lower hinge point distribution angle β and a middle position time support rod length L, wherein R and α determine the spherical hinge point position of the upper support rod and the movable platform, R and β determine the hooke hinge point position of the lower support rod and the static platform, and L determines the middle position height of the movable platform;
(2) selecting an upper hinge point distribution circular radius R, an upper hinge point distribution angle α, a lower hinge point distribution circular radius R, a lower hinge point distribution angle β and a middle position time strut length L as optimization parameters, and determining upper and lower limits of the optimization parameters;
the platform moves in a translational mode along the direction of X, Y, Z with each single degree of freedom for the same displacement to compare the stroke change of each supporting rod, and then the platform rotates around X, Y, Z shafts with each single degree of freedom for the same angle to compare the stroke change of each supporting rod, so that a supporting rod stroke change curve is obtained; combining the motion range and the stroke change curve of the supporting rod to obtain the maximum stroke change of the supporting rod when the supporting rod is translated in the Z direction; therefore, when the parallel mechanism parameter optimization problem is determined, only the stroke of any supporting rod during single-degree-of-freedom motion along the Z axis is researched; therefore, when the movement mode is determined to be sinusoidal movement along the Z axis and the study object is any strut, the strut 1 is taken to simplify the calculation process and reduce the calculation amount;
when the maximum stroke of the supporting rod is minimum, the dynamic force of the parallel mechanism, the static force of the limit pose and the Jacobian matrix can obtain reasonable values, so that the optimal objective function established in the ADAMS is the minimum maximum value of the absolute value of the telescopic quantity of the supporting rod, namely:
f(x)＝min(max|L(x)-L(0)|)
x is an independent variable and consists of design variables R, R, α, β and L, L (0) represents the length of the first strut in the middle position, L (x) represents the length of the first strut when the upper platform moves along the Z axis;
wherein:
x＝[r R α β L]＝[x1x2x3x4x5]
xmin＝[rminRminαminβminLmin]
xmax＝[rmaxRmaxαmaxβmaxLmax]
establishing a constraint function in the ADAMS, wherein the constraint function comprises size constraints of upper and lower platforms of the supporting rod, length constraints of the supporting rod and corner range constraints of upper and lower hinges;
(3) designing a genetic optimization algorithm, comprising encoding and generating initial population, fitness value evaluation detection, selection, crossing, mutation and termination;
encoding and generating an initial population, namely, expressing space variables, namely five optimization parameters R, R, α, β and L of a six-degree-of-freedom parallel mechanism into genotype floating point numbers of a genetic space in a real value encoding mode, then, randomly generating a plurality of chromosomes to be uniformly distributed in the solution space to construct the initial population of the genetic algorithm, wherein the size of the population is 100, N is the size of the population, and the chromosome space is consistent with the solution space and is a continuous real number interval [ L, U](L＝xminAnd U ═ xmax)；
And (3) evaluating and detecting a fitness value: the genetic algorithm is a maximum optimization of the fitness function, thus converting the minimization objective function into a maximum fitness function, i.e., f (x) 1/f (x);
selecting: the selection operation is realized by adopting a gambling wheel selection method, and for an individual xiHas a fitness value of F (x)iI is the serial number of the individual, then the individual xiIs selected probability piIs composed of
Cumulative probability
Rotating the wheel N times, randomly generating a random number t between 0 and 1 when PP rotatesk-1≤t≤PPkThen, individual x is selectedkK is the serial number of the selected individual as the genetic parent;
and (3) crossing: randomly generating a probability, the probability being less than the cross probability pcThen, calculate the crossover operator x'k＝axk+(1-a)xlAs new generation of individual x'kElse x'k＝xk(ii) a Wherein a is a constant over (0,1), xlIs another parent randomly selected, and l is the serial number thereof;
mutation: randomly generating a probability, the probability being less than the mutation probability pmThen, a binary random number q (q ∈ {0,1}) is generated with equal probability, and then a new individual is obtained by mutation according to the following formula
Otherwise x ″)k＝x′kWhere Δ (n, y) ═ yr (1-n/T)bR is [0,1 ]]Uniformly distributing random numbers, wherein y is a variable, n is a current iterative algebra, T is a maximum iterative algebra, and b is a preset constant;
stopping operation when the iteration times reach the maximum iteration algebra T, outputting a solution corresponding to the maximum fitness function value obtained in the genetic process as an optimal solution output, namely the final optimized structural parameters R, R, α, β and L;
(4) adding a six-degree-of-freedom parallel mechanism genetic algorithm into an ADAMS by utilizing a dynamic link library technology, and selecting a motion mode, an optimization objective function, an optimization parameter and a constraint condition in an optimization design dialog box in the ADAMS; and calling a genetic algorithm of the six-degree-of-freedom parallel mechanism in the optimization algorithm so as to complete the optimization of the six-degree-of-freedom parallel mechanism.
2. The method for optimizing the six-degree-of-freedom parallel mechanism according to claim 1, wherein: generating an obj file of a genetic algorithm of a six-degree-of-freedom parallel mechanism, compiling the obj file through ADAMS software to generate a dynamic link library file dll, and establishing a link between ADAMS/View and an objective function by utilizing a dynamic link library technology, thereby successfully operating a self-defined algorithm, namely the genetic algorithm, during the optimization design.
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