CN114434429B - Dynamic precision design method and system for industrial robot - Google Patents
Dynamic precision design method and system for industrial robot Download PDFInfo
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- CN114434429B CN114434429B CN202210281353.8A CN202210281353A CN114434429B CN 114434429 B CN114434429 B CN 114434429B CN 202210281353 A CN202210281353 A CN 202210281353A CN 114434429 B CN114434429 B CN 114434429B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B25J9/00—Programme-controlled manipulators
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- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
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Abstract
The invention discloses a dynamic precision design method and a dynamic precision design system for an industrial robot, wherein the dynamic precision design method comprises the following steps: establishing a theoretical kinetic model considering robot joint friction, joint clearance and tail end processing force; forming an uncertain robot dynamics simulation system based on a Monte Carlo method; providing a robot dynamic precision evaluation index, utilizing correlation analysis to obtain a main uncertain factor affecting the robot dynamic precision, and neglecting a secondary uncertain factor; combining the precision requirement of the parts processed by the robot, establishing a constraint model of the main uncertain factors of the robot, and constructing a multi-objective function integrating dynamic precision evaluation indexes and cost; and calculating a main factor reference range which influences the dynamic accuracy of the robot after optimization, so as to guide the dynamic accuracy design. The method solves the problems that the robot depends on the rule of thumb in the design and manufacturing stage and cannot consider the influence of multiple uncertain factors in actual processing, and has guiding significance compared with the rule of thumb.
Description
Technical Field
The invention belongs to the field of industrial robot precision design, and particularly relates to a dynamic precision design method and system for an industrial robot.
Background
Industrial robots are favored in the fields of automobile manufacturing, machining and the like due to the characteristics of high machining efficiency, wide working range, high flexibility degree and the like, and are gradually introduced into the aviation manufacturing industry, but the traditional precision design method based on kinematics cannot meet the requirements of new generation aviation products on the dynamic precision of robot machining. The reason for this is that the actual kinematics, kinetic parameters and theoretical values of the design phase of each manufactured robot have large errors, and such errors often have uncertainty. In addition, the joint gap, joint friction, end processing force, and the like of the robot are randomly changed. The uncertainty error factors seriously affect the consistency of the positioning precision, the track precision and the dynamic performance of the robot, so that the more comprehensive uncertainty factors in the robot processing process are considered from the aspect of robot dynamics, and research is conducted in the design stage, so that the dynamic precision is improved.
The current precision design of the robot comprises two reciprocal processes of precision analysis and precision optimization allocation. The published patent application of the invention, "a robot precision design method, CN106777422a" analyzes the correspondence between manufacturing precision, motion control precision and robot probability precision value based on a kinematic model, and allocates tolerance items according to the allowable precision remaining amount. The problem of optimal distribution of joint tolerance is studied based on kinematics by taking the position and direction errors and manufacturing cost of the end effector of the robot into account in Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis published by s.s.rao in journal Reliability Engineering & System Safety. Technical problems existing in the prior art: 1) Ignoring uncertainty caused by an error source of the actual robot in manufacturing installation and machining movement processes, and analyzing the certainty of all influencing factors; 2) The robot precision design depends on a rule of thumb, lacks a robot dynamic precision evaluation index, and forms a set of system robot dynamic precision optimization design method.
Disclosure of Invention
The invention provides a dynamic precision design method and a dynamic precision design system for an industrial robot aiming at the defects in the prior art.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the dynamic precision design method of the industrial robot is characterized by comprising the following steps of:
step S1: establishing a robot dynamics model taking joint friction, joint clearance and tail end processing force into consideration;
step S2: forming an uncertain robot dynamics simulation system based on a Monte Carlo method;
step S3: calculating a dynamic accuracy evaluation index of the robot based on the robot dynamics model in the step S1 and the uncertain robot dynamics simulation system in the step S2, and obtaining a main uncertain factor affecting the dynamic accuracy of the robot by utilizing correlation analysis, and ignoring a secondary uncertain factor;
step S4: combining the precision requirement of the parts processed by the robot, establishing a constraint model of the main uncertain factors of the robot, and constructing a multi-objective function integrating dynamic precision evaluation indexes and cost;
step S5: and carrying out multi-objective optimization based on a genetic algorithm, and solving a multi-objective function to obtain a reference range of main uncertain factors affecting the dynamic accuracy of the robot after optimization, so as to guide the dynamic accuracy design.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in the step S1, for the robot with n links, the robot end machining force is considered as the force and moment acting on the link n by the link n+1, and the joint friction model of the robot is respectively builtAnd joint space model
In the method, in the process of the invention,an n×1 joint angular velocity vector; f (f) s Representing static friction; f (f) c Representing coulomb friction; sigma (sigma)Representing the viscous coefficient of friction; v s Representing the stribeck coefficient; delta represents the penetration depth caused by the shaft diameter and the bushing impact; />Indicating the relative impact velocity; k represents a generalized stiffness parameter; d represents a damping parameter;
the final robot dynamics model is:
wherein τ represents an n×1 joint moment vector; θ represents an n×1 joint rotation angle vector;refers to an n x 1 joint angular acceleration vector; m (θ) represents an n×n inertia matrix; />Representing an n x n family of force and centrifugal force matrices; g (θ) represents an n×1 gravity moment vector.
Further, the step S3 specifically includes the following steps:
step S3.1: setting the number N of samples, wherein each sample comprises t uncertain factors of the robot, and the uncertain factors comprise kinematic parameters, dynamic parameters, joint friction, joint clearance and tail end processing force of the robot;
step S3.2: generating N groups of random sample values X according to the distribution rule of t uncertain factors j ＝[x j1 ，…，x jt ]，j＝1，..，N；
Step S3.3: inputting the sample value generated in the step S3.2 into the robot dynamics model in the step S1 to obtain the tail end dynamic precision F (X) j ) Judging whether the dynamic accuracy F of the robot is met a Finally obtaining the number m meeting the dynamic precision requirement;
step S3.4: after the simulation of the N groups of samples is finished, the proposed dynamic accuracy evaluation index P of the robot is obtained F =m/N; carrying out correlation analysis on t uncertain factors and dynamic precision evaluation indexes, and judging the correlation degree between each uncertain factor and the dynamic precision evaluation indexes, thereby determining main uncertain factors affecting the dynamic precision of the robot;
step S3.5: k main uncertain factors affecting the dynamic accuracy of the robot are output.
Further, in the step S3.4, the manner of determining the main uncertainty factor affecting the dynamic accuracy of the robot is specifically as follows:
if the absolute value of the correlation coefficient and the absolute value of the correlation test statistic are larger, the correlation coefficient is a main uncertainty factor, otherwise, the correlation coefficient is a secondary uncertainty factor; assuming that S groups of simulation are performed together, generating N groups of sample values in each group to obtain a dynamic accuracy evaluation index P of the i-th group of simulation F (E) i ；x i For the observed value of a certain uncertainty factor, each group of correlation coefficientsThe formula for the test statistic R is:
in the method, in the process of the invention,for the mean value of the uncertainty element +.>The mean value of the index is evaluated for dynamic accuracy.
Further, the step S4 specifically includes the following steps:
step S4.1: according to k main uncertain factors output in the step S3.5 as design variables, and combining the precision requirements of parts processed by the robot, establishing a constraint model of the main uncertain factors of the robot:
wherein x is 1 ，x 2 ，...，x k For k main uncertainties, e 1a ，e 2a ，...，e ka Lower limit value of k main uncertainty factors, e 1b ，e 2b ，...，e kb An upper limit value that is k major uncertainty factors;
step S4.2: establishing a relation between the manufacturing Cost (Y) of the industrial robot body and a main uncertain factor:
Cost(Y)＝aT -b
wherein T represents tolerance, a and b are cost coefficients, and Y= [ e ] 1a ，e 2a ，...，e ka ，e 1b ，e 2b ，...，e kb ]Design variables that are the primary uncertainty factors;
in combination with the dynamic accuracy evaluation index of the robot, a multi-objective function W (Y) of the accuracy optimization design is constructed as follows:
W(Y)＝ω 1 Cost(Y)+ω 2 /P F (Y)
wherein omega is 1 And omega 2 Is a weight coefficient; p (P) F (Y) represents a dynamic accuracy evaluation index based on the main uncertainty factor.
The invention also provides a dynamic precision design system of the industrial robot, which is characterized by comprising the following components:
a robot dynamics model establishing unit for establishing a robot dynamics model in consideration of joint friction, joint clearance and end processing force;
the uncertain robot dynamics simulation system based on the Monte Carlo method is used for calculating a dynamic accuracy evaluation index of the robot based on a robot dynamics model, obtaining a main uncertain factor affecting the dynamic accuracy of the robot by utilizing correlation analysis, and ignoring a secondary uncertain factor;
the multi-objective function construction unit is used for combining the precision requirements of parts processed by the robot, establishing a constraint model of main uncertain factors of the robot, and constructing a multi-objective function integrating dynamic precision evaluation indexes and cost;
the multi-objective optimization unit is used for carrying out multi-objective optimization based on a genetic algorithm, solving a multi-objective function to obtain a reference range of main uncertain factors affecting the dynamic accuracy of the robot after optimization, and guiding the dynamic accuracy design.
Further, in the robot dynamics model building unit, for the robot with n connecting rods, the robot end machining force is considered as the force and moment acting on the connecting rod n by the connecting rod n+1, and joint friction models of the robot are built respectivelyAnd joint clearance model>
In the method, in the process of the invention,refers to an n x 1 joint angular velocity vector; f (f) s Representing static friction; f (f) c Representing coulomb friction; sigma represents the viscous friction coefficient; v s Representing the stribeck coefficient; delta represents the penetration depth caused by the shaft diameter and the bushing impact; />Indicating the relative impact velocity; k represents a generalized stiffness parameter; d represents a damping parameter;
the final robot dynamics model is:
wherein τ represents an n×1 joint moment vector; θ represents an n×1 joint rotation angle vector;refers to an n x 1 joint angular acceleration vector; m (θ) represents an n×n inertia matrix; />Representing an n x n family of force and centrifugal force matrices; g (θ) represents an n×1 gravity moment vector.
Further, the uncertain robot dynamics simulation system comprises a master control module, a random number module, a robot dynamics model module, a correlation analysis module and a result output module;
the master control module sets a sample number N, wherein each sample comprises t uncertain factors of the robot, and the uncertain factors comprise kinematic parameters, dynamic parameters, joint friction, joint clearances and tail end processing forces of the robot;
the random number module generates N groups of random sample values X according to the distribution rule of t uncertain factors j ＝[x j1 ，...，x jt ]，j＝1，...，N；
The robot dynamics model module inputs the sample value generated by the random number module into the robot dynamics model to obtain the tail end dynamic precision F (X) j ) Judging whether the dynamic accuracy F of the robot is met a Finally obtaining the number m meeting the dynamic precision requirement;
the correlation analysis module obtains the proposed robot dynamic accuracy evaluation index P after the simulation of the N groups of samples is completed F =m/N; carrying out correlation analysis on t uncertain factors and dynamic precision evaluation indexes, and judging the correlation degree between each uncertain factor and the dynamic precision evaluation indexes so as to determine the influence on the dynamic precision of the robotA major uncertainty factor for the degree;
the result output module outputs k main uncertain factors affecting the dynamic accuracy of the robot.
Further, the manner in which the correlation analysis module determines the main uncertainty factor that affects the dynamic accuracy of the robot is specifically as follows:
if the absolute value of the correlation coefficient and the absolute value of the correlation test statistic are larger, the correlation coefficient is a main uncertainty factor, otherwise, the correlation coefficient is a secondary uncertainty factor; assuming that S groups of simulation are performed together, generating N groups of sample values in each group to obtain a dynamic accuracy evaluation index P of the i-th group of simulation F (E) i ；x i For the observed value of a certain uncertainty factor, each group of correlation coefficientsThe formula for the test statistic R is:
in the method, in the process of the invention,for the mean value of the uncertainty element +.>The mean value of the index is evaluated for dynamic accuracy.
Further, the multi-objective function construction unit establishes a constraint model of the main uncertain factors of the robot according to the k main uncertain factors output by the result output module as design variables and the precision requirements of the parts processed by the robot:
wherein x is 1 ，x 2 ，...，x k For k main uncertainties, e 1a ，e 2a ，...，ex a Lower limit value of k main uncertainty factors, e 1b ，e 2b ，...，e kb An upper limit value that is k major uncertainty factors;
then, a relation between the manufacturing Cost (Y) of the industrial robot body and a main uncertain factor is established:
Cost(Y)＝aT -b
wherein T represents tolerance, a and b are cost coefficients, and Y= [ e ] 1a ，e 2a ，...，e ka ，e 1b ，e 2b ，...，e kb ]Design variables that are the primary uncertainty factors;
in combination with the dynamic accuracy evaluation index of the robot, a multi-objective function W (Y) of the accuracy optimization design is constructed as follows:
W(Y)＝ω 1 Cost(Y)+ω 2 /P F (Y)
wherein omega is 1 And omega 2 Is a weight coefficient; p (P) F (Y) represents a dynamic accuracy evaluation index based on the main uncertainty factor.
The beneficial effects of the invention are as follows: according to the invention, a dynamic model in the robot machining motion process is established to form a robot uncertain dynamics simulation system based on the Monte Carlo method, and dynamic precision analysis and optimal design are performed on the basis. The invention considers the uncertain factors in the actual processing dynamic process of the robot, forms a perfect uncertain simulation system, can carry out simulation research and optimal design on the robot in the design stage, and has guiding significance compared with a rule of thumb.
Drawings
Fig. 1 is a flow chart of the operation of the present invention.
FIG. 2 is a schematic diagram of the constituent modules of a robot uncertainty dynamics simulation system formed in accordance with the present invention.
Fig. 3 is a simulation flow chart of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the invention provides a dynamic precision design method of an industrial robot, wherein: the method comprises the following steps:
1. the method comprises the following steps of establishing a dynamic model considering robot joint friction, joint clearance and tail end processing force, wherein the dynamic model comprises the following specific steps:
(1) A kinematic model of the robot is built, and the joint rotation angle theta of the robot connecting rod i i Link offset d i Length of connecting rod a i And joint torsion angle alpha i These 4 parameters establish the pose transformation matrix of the connecting rod i+1 relative to the connecting rod i i T i+1 The method comprises the following steps:
where Rot () represents a rotation matrix transformation, and Trans () represents a translation matrix transformation.
By using the formula (1), the pose transformation matrix of the robot end effector n relative to the base coordinate system 0 can be obtained by sequentially multiplying the pose transformation matrix of the connecting rod i+1 relative to the connecting rod i:
in the method, in the process of the invention, 0 R n a gesture rotation matrix for the robot end effector; 0 p n a position vector for the robotic end effector; 0 1×3 Is a 1 row 3 column all zero matrix.
(2) The dynamic model of the robot is built, and a specific recurrence formula is as follows:
in the method, in the process of the invention,angular velocity and angular acceleration of the joint i are respectively represented; i ε i 、 i ω i 、 i a i 、 i a ci respectively representing the projection of the angular acceleration, the angular velocity, the origin acceleration and the centroid acceleration of the connecting rod i under a connecting rod coordinate system i; i-1 ε i-1 、 i-1 ω i-1 、 i- 1 a i-1 respectively representing the projections of the angular acceleration, the angular velocity and the origin acceleration of the connecting rod i-1 under the connecting rod coordinate system i-1; i-1 Z i-1 ＝[0，0，1] T ； i R i-1 a rotation matrix representing the link coordinate system i-1 relative to the link coordinate system i; i R i+1 a rotation matrix representing the link coordinate system i+1 relative to the link coordinate system i; i+1 P i representing the projection of the distance between the origin of the connecting rod coordinate system i-1 and the origin of the connecting rod coordinate system i in the connecting rod coordinate system i-1; i r ci representing the projection of the centroid of the connecting rod i in the connecting rod coordinate system i; i F i 、 i N i respectively representing the projection of external force and external moment acting on the connecting rod i in a connecting rod coordinate system i; i f i 、 i n i respectively representing the projection of the force and moment of the connecting rod i-1 acting on the connecting rod i in the connecting rod coordinate system i; i+1 f i+1 、 i+1 n i+1 respectively representing the projection of the force and moment of the connecting rod i+1 acting on the connecting rod i in the connecting rod coordinate system i+1; m is m i Representing the mass of the connecting rod i; g represents a gravitational acceleration vector; i I ci an inertial tensor matrix representing the link i relative to the centroid; τ i Representing the driving moment on the joint axis of the connecting rod i.
(3) Regarding a robot with n links, the robot end machining force is considered as a link n+ 1 Forces and moments acting on the connecting rod n and respectively establishing a joint friction model of the robotAnd joint clearance model>
In the method, in the process of the invention,an n×1 joint angular velocity vector; f (f) s Representing static friction; f (f) c Representing coulomb friction; sigma represents the viscous friction coefficient; v s Representing the stribeck coefficient; delta represents the penetration depth caused by the shaft diameter and the bushing impact; />Indicating the relative impact velocity; k represents a generalized stiffness parameter; d represents a damping parameter.
Finally, the robot dynamics model can be written as:
wherein τ represents an n×1 joint moment vector; θ represents an n×1 joint rotation angle vector;a joint angular acceleration vector representing n×1; m (θ) represents an n×n inertia matrix; />Representing an n x n family of force and centrifugal force matrices; g (theta) meterShowing the n x 1 gravity moment vector.
2. The uncertain robot dynamics simulation system based on the Monte Carlo method is formed, and correlation analysis is carried out on the uncertain robot dynamics simulation system based on the Monte Carlo method, and as shown in fig. 2 and 3, the simulation system comprises a master control module, a random number module, a robot dynamics model module, a correlation analysis module and a result output module. The method comprises the following steps:
(1) And a general control module: the number of samples N is set, and each sample comprises t uncertain factors such as kinematic parameters (connecting rod length, joint torsion angle, joint rotation angle and connecting rod offset), dynamic parameters (moment of inertia, mass center position and mass), joint friction, joint clearance, end machining force and the like of the robot. Wherein the kinematic parameters, the dynamic parameters, the joint clearance vector and the joint friction coefficient obey the normal distribution rule, and the initial value m=0 and j=0 is set.
(2) A random number module: let E= [ E ] 1a ，e 2a ，...，e ta ，e 1b ，e 2b ，...，e tb ]，e 1a ，e 2a ，...，e ta A distribution interval lower limit value of t uncertain factors, e 1b ，e 2b ，...，e tb Is an upper limit value. According to the distribution rule of t uncertain factors in the interval, N groups of random sample values X are generated j ＝[x j1 ...，x jt ]，j＝1，...，N。
(3) Robot dynamics model module: inputting the sample value in the random number module into the robot dynamics model in the step 1 to obtain the terminal dynamic precision F (X) j ) Judging whether the dynamic accuracy F of the robot is met a If meeting the requirements of (1) j =1, otherwise, I j =0, the number m=m+i that finally meets the dynamic accuracy requirement j 。
(4) Correlation analysis module: after the simulation of the N groups of samples is finished, the proposed dynamic accuracy evaluation index P of the robot is obtained F (E) =m/N. Here P F (E) The dynamic accuracy evaluation index is a dynamic accuracy evaluation index which considers all uncertain factors, and E is the upper limit and the lower limit of all uncertain factors. Correlating t uncertain design variables with dynamic accuracy assessment indexAnd (3) performing sexual analysis, namely judging the degree of correlation between each random uncertainty factor and the final dynamic precision evaluation index, so as to determine the main influencing factors of the dynamic precision. If the absolute value of the correlation coefficient and the absolute value of the correlation test statistic are large, the absolute value is the main factor. Assuming that S groups of simulation are performed together, generating N groups of sample values in each group to obtain a dynamic accuracy evaluation index P of the i-th group of simulation F (E) i ＝m/N。x i For the observed value of a certain uncertainty factor, each group of correlation coefficientsThe formula for the test statistic R is:
in the method, in the process of the invention,for the mean value of the uncertainty element +.>The mean value of the index is evaluated for dynamic accuracy.
(5) And a result output module: and (4) outputting k main uncertain factors which finally influence the dynamic accuracy of the robot according to the steps (1) - (4).
3. The constraint condition of the design variable of the main uncertain factors is determined, and a multi-objective function for fusing the dynamic precision index and the cost is constructed, specifically:
(1) Constraint conditions: and (3) forming a constraint model of main parameters and non-parameter uncertain factors of the robot according to the k main uncertain factors determined in the step (2) as design variables and combining the requirements of the machined parts of the robot, the manufacturing precision of the body and the like. The main parameters and non-parameters include the uncertainty of the kinematic parameters of the robot, the uncertainty of the kinetic parameters, and the uncertainty of the non-parameters such as joint friction, joint play, and end-working forces.
Wherein x is 1 ，x 2 ，..，x k For k main uncertainties, e 1a ，e 2a ，...，e ka Lower limit value for k uncertainty factors, e 1b ，e 2b ，...，e kb Is the upper limit of k uncertainty factors.
(2) Multi-objective function: the relationship between the manufacturing cost of the industrial robot body and the uncertainty factor is established by the following steps:
Cost(Y)＝aT -b (11)
wherein T represents tolerance, a and b are cost coefficients, and Y= [ e ] 1a ，e 2a ，...，e ka ，e 1b ，e 2b ，...，e kb ]Design variables that are the primary uncertainty factor.
The dynamic accuracy evaluation index requirement of the robot is combined, and the final accuracy optimization design objective function is that
W(Y)＝ω 1 Cost(Y)+ω 2 /P F (Y) (12)
Wherein omega is 1 And omega 2 Is a weight coefficient; p (P) F (Y) means a dynamic accuracy evaluation index based on the main uncertainty factor.
4. The genetic algorithm-based multi-objective optimization is carried out, specifically: the main uncertain factors to be optimized are programmed to be turned into chromosomes with specific system, different chromosomes are utilized to form an initial population, the initial population is generated randomly, the initial population is used as an initial solution of a problem, the optimal solution can be obtained through repeated operations of 3 operators of replication, intersection and variation and iterative evolution, and finally the main factor reference range which influences the dynamic accuracy of the robot after the optimization is solved, so that the dynamic accuracy design is guided.
In addition, the invention also provides an industrial robot dynamic precision design system, which comprises the following components:
a robot dynamics model establishing unit for establishing a robot dynamics model in consideration of joint friction, joint clearance and end processing force;
the uncertain robot dynamics simulation system based on the Monte Carlo method is used for calculating a dynamic accuracy evaluation index of the robot based on a robot dynamics model, obtaining a main uncertain factor affecting the dynamic accuracy of the robot by utilizing correlation analysis, and ignoring a secondary uncertain factor;
the multi-objective function construction unit is used for combining the precision requirements of parts processed by the robot, establishing a constraint model of main uncertain factors of the robot, and constructing a multi-objective function integrating dynamic precision evaluation indexes and cost;
the multi-objective optimization unit is used for carrying out multi-objective optimization based on a genetic algorithm, solving a multi-objective function to obtain a reference range of main uncertain factors affecting the dynamic accuracy of the robot after optimization, and guiding the dynamic accuracy design.
The working modes of the components of the dynamic precision design system of the industrial robot correspond to the method.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above examples, and all technical solutions belonging to the concept of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to the invention without departing from the principles thereof are intended to be within the scope of the invention as set forth in the following claims.
Claims (6)
1. The dynamic precision design method of the industrial robot is characterized by comprising the following steps of:
step S1: establishing a robot dynamics model taking joint friction, joint clearance and tail end processing force into consideration;
step S2: forming an uncertain robot dynamics simulation system based on a Monte Carlo method;
step S3: calculating a dynamic accuracy evaluation index of the robot based on the robot dynamics model in the step S1 and the uncertain robot dynamics simulation system in the step S2, and obtaining a main uncertain factor affecting the dynamic accuracy of the robot by utilizing correlation analysis, and ignoring a secondary uncertain factor; the step S3 specifically includes the following steps:
step S3.1: setting the number N of samples, wherein each sample comprises t uncertain factors of the robot, and the uncertain factors comprise kinematic parameters, dynamic parameters, joint friction, joint clearance and tail end processing force of the robot;
step S3.2: generating N groups of random sample values X according to the distribution rule of t uncertain factors j ＝[x j1 ,…,x jt ]，j＝1,…,N；
Step S3.3: inputting the sample value generated in the step S3.2 into the robot dynamics model in the step S1 to obtain the tail end dynamic precision F (X) j ) Judging whether the dynamic accuracy F of the robot is met a Finally obtaining the number m meeting the dynamic precision requirement;
step S3.4: after the simulation of the N groups of samples is finished, the proposed dynamic accuracy evaluation index P of the robot is obtained F =m/N; carrying out correlation analysis on t uncertain factors and dynamic precision evaluation indexes, and judging the correlation degree between each uncertain factor and the dynamic precision evaluation indexes, thereby determining main uncertain factors affecting the dynamic precision of the robot; in the step S3.4, the manner of determining the main uncertain factors affecting the dynamic accuracy of the robot is specifically as follows:
if the absolute value of the correlation coefficient and the absolute value of the correlation test statistic are larger, the correlation coefficient is a main uncertainty factor, otherwise, the correlation coefficient is a secondary uncertainty factor; assuming that S groups of simulation are performed together, generating N groups of sample values in each group to obtain a dynamic accuracy evaluation index P of the i-th group of simulation F (E) i ；x i For the observed value of a certain uncertainty factor, each group of correlation coefficientsThe formula for the test statistic R is:
in the method, in the process of the invention,for the mean value of the uncertainty element +.>The average value of the dynamic precision evaluation index is obtained;
step S3.5: outputting k main uncertain factors affecting the dynamic accuracy of the robot;
step S4: combining the precision requirement of the parts processed by the robot, establishing a constraint model of the main uncertain factors of the robot, and constructing a multi-objective function integrating dynamic precision evaluation indexes and cost;
step S5: and carrying out multi-objective optimization based on a genetic algorithm, and solving a multi-objective function to obtain a reference range of main uncertain factors affecting the dynamic accuracy of the robot after optimization, so as to guide the dynamic accuracy design.
2. The method for dynamic accuracy design of an industrial robot according to claim 1, wherein: in the step S1, for a robot with n links, the robot end machining force is considered as the force and moment acting on the link n by the link n+1, and joint friction models of the robot are respectively builtAnd joint clearance model>
In the method, in the process of the invention,an n×1 joint angular velocity vector; f (f) s Representing static friction; f (f) c Representing coulomb friction; sigma represents the viscous friction coefficient; v s Representing the stribeck coefficient; delta represents the penetration depth caused by the shaft diameter and the bushing impact; />Indicating the relative impact velocity; k represents a generalized stiffness parameter; d represents a damping parameter;
the final robot dynamics model is:
wherein τ represents an n×1 joint moment vector; θ represents an n×1 joint rotation angle vector;refers to an n x 1 joint angular acceleration vector; m (θ) represents an n×n inertia matrix; />Representing an n x n family of force and centrifugal force matrices; g (θ) represents an n×1 gravity moment vector.
3. The method for dynamic accuracy design of an industrial robot according to claim 1, wherein: the step S4 specifically includes the following steps:
step S4.1: according to k main uncertain factors output in the step S3.5 as design variables, and combining the precision requirements of parts processed by the robot, establishing a constraint model of the main uncertain factors of the robot:
wherein x is 1 ,x 2 ,…,x k For k main uncertainties, e 1a ,e 2a ,…,e ka Lower limit value of k main uncertainty factors, e 1b ,e 2b ,…,e kb An upper limit value that is k major uncertainty factors;
step S4.2: establishing a relation between the manufacturing Cost (Y) of the industrial robot body and a main uncertain factor:
Cost(Y)＝aT -b
wherein T represents tolerance, a and b are cost coefficients, and Y= [ e ] 1a ,e 2a ,…,e ka ,e 1b ,e 2b ,…,e kb ]Design variables that are the primary uncertainty factors;
in combination with the dynamic accuracy evaluation index of the robot, a multi-objective function W (Y) of the accuracy optimization design is constructed as follows:
W(Y)＝ω 1 Cost(Y)+ω 2 /P F (Y)
wherein omega is 1 And omega 2 Is a weight coefficient; p (P) F (Y) represents a dynamic accuracy evaluation index based on the main uncertainty factor.
4. An industrial robot dynamic accuracy design system, comprising:
a robot dynamics model establishing unit for establishing a robot dynamics model in consideration of joint friction, joint clearance and end processing force;
the uncertain robot dynamics simulation system based on the Monte Carlo method is used for calculating a dynamic accuracy evaluation index of the robot based on a robot dynamics model, obtaining a main uncertain factor affecting the dynamic accuracy of the robot by utilizing correlation analysis, and ignoring a secondary uncertain factor; the uncertain robot dynamics simulation system comprises a master control module, a random number module, a robot dynamics model module, a correlation analysis module and a result output module;
the master control module sets a sample number N, wherein each sample comprises t uncertain factors of the robot, and the uncertain factors comprise kinematic parameters, dynamic parameters, joint friction, joint clearances and tail end processing forces of the robot;
the random number module generates N groups of random sample values X according to the distribution rule of t uncertain factors j ＝[x j1 ,…,x jt ]，j＝1,…,N；
The robot dynamics model module inputs the sample value generated by the random number module into the robot dynamics model to obtain the tail end dynamic precision F (X) j ) Judging whether the dynamic accuracy F of the robot is met a Finally obtaining the number m meeting the dynamic precision requirement;
the correlation analysis module obtains the proposed robot dynamic accuracy evaluation index P after the simulation of the N groups of samples is completed F =m/N; carrying out correlation analysis on t uncertain factors and dynamic precision evaluation indexes, and judging the correlation degree between each uncertain factor and the dynamic precision evaluation indexes, thereby determining main uncertain factors affecting the dynamic precision of the robot; the method for determining the main uncertain factors affecting the dynamic accuracy of the robot by the correlation analysis module is specifically as follows:
if the absolute value of the correlation coefficient and the absolute value of the correlation test statistic are larger, the correlation coefficient is a main uncertainty factor, otherwise, the correlation coefficient is a secondary uncertainty factor; assuming that S groups of simulation are performed together, generating N groups of sample values in each group to obtain a dynamic accuracy evaluation index P of the i-th group of simulation F (E) i ；x i For the observed value of a certain uncertainty factor, each group of correlation coefficientsThe formula for the test statistic R is:
where x is the mean of the uncertainty factor,the average value of the dynamic precision evaluation index is obtained;
the result output module outputs k main uncertain factors affecting the dynamic accuracy of the robot;
the multi-objective function construction unit is used for combining the precision requirements of parts processed by the robot, establishing a constraint model of main uncertain factors of the robot, and constructing a multi-objective function integrating dynamic precision evaluation indexes and cost;
the multi-objective optimization unit is used for carrying out multi-objective optimization based on a genetic algorithm, solving a multi-objective function to obtain a reference range of main uncertain factors affecting the dynamic accuracy of the robot after optimization, and guiding the dynamic accuracy design.
5. An industrial robot dynamic accuracy design system as claimed in claim 4, wherein: in the robot dynamics model building unit, for a robot with n connecting rods, the robot tail end processing force is considered as the force and moment acting on the connecting rod n by the connecting rod n+1, and joint friction models of the robot are built respectivelyAnd joint clearance model>
In the method, in the process of the invention,refers to an n x 1 joint angular velocity vector; f (f) s Representing static friction; f (f) c Representing coulomb friction; sigma represents the viscous friction coefficient; v s Representing the stribeck coefficient; delta represents the penetration depth caused by the shaft diameter and the bushing impact; />Indicating the relative impact velocity; k represents a generalized stiffness parameter; d represents a damping parameter;
the final robot dynamics model is:
wherein τ represents an n×1 joint moment vector; θ represents an n×1 joint rotation angle vector;refers to an n x 1 joint angular acceleration vector; m (θ) represents an n×n inertia matrix; />Representing an n x n family of force and centrifugal force matrices; g (θ) represents an n×1 gravity moment vector.
6. An industrial robot dynamic accuracy design system as claimed in claim 4, wherein: the multi-objective function construction unit establishes a constraint model of the main uncertain factors of the robot according to the k main uncertain factors output by the result output module as design variables and the precision requirements of the parts processed by the robot:
wherein x is 1 ,x 2 ,...,x k For k main uncertainties, e 1a ,e 2a ,...,e ka Lower limit value of k main uncertainty factors, e 1b ,e 2b ,...,e kb An upper limit value that is k major uncertainty factors;
then, a relation between the manufacturing Cost (Y) of the industrial robot body and a main uncertain factor is established:
Cost(Y)＝aT -b
wherein T represents tolerance, a and b are cost coefficients, and Y= [ e ] 1a ,e 2a ,…,e ka ,e 1b ,e 2b ,…,e kb ]Design variables that are the primary uncertainty factors;
in combination with the dynamic accuracy evaluation index of the robot, a multi-objective function W (Y) of the accuracy optimization design is constructed as follows:
W(Y)＝ω 1 Cost(Y)+ω 2 /P F (Y)
wherein omega is 1 And omega 2 Is a weight coefficient; p (P) F (Y) represents a dynamic accuracy evaluation index based on the main uncertainty factor.
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