Joint space uniform robot pose sampling method

Abstract

The application discloses a kind of joint space uniform robot pose sampling methods, it includes the following steps: A, obtains robot joint workspace;The kinematic model of robot is used to correspond the working range of robot from three-dimensional space to robot joint space, and the first three joint data of robot are taken to draw, obtain the joint workspace of robot, i.e.joint working surface;B, using UV mapping is mapped to UV plane using joint working surface;C, using UV back reflection obtains robot sampling pose.The method of the application uses UV mapping to map the joint space working surface of robot to UV plane, which is convenient for robot pose sampling.After sampling on the UV plane, the UV back reflection is realized using the barycentric coordinate method, and the robot pose obtained has good correspondence and high calculation accuracy.The robot pose obtained using the method of the application is used for robot dynamic performance sampling, and the data error obtained is closer to normal distribution.Using these data to predict the dynamic performance of the robot, the prediction result is better.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of robot kinematics research, and particularly relates to a robot pose sampling method with uniform distribution in joint space. BACKGROUND

[0002] Robot dynamic characteristics, 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 pose, and the change relationship is nonlinear. In order to obtain the dynamic characteristics of the robot, the dynamic characteristics of the robot need to be sampled at different robot poses, and statistical methods are used to predict the dynamic characteristic parameters. The distribution of the robot pose has an impact on the prediction quality of the dynamic characteristics. When the distribution of the robot pose for dynamic characteristic sampling has some bias, 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, obtaining uniformly distributed robot poses is very important for robot dynamic characteristic prediction.

[0003] In order to obtain uniformly distributed robot poses, the existing robot pose sampling method usually determines uniformly distributed robot end poses in three-dimensional space, and then converts to obtain robot poses.

[0004] This method selects uniformly distributed positions in three-dimensional space as robot end positions, and selects attitudes consistent with the movement direction of the robot end as robot end attitudes. These robot end positions and attitudes can be integrated into robot end poses, including robot end position coordinates and attitude matrices. Using robot kinematics to process robot end poses can obtain corresponding robot poses.

[0005] The existing robot pose sampling method in three-dimensional space is simple and intuitive, easy to understand and operate. The robot poses obtained by this sampling method are uniformly distributed in three-dimensional space, but the distribution in joint space may not be uniform. This is because the robot kinematics model is a nonlinear model, and the distribution of the robot pose between three-dimensional space and joint space also has a nonlinear relationship. According to the non-uniformly distributed robot pose, the error distribution of the identification result does not conform to the normal distribution and may have some unknown bias. The robot dynamic characteristics predicted according to this measurement result have errors.

[0006] Therefore, it is necessary to provide a robot pose sampling method with uniform distribution in joint space. SUMMARY

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

[0008] To achieve the above main purpose, the application discloses a joint space uniform robot pose sampling method, which comprises the following steps:

[0009] A, obtaining a robot joint workspace; using a kinematics model of the robot to correspond the working range of the robot from a three-dimensional space to a robot joint space, and taking the first three joint data of the robot to plot, to obtain a robot joint workspace, i.e. a joint working surface (a three-dimensional working surface);

[0010] B, using UV mapping to map the joint working surface to a UV plane; UV unfolding is a method of unfolding a three-dimensional model surface into a two-dimensional UV plane in computer graphics, and 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, using UV reflection to obtain a robot sampling pose. UV reflection can map points in a two-dimensional UV plane back to a three-dimensional working surface. Sampling on a two-dimensional UV plane and performing UV reflection can obtain a sampling point on a three-dimensional working space.

[0012] The method of the application can be used for sampling robot poses, and the robot pose sampling points obtained by sampling are uniformly distributed in the robot joint space. The uniformly distributed robot poses can be used for robot dynamic characteristic sampling.

[0013] In the application, the three-dimensional working surface sampling points can restore the robot sampling pose, and the obtained sampling pose is uniformly distributed in the joint space, meeting the needs of robot dynamic characteristic sampling pose.

[0014] According to a specific embodiment of the application, in step B, the LSCM method is used for surface parameterization of the joint working surface to map the joint working surface to a two-dimensional UV plane.

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

[0016] B1, generating a triangular mesh according to the point cloud data of the joint working surface;

[0017] B2, using the least squares conformal mapping (LSCM) to perform UV unfolding on the triangular mesh form of the joint working surface.

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

[0019] The LSCM is used to establish a mapping from the three-dimensional working surface to the two-dimensional UV plane, and the three-dimensional working surface and the triangular mesh in the two-dimensional UV plane have "conformity", i.e., the local angles of the corresponding triangular patches are the same. According to one specific embodiment of the present application, in step B2, the vertex coordinates of a triangular patch A on the joint working surface are P1=(x1, y1, z1), P2=(x2, y2, z2), and P3=(x3, y3, z3), and the vertex coordinates of the corresponding triangular patch B in the two-dimensional UV plane are U1=(u1, v1), U2=(u2, v2), and U3=(u3, v3); the two edge vectors P 12 and P 13 of the triangular patch A in the three-dimensional space are in the form of

[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 two edge vectors U 12 and U 13 of the triangular patch B in the two-dimensional UV plane are in the form of

[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 conformity between the triangular patches A and B, and the calculation method of the conformal energy E is

[0026]

[0027] where i and j are the triangular vertex numbers; when the conformal energy of the two triangular patches is calculated, only the energy of the two corresponding edges of the two triangular patches needs to be calculated, because a triangular patch can be completely defined according to the two edges and the included angle; C is a 2x3 conformal matrix used to map the three-dimensional vector P ij to the two-dimensional UV plane; the conformal matrix is in the form of

[0028]

[0029] where a, b, c, and d are parameters to be solved.

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

[0031] In order to ensure the uniqueness of the U ij result, according to one specific embodiment of the present application, the coordinates of at least two vertices are fixed in the UV plane to determine the scale and pose of the two-dimensional UV plane.

[0032] According to one specific embodiment of the present application, 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 on the joint working surface is searched so that the data point is closest to the interpolation sampling point, and the data point on the joint working surface obtained is taken as the robot pose sampling point; the sampling point restored on the joint working surface is the sampling pose of the robot.

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

[0034] C1, a uniform sampling point is set on the UV plane to obtain a series of UV coordinates;

[0035] C2, assuming that the UV coordinate of a sampling point is U = (u, v); the triangular mesh of the UV plane is traversed to find a triangle containing the coordinate U, and the vertex coordinates of the triangle are assumed to be U1 = (u1, v1), U2 = (u2, v2) and U3 = (u3, v3);

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

[0037] U = λ1U1 + λ2U2 + λ3U3

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

[0039] C4, the barycentric coordinates are used to interpolate the coordinates P1, P2 and P3 of the corresponding vertexes of the triangle on the joint working surface to obtain the interpolation sampling point

[0040] P = λ1P1 + λ2P2 + λ3P3;

[0041] C5, finding a data point on the joint working surface which is closest to the interpolation sampling point, the data point being a coordinate of a corresponding point of the sampling point coordinate U on the UV plane on the joint working surface;

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

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

[0044] The method of the present application can uniformly sample robot poses in the robot joint space, and the spacing between adjacent sampling poses is similar. The method of the present application uses UV mapping to map the robot joint space working surface to the UV plane, which facilitates robot pose sampling. The method of the present application uses the barycentric coordinate method to realize UV back reflection after sampling on the UV plane, and the corresponding robot poses have good calculation accuracy. Using the robot poses obtained by the method of the present application to sample the robot dynamic performance, the data error is closer to the normal distribution. Using these data to predict the robot dynamic performance, the prediction result is better.

[0045] In order to more clearly illustrate the purpose, technical scheme and advantages of the present application, the present application will be further described in detail below with reference to the drawings and specific embodiments. BRIEF DESCRIPTION OF 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 is the UV plane of the robot joint space surface mapping and the sampling points in Example 1;

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

[0050] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application, but it should be understood that the following embodiments and detailed description are merely for illustrative purposes and do not limit the scope of protection of the present application.

[0051] Example 1

[0052] The present embodiment provides a robot pose sampling method with uniform joint space, which comprises the following steps:

[0053] A, get the joint workspace of the robot; the working range of the robot end in three-dimensional space is shown in Figure 1 . Using the kinematic model of the robot, the working range of the robot is corresponded from three-dimensional space to the joint space of the robot, and the first three joint data of the robot are plotted to obtain the joint workspace of the robot (as shown in Figure 2 ), that is, the joint working surface (three-dimensional working surface);

[0054] B, using UV mapping to map the joint working surface to the UV plane; using the LSCM method to parameterize the joint working surface, the joint working surface is mapped to the two-dimensional UV plane. In this plane, uniform sampling is easy to carry out. The obtained UV plane and the sampling points on the UV plane are shown in Figure 3 .

[0055] C, using UV back reflection to obtain the sampling configuration of the robot; using the barycentric coordinate method to obtain the linear relationship between the UV plane sampling points and the surrounding points, according to the linear relationship, the joint working surface is interpolated to obtain the interpolation sampling points; find the data points on the joint working surface, so that the data points are closest to the interpolation sampling points, the data points on the joint working surface obtained can be used as the sampling configuration of the robot. The sampled joint working surface of the robot is shown in Figure 4 ; the sampling points on the obtained joint space surface are restored to correspond to the sampling configuration of the robot, and the sampling configuration of the robot can be restored according to these sampling points.

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

[0057] B1, generating a triangular mesh according to the point cloud data of the joint working surface;

[0058] B2, using least squares conformal mapping (Least Squares Conformal Maps, LSCM) to UV unfold the joint working surface in the form of triangular mesh.

[0059] In step B2, the vertex coordinates of a triangular patch A on the joint working surface are 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 of triangular patch A in three-dimensional space are P 12 and P 13 , which are in the form of

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

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

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

[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 triangular patches A and B, and the calculation method of the conformal energy E is

[0066]

[0067] Where i, j are triangular vertex numbers; C is a 2x3 conformal matrix used to map the three-dimensional vector P ij to the two-dimensional UV plane; the conformal matrix is in the form of

[0068]

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

[0070] The smaller the value of the conformal energy E, the better the conformality of the triangular patches A and B; when the conformal energy E is 0, the triangular patches A and B are conformal; the value of the conformal energy E is minimized to identify the values of the parameters a, b, c, and d; when the parameters a, b, c, and d are known, the conformal energy E = 0 evolves into a linear equation about all the coordinates U ij ; the least square method is used to solve the linear equation to obtain all the U ij coordinates.

[0071] In order to ensure the uniqueness of the U ij result, at least two vertex coordinates in the UV plane are fixed to determine the scale and pose of the two-dimensional UV plane.

[0072] Step C specifically comprises the following steps:

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

[0074] C2, setting the UV coordinate of a sampling point as U = (u, v); traversing the triangular mesh of the UV plane, finding a triangle containing the coordinate U, setting the vertex coordinates of the triangle as U1 = (u1, v1), U2 = (u2, v2), and U3 = (u3, v3);

[0075] C3, calculate the weight of the coordinate U relative to the triangle vertices U1, U2 and U3 = (u3, v3), the result is 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 barycentric coordinates of the coordinate U;

[0078] C4, using 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 point

[0079] P = λ1P1+ λ2P2+ λ3P3;

[0080] C5, 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 is the coordinate of the corresponding point of the sampling point coordinate U on the joint working surface in the UV plane;

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

[0082] Although the present application is described above by way of examples, the above examples are only used to exemplarily describe the implementable solutions of the present application, and are not used to limit the protection scope of the present application, and any equivalent substitutions or changes made by those skilled in the art according to the present application should also be covered by the protection scope defined by the claims of the present application.

Claims

1. A method for uniformly distributed robot configuration sampling in joint space, characterized in that, Includes the following steps: 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 joint space, and take the data of the robot's first three joints to draw, thus obtaining the robot joint workspace, i.e. the joint working surface; B. Map the joint working surface to a UV plane using UV mapping; in step B, the LSCM method is used to parameterize the joint working surface and map it to a two-dimensional UV plane; step B includes 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 perform UV unwrapping on the joint working surface in the form of a triangular mesh; 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), and P3 = (x3, y3, z3). The vertex coordinate system of the corresponding triangular patch B on the two-dimensional UV plane is U1 = (u1, v1), U2 = (u2, v2), and U3 = (u3, v3). The two edge vectors P1 and P2 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) P 13 =P3-P1=(x3-x1,y3-y1,z3-z1) Correspondingly, the edge vector U of the triangular 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 conformal energy E is used to measure the conformality between triangular facets A and B. The method for calculating the conformal energy E is as follows: Where i and j are the vertex numbers of the triangle; C is a 2×3 conformal matrix used to encode the three-dimensional vector P ij Mapped to a two-dimensional UV plane; The conformal matrix is ​​in the form of Where a, b, c, and d are the parameters that need to be solved; C. Use UV retroreflection to obtain the robot's sampling configuration.

2. The robot configuration sampling method according to claim 1, characterized in that, The smaller the conformal energy E, the better the conformality of triangular faces A and B; when the conformal energy E is 0, triangular faces A and B are conformal; minimizing the value of the conformal energy E helps identify the values ​​of parameters a, b, c, and d; when parameters a, b, c, and d are known, the conformal energy E = 0 evolves into a state of conformality with respect to all coordinates U. ij The linear equations are obtained; the least squares method is used to solve the linear equations to obtain all U. ij coordinate.

3. The robot configuration sampling method according to claim 2, characterized in that, The coordinates of at least two vertices in the UV plane are fixed to determine the scale and orientation of the two-dimensional UV plane.

4. The robot configuration sampling method according to claim 1, characterized in that, In step C, the linear relationship between the UV plane sampling points and surrounding points is obtained using the centroid coordinate method. Based on this linear relationship, the joint working surface is interpolated to obtain interpolated sampling points. Data points are found on the joint working surface such that the data points are closest to the interpolated sampling points. The data points obtained on the joint working surface are used as robot configuration sampling points. The sampling points restored on the joint working surface are the robot's sampling configuration.

5. The robot configuration sampling method according to claim 4, characterized in that, Step C includes the following steps: C1. Set uniform sampling points on the UV plane to obtain a series of UV coordinates; C2. Let the UV coordinates of a certain sampling point be U = (u, v); traverse the triangular mesh of the UV plane to find the triangle containing the coordinates U, and let the vertex coordinates of the triangle be U1 = (u1, v1), U2 = (u2, v2), U3 = (u3, v3); C3. Calculate the weights of coordinate U relative to the triangle vertices U1, U2, and U3 = (u3, v3), resulting in λ1, λ2, and λ3. U = λ1U1 + λ2U2 + λ3U3 Where λ1+λ2+λ3=1; the weighting coefficients λ1, λ2 and λ3 are called the centroid coordinates of coordinate U; C4. Using the centroid coordinates, interpolate the coordinates P1, P2, and P3 of the corresponding triangle vertices on the joint working surface to obtain the interpolation sampling points. P = λ1P1 + λ2P2 + λ3P3; C5. Find a data point on the joint working surface such that the data point is closest to the interpolation sampling point. The data point is the coordinate of the corresponding point on the joint working surface of the sampling point U on the UV plane. C6. Perform steps C2-C5 on all sampled UV coordinates to obtain the sampling points on the working surface of the joint.

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