CN113656902A - Error sensitivity analysis method for working end pose of multi-axis motion platform - Google Patents
Error sensitivity analysis method for working end pose of multi-axis motion platform Download PDFInfo
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Abstract
The invention discloses an error sensitivity analysis method for the working end pose of a multi-axis motion platform, which relates to the technical field of sensitivity analysis of multi-axis motion platforms, and adopts the technical scheme that: establishing an error model for the multi-axis precision motion platform through a homogeneous transformation matrix algorithm; obtaining error distribution of a multi-axis motion platform and various weights of a working end; obtaining the variance ratio of each 5 geometric errors by a Monte Carlo method according to an error model; calculating a geometric error sensitivity coefficient; comparing the sizes of the coefficients to obtain a geometric error sensitivity order. The method combines the geometric structure relationship of the multi-axis motion platform, and expresses the sensitivity of the geometric errors through numerical values by means of variance, so that the problem that the process of distinguishing the geometric errors is difficult and complicated is solved, and the method can provide support for the research based on the aspect of errors.
Description
Technical Field
The invention relates to the technical field of multi-axis motion platform sensitivity analysis, in particular to an error sensitivity analysis method for a working terminal pose of a multi-axis motion platform.
Background
The multi-axis motion platform is widely used in the manufacturing industry of the present society, for example, a three-axis numerical control machine tool used in numerical control machining, a multi-axis motion system used in the field of precision machining, and the like. In the manufacturing industry, errors determine the quality of products, and how to reduce the errors and improve the quality of the products becomes a problem to be solved urgently.
In the working process of the multi-axis motion platform, errors of the platform are mainly caused by geometric errors, vibration, load, friction and other errors and thermal errors, wherein the geometric errors have the greatest influence on the multi-axis motion platform. The geometric errors comprise installation errors and motion errors, wherein the installation errors comprise orthogonal errors among the translation units, orthogonal errors among the rotation units and quantity parallelism errors between the translation units and the rotation units, and the motion errors comprise positioning errors, perpendicularity errors, pitching errors, deflection errors, rolling errors and the like. The number of the geometric errors is large, and the number of the geometric errors in the six-axis motion platform reaches 48, so that the geometric errors can be effectively distinguished through the sensitivity research on the geometric errors of the multi-axis motion platform, and the accuracy of the multi-axis motion platform can be conveniently analyzed and improved.
S.m. uram and j. von neumann in 1945 propose a new probabilistic-based solution to the problem, which is known as MonteCarlo, a famous gambling city of morna to embody randomness. The calculation principle is mainly based on probability statistics, sampling statistics is carried out on random projection points, and then calculation and processing are carried out to obtain an estimation result. The development of electronic digital computers provides effective tools for such large-scale random experiments, so that the Monte Carlo method is widely applied to the fields of nuclear science, artificial intelligence, medicine, management science and the like. Recently reported AI algorithms such as AlphaGo-Zero, Alpha-Zero, etc. successfully search using MonteCarlo method; in the numerical calculation of nuclear physics, the MonteCarlo method has an irreplaceable role. The MonteCarlo method generates a random number by providing a pattern, and performs simulation using the random number to obtain a corresponding real result.
Due to the large number of geometric errors in the multi-axis motion platform and the complexity of sensitivity analysis of most single directions of the working tip or the working tip, the traditional error sensitivity analysis method is difficult to distinguish.
Disclosure of Invention
The invention aims to provide an error sensitivity analysis method for the working end pose of a multi-axis motion platform, which can effectively distinguish the geometric 5 error of the multi-axis motion platform through the sensitivity research on the geometric error of the multi-axis motion platform so as to facilitate the analysis and the improvement of the precision of the multi-axis motion platform.
The technical purpose of the invention is realized by the following technical scheme: an error sensitivity analysis method for the working end pose of a multi-axis motion platform comprises the following steps:
1) establishing an error model for the multi-axis motion platform through a homogeneous transformation matrix algorithm;
2) obtaining error distribution of the multi-axis motion platform and each weight of a working end of the multi-axis motion platform;
3) obtaining the variance ratio of each geometric error by utilizing a Monte Carlo method according to the error model in the step 1);
4) calculating a sensitivity coefficient of the geometric error according to each weight of the working end of the multi-axis motion platform in the step 2) and the variance ratio of each geometric error in the step 3);
5) comparing the sensitivity coefficients in the step 4) to obtain the order of the sensitivity of the geometric errors.
The specific method for establishing the error model for the multi-axis motion platform in the step 1) comprises the following steps:
A) establishing a topological structure of a multi-axis motion platform, and performing low-order body array description on the topological structure, wherein the low-order body array description on the topological structure comprises the following steps:
selecting an inertial reference system B in the topology0Body from said B0One typical body is selected as BjA body, said BjThe n-order lower sequence body of (A) is BiSaid B isjAnd BiThe relationship between them is:
Ln(j)＝i； (1)
wherein L is a lower sequence body, and n is an order;
B) establishing an ideal pose matrix of the multi-axis motion platform based on a homogeneous transformation matrix and the low-order body array description of the multi-axis motion platform, wherein the calculation formula is as follows:
wherein, VjAs an initial pose vector, P, in the working end coordinate systemlIs the ideal pose matrix after the movement of the top unit, MoFor coordinate system offset matrix between units in platform installation, MmMotion matrixes of each unit of the platform are used for describing motion poses of each unit of the platform on different degrees of freedom; x, Y and Z are translational displacement along X, Y and Z axes of the platform, alpha, beta and gamma are rotational displacement around U, V and W axes of the platform, subscripts X, Y, Z, U, V and W of symbols respectively represent a translational motion unit of X, Y and Z and a rotational motion unit of U, V and W, superscripts m of symbols represent motion, and superscripts o of symbols represent coordinate system offset;
C) establishing an actual pose matrix of the multi-axis motion platform based on the homogeneous transformation matrix and the low-order body array description of the multi-axis motion platform, wherein the calculation formula is as follows:
wherein, PRIs the actual pose matrix after the movement of the top unit, MaFor a matrix of assembly errors between units of the motion platform, MkThe motion error matrix is generated after each motion unit of the platform acts, X, Y and Z are linear errors along X, Y and Z axes of the platform, and delta alpha, delta beta and delta gamma are angle errors around U, V and W axes of the platform; the symbol superscript k indicates the motion error and the symbol superscript a indicates the assembly error;
D) carrying out error modeling on the multi-axis motion platform, selecting a reference rectangular coordinate system on the multi-axis motion platform, establishing a rectangular coordinate system on each multi-axis motion platform, and establishing an error model according to the ideal pose change and the actual pose change of the multi-axis motion platform, wherein the error model is expressed by the difference between an actual pose matrix and an ideal pose matrix, and the formula is as follows:
E＝PR-Pl (12)；
and E is an error model of the multi-axis motion platform.
The error model in the above method only includes geometric errors, where the geometric errors include static errors and motion errors; the static errors comprise assembly errors, and the motion errors comprise positioning errors, straightness errors, deflection errors, pitching errors, rolling errors, axial errors, inclination errors, radius errors and angle errors;
when the degree of freedom of the multi-axis motion platform is more than 3, the assembly error quantity calculation formula is as follows:
K＝3(n-2) (13)；
wherein n is the degree of freedom of the motion platform.
The step 2) in the above method comprises:
and measuring each geometric error distribution in the error model through the laser interferometer, and measuring each motion unit under the condition of inquiring data or ensuring the same result to obtain each weight of the working end.
The variance ratio of the geometric error and the error mapped at the working end is obtained by a Monte Carlo method in the step 3), and is realized by the following formula:
in the formula, VjifThe variance, V, of a certain degree of freedom error at the working end of the ideal and actual motion platform is representedjisThe variance B representing the set error is a variance ratio, j is a space, i is a degree of freedom, if j is 1, the translation space is the x direction, i is 1, B is the x directionjiI.e. the variance ratio in the x-direction translation direction.
The sensitivity coefficient in step 4) of the above method is realized by the following formula:
wherein M iskIs the combined sensitivity factor, δ, of the k-th error parameterjiTo influence the weight coefficients, BjiIs the variance ratio.
The specific method for obtaining the order of the sensitivity of the geometric errors in step 5) in the above method is as follows: the geometric errors are classified and sorted according to the sensitivity coefficient, and are classified into 'very sensitive', 'sensitive' and 'insensitive' according to the size relation between the geometric errors and 1, and the geometric errors are classified into 'very sensitive', sensitive 'and' insensitive 'when the geometric errors are more than 1, sensitive' when the geometric errors are equal to 1 and insensitive when the geometric errors are less than 1; then, the sensitivity coefficients in each class are arranged in sequence from large to small.
In conclusion, the invention has the following beneficial effects: according to the method for analyzing the error sensitivity of the working terminal pose of the multi-axis motion platform, the system precision of the generated geometric error model of the multi-axis motion platform meets the requirement of the precision. The problem to be solved by the invention is based on the multi-axis motion platform optimization error modeling method of the Monte Carlo algorithm, the Monte Carlo algorithm can directly process the problem, the process is simple, the problem is conveniently solved, and then the geometric error sensitivity analysis of the working end pose of the multi-degree-of-freedom pose control system based on the platform geometric relation can effectively provide effective help for error research and error reduction. The number of the geometric errors in the six-axis motion platform reaches 48, the geometric errors can be effectively distinguished through the sensitivity research on the geometric errors of the multi-axis motion platform, and the optimized error modeling method can balance the calculation efficiency and the system precision; according to the method, the geometric structure relation of the multi-axis motion platform is represented by the sensitivity of the geometric errors through the numerical value by means of the variance, so that the problem that the process of distinguishing the geometric errors is difficult and complicated is solved, and the method can provide support for research based on the aspect of errors.
Drawings
FIG. 1 is a flowchart of a method for analyzing error sensitivity of a working end pose of a multi-axis motion platform according to an embodiment of the present invention;
FIG. 2 is a model diagram of a laser auto-coupling machine for a method for analyzing error sensitivity of a working end pose of a multi-axis motion platform according to an embodiment of the present invention;
FIG. 3 shows geometric errors of a method for analyzing error sensitivity of a pose of a working end of a multi-axis motion platform according to an embodiment of the invention
A flow chart of a calculation method;
FIG. 4 is a schematic diagram of a two-degree-of-freedom motion rigid body geometry of a multi-axis motion platform working end pose error sensitivity analysis method according to an embodiment of the present invention;
FIG. 5 is a schematic view of a two-degree-of-freedom kinematic rigid body lower assembly translation according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of the rotation of a rigid body lower two-degree-of-freedom motion component in the method for analyzing the error sensitivity of the pose of the working end of a multi-axis motion platform according to the embodiment of the present invention;
FIG. 7 is a schematic view of the translational motion of the components on the rigid body with two degrees of freedom in the method for analyzing the error sensitivity of the pose of the working end of the multi-axis motion platform according to the embodiment of the present invention;
fig. 8 is a schematic diagram of rotation of components on a two-degree-of-freedom motion rigid body in the method for analyzing the error sensitivity of the working end pose of the multi-axis motion platform according to the embodiment of the present invention.
Detailed Description
The present invention is described in further detail below with reference to figures 1-8.
Example (b): a method for analyzing the error sensitivity of the working end pose of a multi-axis motion platform is shown in figure 1 and comprises the following steps:
1) error modeling: the method comprises the following steps of establishing an error model for a multi-axis precision motion platform through a homogeneous transformation matrix algorithm:
A) establishing a topological structure of the multi-axis motion platform, and performing low-order body array description on the topological structure, wherein the performing low-order body array description on the topological structure comprises the following steps:
the inertial reference in the selected topology is B0Body, from B0One typical body is selected as BjBody, BjThe n-order lower sequence body of (A) is Bi，BjAnd BiThe relationship between them is:
Ln(j)＝i；
wherein L is a lower sequence body, and n is an order;
B) establishing an ideal pose matrix of the multi-axis motion platform based on the homogeneous transformation matrix and the low-order body array description of the multi-axis motion platform, wherein the calculation formula is as follows:
wherein, VjAs an initial pose vector, P, in the working end coordinate systemlIs the ideal pose matrix after the movement of the top unit, MoFor coordinate system offset matrix between units in platform installation, MmMotion matrixes of each unit of the platform are used for describing motion poses of each unit of the platform on different degrees of freedom; x, Y and Z are translational displacement along X, Y and Z axes of the platform, alpha, beta and gamma are rotational displacement around U, V and W axes of the platform, subscripts X, Y, Z, U, V and W of symbols respectively represent a translational motion unit of X, Y and Z and a rotational motion unit of U, V and W, superscripts m of symbols represent motion, and superscripts o of symbols represent coordinate system offset;
C) establishing an actual pose matrix of the multi-axis motion platform based on the homogeneous transformation matrix and the low-order body array description of the multi-axis motion platform, wherein the calculation formula is as follows:
wherein, PRIs the actual pose matrix after the movement of the top unit, MaFor a matrix of assembly errors between units of the motion platform, MkThe motion error matrix is generated after each motion unit of the platform acts, X, Y and Z are linear errors along X, Y and Z axes of the platform, and delta alpha, delta beta and delta gamma are angle errors around U, V and W axes of the platform; the symbol superscript k indicates the motion error and the symbol superscript a indicates the assembly error;
D) carrying out error modeling on the multi-axis motion platform, selecting a reference rectangular coordinate system on the multi-axis motion platform, establishing a rectangular coordinate system on each multi-axis motion platform, establishing an error model according to the ideal pose change and the actual pose change of the multi-axis motion platform, wherein the error model is expressed by the difference between an actual pose matrix and an ideal pose matrix, and the formula is as follows:
E＝PR-Pl；
and E is an error model of the multi-axis motion platform.
The error model only comprises geometric errors, wherein the geometric errors comprise static errors and motion errors; the static errors comprise assembly errors, and the motion errors comprise positioning errors, straightness errors, deflection errors, pitching errors, rolling errors, axial errors, inclination errors, radius errors and angle errors;
when the degree of freedom of the multi-axis motion platform is more than 3, the assembly error quantity calculation formula is as follows:
K＝3(n-2)；
wherein n is the degree of freedom of the motion platform.
2) Error distribution and weight: obtaining error distribution of a multi-axis motion platform and various weights of a working end;
the weights of all directions of the working end of the instrument can be obtained by using technical data on a manual or through control variable measurement, such as obtaining the position change ratio of each degree of freedom for the laser coupler control light power change value, and the measurement coordinate offset and error distribution of the laser interferometer and the influence weights of all directions of the working end of the multi-axis motion platform are obtained. The manual is a product specification, and corresponding specification parameters are obtained from the specification.
3) Error variance ratio: the method comprises the following steps of obtaining the variance ratio of each geometric error by utilizing a Monte Carlo method according to an error model, obtaining the variance ratio of the geometric errors and the errors mapped at the working end by utilizing the Monte Carlo method, and realizing the following formula:
in the formula, VjifThe variance, V, of a certain degree of freedom error at the working end of the ideal and actual motion platform is representedjisThe variance of the set error is shown, B is the variance ratio, j is the space, and i is the degree of freedom. If j is 1, i is x direction, B is translation spacejiI.e. the variance ratio in the x-direction translation direction.
4) Calculating the sensitivity coefficient: calculating a geometric error sensitivity coefficient in combination, wherein the sensitivity coefficient is realized by the following formula:
wherein M iskIs the combined sensitivity factor, δ, of the k-th error parameterjiTo influence the weight coefficients, BjiIs the variance ratio.
5) Order of sensitivity was obtained: comparing the sizes of the coefficients to obtain a geometric error sensitivity order. The geometric errors are classified and sorted according to the sensitivity coefficient, and are classified into three types of 'very sensitive' (> 1), 'sensitive' (-1) and 'insensitive' (< 1) according to the size relationship between the geometric errors and 1; the sensitivity coefficients in each class are arranged in descending order, and may be "level 1", "level 2", "level 3" … ….
In one possible embodiment, the laser auto-coupler is set to the base reference frame at the intersection of the X, Y direction perpendicular to the base through the center of rotation of U, V, with the axes of the frame parallel to the direction of motion of the corresponding motion unit. Secondly, the intersection point of the table surface normal and the motion unit is set as the origin of the motion unit coordinate system, each axis is parallel to the base reference coordinate system, and the model diagram of the laser auto-coupling machine is shown in fig. 2:
the laser automatic coupling machine is composed of six motion units of three translation units X, Y, Z and three rotation units U, V, W, and can be divided into a lower motion chain composed of an x axis, a y axis, a v axis and a u axis and an upper motion chain composed of a z axis and a w axis. In the multi-axis motion platform, the total of 48 geometric errors including 12 installation errors and 36 motion errors are included. As shown in tables 1 and 2:
TABLE 1 physical significance of motion errors
TABLE 2 physical significance of installation errors
The motion platforms with different degrees of freedom have slightly different concrete expression forms due to the difference of structures, and the error model recorded by the formula is abstract and unified expression of the model. The method is suitable for a multi-degree-of-freedom motion system, and is not limited to a specific motion platform structure configuration, such as a motion chain with one degree of freedom under two degrees of freedom on a three-axis pneumatic sliding table. Therefore, the modeling is carried out specifically for a specific motion platform, and the modeling is essential in nature. Regarding the kinematic chain matrix on the coaxial laser automatic coupling machine as an ideal kinematic matrix, and regarding the lower kinematic chain matrix as an actual kinematic matrix, according to the modeling process, the error model of the laser coupling machine can be established:
the upper kinematic chain pose matrix may be represented as:
the lower kinematic chain pose matrix may be represented as:
where P is a position compensation matrix, S is a mounting error matrix, T is a motion matrix, K is a motion error matrix, and subscripts x, y, z, u, v, w represent the expressed axes of motion. The X, Y, Z, U, V and W without the superscript and the subscript respectively represent the motion amount along the directions of the X axis, the Y axis, the Z axis, the U axis, the V axis and the W axis, and the terms of the X, Y, Z, U, V and W with the superscript and the subscript are error terms, wherein the upper table k represents the motion error, and the lower table X, Y, Z, U, V and W respectively represent the motion axis where the error is located. X, y, z, u, v, w, including the table below, represent the amount of positional compensation, and the table letters represent the adjacent axes of motion that are compensated. α, β, γ denote mounting errors in rotation along x, y, z, respectively, and the subscripts denote the axes involved in generating the mounting errors. Pgis、PugjxDenotes the upper and lower jig compensation matrices, zwgjs、zugjxThe compensation quantity of the positions of the upper clamp and the lower clamp is obtained; es、ExAnd respectively representing an upper kinematic chain pose matrix and a lower kinematic chain pose matrix.
The error model of the laser coupler is:
E＝Ex-Es
where E is the error matrix of the optocoupler.
The technical data in the manual are used to obtain the coordinate offset (table 3) and error distribution (table 4) of the laser interferometer measurement, and the influence weight (table 5) of each direction of the working end of the laser coupler.
TABLE 3 distance between degrees of freedom (mm)
TABLE 4 error distribution Range (μm)
TABLE 5 weight of influence of each direction at work end
| Degree of freedom | X | Y | Z | U | V | W |
| Weight of influence | 1 | 1 | 0.0625 | 0.0881 | 0.0881 | 0.0881 |
Sensitivity analysis was performed according to the above method to
For the purpose of illustration, FIG. 3 is
The sensitivity is a specific process, wherein i in FIG. 3 is x, y, z, u, v, w.
From tables 4 and 5, respectively
The distribution range of (1) is (-2.0, 2.0) and the influence weight of the instrument in each direction at the working end. An error model is established for the instrument through matlab, and firstly, Monte Carlo algorithm is used for obtaining
Value set and the geometric variance V will
The values are brought into an error model, the error value geometry corresponding to each direction of the working end is obtained, and the set variance V is calculatediAnd i represents the direction values of x, y, z, u, v and w. The variance ratio B of each direction can be obtainedi＝V/ViThe variance ratio BiAnd the sensitivity coefficient can be obtained by substituting the sum weight coefficient into a formula.
Geometric error
The sensitivity calculations are described in table 6.
TABLE 6 geometric errors
Sensitivity calculation
The results of the error sensitivity analysis are shown in table 7.
TABLE 7 results of geometric error sensitivity
TABLE 8 error sensitivity classification
From the above results it can be seen that:
errors in angle on the X motion unit are most sensitive, while sensitivity in the Z and W directions is the worst.
The sensitivity coefficients in the X direction and the Y direction are 1, and the method is a sensitive type.
And 3, the error of the Z axis on the W axis, the displacement projection of the working end is in the X axis and Y axis directions, the displacement change in the direction has larger influence on the optical power, the sensitivity is also larger, and the sensitivity of the geometric error item is known by distinguishing and classifying the sensitivity of the geometric error, the sensitivity distribution is correspondingly linked with the geometric structure relationship of the motion platform, and the relationship is analyzed as follows. As shown in fig. 4, the height of the two rigid bodies A, B is h. When the rigid body a is displaced by x, the rigid body B is displaced by y, and x ═ y is known from a geometric relationship, as shown in fig. 5. When the rigid body a is displaced by a distance θ, it can be seen from the geometric relationship L θ · h that displacement by a distance a 2h and inclination by an angle θ occur at B, as shown in fig. 6. When the rigid body B is displaced by x, the rigid body B is displaced by y in B, and x ═ y is known from a geometric relationship, as shown in fig. 7. When the rigid body B is displaced by the distance θ, it is known from the geometric relationship L θ · h that displacement by the distance B h and inclination by the angle θ occur at B, as shown in fig. 8. The sensitivity of the error in terms of angle is greater the further away from the working end, while the error in terms of straight line is unchanged, given the same geometric error distribution input.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.
Claims (6)
1. An error sensitivity analysis method for the working end pose of a multi-axis motion platform is characterized by comprising the following steps: the method comprises the following steps:
1) establishing an error model for the multi-axis motion platform through a homogeneous transformation matrix algorithm;
2) obtaining error distribution of the multi-axis motion platform and each weight of a working end of the multi-axis motion platform;
3) obtaining the variance ratio of each geometric error by utilizing a Monte Carlo method according to the error model in the step 1);
4) calculating a sensitivity coefficient of the geometric error according to each weight of the working end of the multi-axis motion platform in the step 2) and the variance ratio of each geometric error in the step 3);
5) comparing the sensitivity coefficients in the step 4) to obtain the order of the sensitivity of the geometric errors.
2. The method for analyzing the error sensitivity of the working end pose of the multi-axis motion platform according to claim 1, wherein the method comprises the following steps: the specific method for establishing the error model for the multi-axis motion platform in the step 1) comprises the following steps:
A) establishing a topological structure of a multi-axis motion platform, and performing low-order body array description on the topological structure, wherein the low-order body array description on the topological structure comprises the following steps:
selecting an inertial reference system B in the topology0Body from said B0One typical body is selected as BjA body, said BjThe n-order lower sequence body of (A) is BiSaid B isjAnd BiThe relationship between them is:
Ln(j)＝i； (1)
wherein L is a lower sequence body, and n is an order;
B) establishing an ideal pose matrix of the multi-axis motion platform based on a homogeneous transformation matrix and the low-order body array description of the multi-axis motion platform, wherein the calculation formula is as follows:
wherein, VjAs an initial pose vector, P, in the working end coordinate systemlIs the ideal pose matrix after the movement of the top unit, MoFor coordinate system offset matrix between units in platform installation, MmMotion matrixes of each unit of the platform are used for describing motion poses of each unit of the platform on different degrees of freedom; x, Y and Z are translational displacement along X, Y and Z axes of the platform, alpha, beta and gamma are rotational displacement around U, V and W axes of the platform, subscripts X, Y, Z, U, V and W of symbols respectively represent a translational motion unit of X, Y and Z and a rotational motion unit of U, V and W, superscripts m of symbols represent motion, and superscripts o of symbols represent coordinate system offset;
C) establishing an actual pose matrix of the multi-axis motion platform based on the homogeneous transformation matrix and the low-order body array description of the multi-axis motion platform, wherein the calculation formula is as follows:
wherein, PRIs the actual pose matrix after the movement of the top unit, MaFor a matrix of assembly errors between units of the motion platform, MkFor the motion error matrix generated after the motion of each motion unit of the platform, X, Y, z are X, Y along the platformThe linear error of the Z axis, delta alpha, delta beta and delta gamma are angle errors around the U, V and W axes of the platform; the symbol superscript k indicates the motion error and the symbol superscript a indicates the assembly error;
D) carrying out error modeling on the multi-axis motion platform, selecting a reference rectangular coordinate system on the multi-axis motion platform, establishing a rectangular coordinate system on each multi-axis motion platform, and establishing an error model according to the ideal pose change and the actual pose change of the multi-axis motion platform, wherein the error model is expressed by the difference between an actual pose matrix and an ideal pose matrix, and the formula is as follows:
E＝PR-Pl (12)；
and E is an error model of the multi-axis motion platform.
3. The method for analyzing the error sensitivity of the working end pose of the multi-axis motion platform according to claim 1, wherein the method comprises the following steps: the error model only comprises geometric errors, wherein the geometric errors comprise static errors and motion errors; the static errors comprise assembly errors, and the motion errors comprise positioning errors, straightness errors, deflection errors, pitching errors, rolling errors, axial errors, inclination errors, radius errors and angle errors;
when the degree of freedom of the multi-axis motion platform is more than 3, the assembly error quantity calculation formula is as follows:
K＝3(n-2) (13)；
wherein n is the degree of freedom of the motion platform.
4. The method for analyzing the error sensitivity of the working end pose of the multi-axis motion platform according to claim 1, wherein the method comprises the following steps: the variance ratio of the geometric error and the error mapped at the working end is obtained by a Monte Carlo method in the step 3), and is realized by the following formula:
in the formula (I), the compound is shown in the specification,Vjifthe variance, V, of a certain degree of freedom error at the working end of the ideal and actual motion platform is representedjisThe variance of the set error is shown, B is the variance ratio, j is the space, and i is the degree of freedom.
5. The method for analyzing the error sensitivity of the working end pose of the multi-axis motion platform according to claim 1, wherein the method comprises the following steps: the sensitivity coefficient in the step 4) is realized by the following formula:
wherein M iskIs the combined sensitivity factor, δ, of the k-th error parameterjiTo influence the weight coefficients, BjiIs the variance ratio.
6. The method for analyzing the error sensitivity of the working end pose of the multi-axis motion platform as recited in claim 1, wherein the method comprises the following steps: the specific method for obtaining the order of the sensitivity of the geometric errors in the step 5) is as follows: the geometric errors are classified and sorted according to the sensitivity coefficient, and are classified into 'very sensitive', 'sensitive' and 'insensitive' according to the size relation between the geometric errors and 1, and the geometric errors are classified into 'very sensitive', sensitive 'and' insensitive 'when the geometric errors are more than 1, sensitive' when the geometric errors are equal to 1 and insensitive when the geometric errors are less than 1; then, the sensitivity coefficients in each class are arranged in sequence from large to small.
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| CN116909240A (en) * | 2023-09-13 | 2023-10-20 | 深圳市今天国际智能机器人有限公司 | Loading and unloading vehicle dynamic path planning method and system of AGV trolley and related medium |
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