Robot configuration sampling method for joint space uniform distribution

Abstract

The invention discloses a robot configuration sampling method for joint space uniform distribution. The method comprises the following steps: A, acquiring a robot joint working space; a kinematic model of the robot is used for enabling the working range of the robot to correspond to a robot joint space from a three-dimensional space, first three-joint data of the robot are taken for drawing, and a robot joint working space, namely a joint working curved surface, is obtained; b, mapping the joint working curved surface to a UV plane by using UV mapping; and C, obtaining the sampling configuration of the robot by using UV retroreflection. According to the method, the robot joint space working curved surface is mapped to the UV plane through UV mapping, and robot configuration sampling is facilitated. UV retroreflection is realized by using a barycentric coordinate method after sampling on a UV plane, so that the obtained robot configuration is good in correspondence and high in calculation precision. The robot configuration obtained through the method is used for robot dynamic performance sampling, and the obtained data error is closer to normal distribution. The dynamic performance of the robot is predicted by using the data, and the prediction result quality is better.

Description

Technical Field

[0001] The invention belongs to the field of robot kinematics research, and in particular relates to a robot configuration sampling method with uniform joint space distribution. Background Art

[0002] The dynamic characteristics of the robot, including natural frequency, damping ratio, dynamic stiffness, modal mass, etc., determine the dynamic performance of the robot and are very important dynamic properties. The dynamic characteristics of the robot change with the change of the robot configuration, and the change relationship is nonlinear. In order to obtain the dynamic characteristics of the robot, it is necessary to sample the dynamic characteristics of the robot under different robot configurations and use statistical methods to predict the dynamic characteristic parameters. The distribution of the robot configuration has an impact on the prediction quality of the dynamic characteristics. When there is a certain bias in the distribution of the robot configuration used for dynamic characteristic sampling, the error of the measured dynamic characteristic parameters may not be random, resulting in errors in the prediction results of the robot dynamic characteristics based on statistical methods. Therefore, it is very important to obtain a uniformly distributed robot configuration for the prediction of the robot dynamic characteristics.

[0003] In order to obtain a uniformly distributed robot configuration, existing robot configuration sampling methods usually determine the uniformly distributed robot end posture in three-dimensional space and then transform it to obtain the robot configuration.

[0004] This method selects uniformly distributed positions in three-dimensional space as the robot end position, and selects the posture consistent with the robot end motion direction as the robot end posture. These robot end positions and postures can be integrated into the robot end posture, including the robot end position coordinates and posture matrix. Using robot kinematics to process the robot end posture, the corresponding robot configuration can be obtained.

[0005] The existing robot configuration sampling method in three-dimensional space is simple and intuitive, easy to understand and operate. The robot configuration obtained by this sampling method is evenly distributed in three-dimensional space, but may be unevenly distributed in joint space. This is because the robot kinematic model is a nonlinear model, and the distribution of the robot configuration in three-dimensional space and joint space also has a nonlinear relationship. The error distribution of the identification result does not obey the normal distribution and may have some undetermined tendency when identifying the robot dynamic characteristics based on the non-uniformly distributed robot configuration. The robot dynamic characteristics predicted based on this measurement result have errors.

[0006] Therefore, providing a robot configuration sampling method with uniform distribution of joint space has become a problem that needs to be solved in the industry. Summary of the invention

[0007] In order to solve the deficiencies in the prior art, the main purpose of the present invention is to provide a robot configuration sampling method with uniform distribution of joint space.

[0008] In order to achieve the above main purpose, the present invention discloses a robot configuration sampling method with uniform distribution of joint space, which comprises the following steps:

[0009] A. Obtain the robot joint workspace; use the robot's kinematic model to map the robot's working range from the three-dimensional space to the robot's joint space, and take the robot's first three joint data for drawing to obtain the robot's joint workspace, that is, the joint working surface (three-dimensional working surface);

[0010] B. Use UV mapping to map the joint working surface to the UV plane; UV unfolding is a method in computer graphics to unfold a three-dimensional mold surface into a two-dimensional UV plane. There is a unique mapping relationship between each point on the three-dimensional surface and the corresponding point on the two-dimensional UV plane.

[0011] C. Use UV reflection to obtain the robot sampling configuration. UV reflection can map points in the two-dimensional UV plane back to the three-dimensional work surface. Sampling on the two-dimensional UV plane and performing UV reflection can obtain sampling points on the three-dimensional work space.

[0012] The method of the present invention can be used to sample the robot configuration, and the sampled robot configuration sampling points are evenly distributed in the robot joint space. This evenly distributed robot configuration can be used to sample the dynamic characteristics of the robot.

[0013] In the present invention, the sampling configuration of the robot can be restored according to the sampling points of the three-dimensional working surface, and the obtained sampling configuration is evenly distributed in the joint space, meeting the needs of the sampling configuration of the dynamic characteristics of the robot.

[0014] According to a specific implementation of the present invention, in step B, the LSCM method is used to perform surface parameterization on the joint working surface, and the joint working surface is mapped to a two-dimensional UV plane.

[0015] According to a specific embodiment of the present invention, step B comprises the following steps:

[0016] B1. Generate a triangular mesh based on the point cloud data of the joint working surface;

[0017] B2. Use Least Squares Conformal Maps (LSCM) to UV unfold the joint working surface in the form of a triangular mesh.

[0018] Using the LSCM method for UV unfolding can ensure the common shape of the triangular facets, reduce the distortion from the three-dimensional working surface to the two-dimensional UV plane, and make the corresponding mapping relationship more uniform.

[0019] Use LSCM to establish a mapping from a three-dimensional working surface to a two-dimensional UV plane. The three-dimensional working surface and the triangular mesh in the two-dimensional UV plane have "conformality", that is, the local angles of the corresponding triangular facets are the same. According to a specific implementation of the present invention, in step B2, let the vertex coordinates of a triangular facet A on the joint working surface be P1=(x1, y1, z1), P2=(x2, y2, z2), P3=(x3, y3, z3), and the vertex coordinate system of the corresponding triangular facet B on the two-dimensional UV plane be U1=(u1, v1), U2=(u2, v2), U3=(u3, v3); the two edge vectors P of the triangular facet A in three-dimensional space are 12 With P 13 The form is

[0020] P 12 =P2-P1=(x2-x1,y2-y1,z2-z1)

[0021] P 13 =P3-P1=(x3-x1,y3-y1,z3-z1)

[0022] Correspondingly, the edge vector U corresponding to the triangle patch B in the two-dimensional UV plane 12 and U 13 The form is

[0023] U 12 =U2-U1=(u2-u1,v2-v1)

[0024] U 13 =U3-U1=(u3-u1,v3-v1)

[0025] The conformal energy E is used to measure the conformality between the triangle patches A and B. The calculation method of the conformal energy E is as follows:

[0026]

[0027] Where i and j are the triangle vertex numbers. When calculating the conformal energy of two triangles, we only need to calculate the energy of the two corresponding edges of the two triangles, because a triangle can be completely defined based on the two edges and their angle. C is a 2×3 conformal matrix used to transform the three-dimensional vector P ij Mapped to a 2D UV plane; the conformal matrix is ​​of the form

[0028]

[0029] Where a, b, c and d are the parameters that need to be solved.

[0030] According to a specific embodiment of the present invention, the smaller the value of conformal energy E, the better the conformality of triangular facets A and B; when conformal energy E is 0, triangular facets A and B are conformal; the value of conformal energy E is minimized to identify the values ​​of parameters a, b, c and d; when parameters a, b, c and d are known, conformal energy E=0 evolves to about all coordinates U ij The linear equation is solved by the least square method to obtain all U ij coordinate.

[0031] To ensure U ij Uniqueness of the result: According to a specific embodiment of the present invention, the coordinates of at least two vertices are fixed in the UV plane to determine the scale and posture of the two-dimensional UV plane.

[0032] According to a specific implementation of the present invention, in step C, the barycentric coordinate method is used to obtain the linear relationship between the UV plane sampling point and the surrounding points, and the joint working surface is interpolated according to the linear relationship to obtain the interpolation sampling point; the data point is searched on the joint working surface so that the data point is closest to the interpolation sampling point, and the data point on the joint working surface is used as the robot configuration sampling point; the sampling point restored on the joint working surface is the sampling configuration of the robot.

[0033] According to a specific embodiment of the present invention, step C comprises the following steps:

[0034] C1. Set uniform sampling points on the UV plane to obtain a series of UV coordinates;

[0035] C2. Let the UV coordinates of a certain sampling point be U = (u, v); traverse the triangular mesh of the UV plane, find the triangle containing the coordinate U, and let the vertex coordinates of the triangle be U1 = (u1, v1), U2 = (u2, v2), U3 = (u3, v3);

[0036] C3, calculate the weight of coordinate U relative to triangle vertices U1, U2 and U3 = (u3, v3), the results are λ1, λ2 and λ3,

[0037] U=λ1U1+λ2U2+λ3U3

[0038] Where λ1+λ2+λ3=1; the weight coefficients λ1, λ2 and λ3 are called the centroid coordinates of the coordinate U;

[0039] C4. Use the barycentric coordinates to interpolate the coordinates P1, P2, and P3 of the corresponding triangle vertices on the joint working surface to obtain the interpolation sampling points

[0040] P = λ1P1 + λ2P2 + λ3P3;

[0041] C5, find a data point on the joint working surface, so that the data point is closest to the interpolation sampling point, and the data point is the coordinate of the sampling point coordinate U on the UV plane corresponding to the point on the joint working surface;

[0042] C6. Perform steps C2-C4 on all sampled UV coordinates to obtain sampling points on the joint working surface.

[0043] The present invention has the following beneficial effects:

[0044] The method of the present invention can directly uniformly sample the robot configuration in the robot joint space, and the spacing between adjacent sampled configurations is close. The method of the present invention uses UV mapping to map the working surface of the robot joint space to the UV plane, which is convenient for robot configuration sampling. After sampling on the UV plane, the center of gravity coordinate method is used to realize UV ​​reflection, so that the robot configuration has good correspondence and high calculation accuracy. The robot configuration obtained by the method of the present invention is used to sample the robot dynamic performance, and the obtained data error is closer to the normal distribution. Using these data to predict the dynamic performance of the robot, the quality of the prediction result is better.

[0045] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is the working range of the robot end in three-dimensional space in Example 1;

[0047] Figure 2 is the joint working surface of the robot in the joint space in Example 1;

[0048] Figure 3 are the UV plane and sampling points of the robot joint space surface mapping in Example 1;

[0049] Figure 4 It is the joint working surface and sampling points of the robot in the joint space in Example 1. DETAILED DESCRIPTION

[0050] In the following description, many specific details are explained in conjunction with the embodiments to facilitate a full understanding of the present invention. However, it should be understood that the following embodiments and detailed descriptions are only for illustrative purposes and do not limit the scope of protection of the present invention.

[0051] Example 1

[0052] This embodiment provides a robot configuration sampling method with uniform distribution of joint space, which comprises the following steps:

[0053] A. Obtain the robot joint working space; the working range of the robot end in three-dimensional space is as follows Figure 1 As shown. Use the robot's kinematic model to map the robot's working range from three-dimensional space to the robot's joint space, and take the robot's first three joint data for drawing to obtain the robot's joint working space (as shown in Figure 1). Figure 2 As shown), that is, the joint working surface (three-dimensional working surface);

[0054] B. Use UV mapping to map the joint working surface to the UV plane; use the LSCM method to parameterize the joint working surface and map the joint working surface to a two-dimensional UV plane. It is easy to perform uniform sampling on this plane. The obtained UV plane and the sampling points on the UV plane are as follows: Figure 3 shown.

[0055] C. Use UV reflection to obtain the robot sampling configuration; use the barycentric coordinate method to obtain the linear relationship between the UV plane sampling point and the surrounding points, interpolate the joint working surface according to this linear relationship to obtain the interpolation sampling point; find the data point on the joint working surface so that the data point is closest to the interpolation sampling point, and the data point on the joint working surface can be used as the robot configuration sampling point. The robot joint working surface after sampling is as follows: Figure 4 As shown; the restored sampling points on the joint space surface correspond to the robot sampling configuration, and the robot's sampling configuration can be restored based on these sampling points.

[0056] Wherein, step B specifically includes the following steps:

[0057] B1. Generate a triangular mesh based on the point cloud data of the joint working surface;

[0058] B2. Use Least Squares Conformal Maps (LSCM) to UV unfold the joint working surface in the form of a triangular mesh.

[0059] In step B2, let the vertex coordinates of a triangular patch A on the joint working surface be P1 = (x1, y1, z1), P2 = (x2, y2, z2), P3 = (x3, y3, z3), and the vertex coordinates of the corresponding triangular patch B on the two-dimensional UV plane be U1 = (u1, v1), U2 = (u2, v2), U3 = (u3, v3); the two edge vectors P of the triangular patch A in three-dimensional space are 12 With P 13 The form is

[0060] P 12 =P2-P1=(x2-x1,y2-y1,z2-z1)

[0061] P13 =P3-P1=(x3-x1,y3-y1,z3-z1)

[0062] Correspondingly, the edge vector U corresponding to the triangle patch B in the two-dimensional UV plane 12 and U 13 The form is

[0063] U 12 =U2-U1=(u2-u1,v2-v1)

[0064] U 13 =U3-U1=(u3-u1,v3-v1)

[0065] The conformal energy E is used to measure the conformality between the triangle patches A and B. The calculation method of the conformal energy E is as follows:

[0066]

[0067] Where i, j are the triangle vertex numbers; C is a 2×3 conformal matrix used to transform the three-dimensional vector P ij Mapped to a 2D UV plane; the conformal matrix is ​​of the form

[0068]

[0069] Where a, b, c and d are the parameters that need to be solved.

[0070] The smaller the value of conformal energy E, the better the conformality of triangles A and B. When conformal energy E is 0, triangles A and B are conformal. The value of conformal energy E is minimized to identify the values ​​of parameters a, b, c, and d. When parameters a, b, c, and d are known, conformal energy E = 0 evolves to ij The linear equation is solved by the least square method to obtain all U ij coordinate.

[0071] To ensure U ij The uniqueness of the result, fix the coordinates of at least two vertices in the UV plane to determine the scale and posture of the two-dimensional UV plane.

[0072] Step C specifically includes the following steps:

[0073] C1. Set uniform sampling points on the UV plane to obtain a series of UV coordinates;

[0074] C2. Let the UV coordinates of a certain sampling point be U = (u, v); traverse the triangular mesh of the UV plane, find the triangle containing the coordinate U, and let the vertex coordinates of the triangle be U1 = (u1, v1), U2 = (u2, v2), U3 = (u3, v3);

[0075] C3, calculate the weight of coordinate U relative to triangle vertices U1, U2 and U3 = (u3, v3), the results are λ1, λ2 and λ3,

[0076] U=λ1U1+λ2U2+λ3U3

[0077] Where λ1+λ2+λ3=1; the weight coefficients λ1, λ2 and λ3 are called the centroid coordinates of the coordinate U;

[0078] C4. Use the barycentric coordinates to interpolate the coordinates P1, P2, and P3 of the corresponding triangle vertices on the joint working surface to obtain the interpolation sampling points

[0079] P = λ1P1 + λ2P2 + λ3P3;

[0080] C5, find a data point on the joint working surface, so that the data point is closest to the interpolation sampling point, and the data point is the coordinate of the sampling point coordinate U on the UV plane corresponding to the point on the joint working surface;

[0081] C6. Perform steps C2-C4 on all sampled UV coordinates to obtain sampling points on the joint working surface.

[0082] Although the present invention has been described above through embodiments, the above embodiments are only used to exemplarily describe the feasible implementation schemes of the present invention, and are not used to limit the protection scope of the present invention. Any equivalent substitutions or changes made by those skilled in the art in accordance with the present invention should also be covered by the protection scope defined by the claims of the present invention.

Claims

1. A robot configuration sampling method with uniform distribution of joint space, characterized in that: The steps include: A. Obtain the robot joint workspace; use the robot's kinematic model to map the robot's working range from three-dimensional space to the robot's joint space, and take the robot's first three joint data for drawing to obtain the robot's joint workspace, that is, the joint working surface; B. Mapping the joint working surface to a UV plane using UV mapping; C. Use UV retroreflection to obtain the robot sampling configuration.

2. The robot configuration sampling method according to claim 1, characterized in that: In the step B, the joint working surface is parameterized using the LSCM method, and the joint working surface is mapped to a two-dimensional UV plane.

3. The robot configuration sampling method according to claim 2, characterized in that: The step B comprises the following steps: B1. Generate a triangular mesh based on the point cloud data of the joint working surface; B2. Use least squares conformal mapping to UV unfold the joint working surface in the form of a triangular mesh.

4. The robot configuration sampling method according to claim 3, characterized in that: In step B2, the vertex coordinates of a triangular patch A on the joint working surface are assumed to be P1=(x1, y1, z1), P2=(x2, y2, z2), P3=(x3, y3, z3), and the vertex coordinates of the corresponding triangular patch B on the two-dimensional UV plane are U1=(u1, v1), U2=(u2, v2), U3=(u3, v3); the two edge vectors P of the triangular patch A in three-dimensional space are 12 With P 13 The form is P 12 =P2-P1=(x2-x1,y2-y1,z2-z1) <h2 style=";text-align:left;direction:ltr">P<h2 style=";text-align:left;direction:ltr"> 13 <h2 style=";text-align:left;direction:ltr"> (P3-P1)(x3-x1,y3-y1,z3-z1) Correspondingly, the edge vector U corresponding to the triangle patch B in the two-dimensional UV plane 12 and U 13 The form is SHE IS 12 =U2-U1=(u2-u1,v2-v1) U 13 =U3-U1=(u3-u1,v3-v1) The conformality between the triangle patches A and B is measured using the conformal energy E, which is calculated as follows: Where i, j are the triangle vertex numbers; C is a 2×3 conformal matrix used to transform the three-dimensional vector P ij Mapped to a 2D UV plane; the conformal matrix is ​​of the form Where a, b, c and d are the parameters that need to be solved.

5. The robot configuration sampling method according to claim 4, characterized in that: The smaller the value of conformal energy E, the better the conformality of triangles A and B. When conformal energy E is 0, triangles A and B are conformal. The value of conformal energy E is minimized to identify the values ​​of parameters a, b, c, and d. When parameters a, b, c, and d are known, conformal energy E = 0 evolves to ij The linear equation is solved by the least square method to obtain all U ij coordinate.

6. The robot configuration sampling method according to claim 5, characterized in that: Fix the coordinates of at least two vertices in the UV plane to determine the scale and posture of the two-dimensional UV plane.

7. The robot configuration sampling method according to claim 1, characterized in that: In the step C, the linear relationship between the UV plane sampling point and the surrounding points is obtained by using the barycentric coordinate method, and the joint working surface is interpolated according to the linear relationship to obtain the interpolation sampling point; the data point is searched on the joint working surface so that the data point is closest to the interpolation sampling point, and the data point on the joint working surface is used as the robot configuration sampling point; the sampling point restored on the joint working surface is the sampling configuration of the robot.

8. The robot configuration sampling method according to claim 7, characterized in that: The step C comprises the following steps: C1. Setting uniform sampling points on the UV plane to obtain a series of UV coordinates; C2. Let the UV coordinate of a certain sampling point be U = (u, v); traverse the triangular mesh of the UV plane, find the triangle containing the coordinate U, and let the vertex coordinates of the triangle be U1 = (u1, v1), U2 = (u2, v2), U3 = (u3, v3); C3, calculate the weight of coordinate U relative to triangle vertices U1, U2 and U3 = (u3, v3), the results are λ1, λ2 and λ3, U=λ1U1+λ2U2+λ3U3 Where λ1+λ2+λ3=1; the weight coefficients λ1, λ2 and λ3 are called the centroid coordinates of the coordinate U; C4, use the centroid coordinates to interpolate the coordinates P1, P2 and P3 of the corresponding triangle vertices on the joint working surface to obtain interpolation sampling points P = λ1P1 + λ2P2 + λ3P3; C5, searching for a data point on the joint working surface so that the data point is closest to the interpolation sampling point, and the data point is the coordinate of the point corresponding to the sampling point coordinate U on the UV plane on the joint working surface; C6. Perform steps C2-C5 on all sampled UV coordinates to obtain sampling points on the joint working surface.

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