VARIABLE-PARAMETER STIFFNESS IDENTIFICATION AND MODELING METHOD FOR INDUSTRIAL ROBOT

Abstract

Disclosed is a variable-parameter stiffness identification and modeling method for an industrial robot. An effective working space of a robot is divided into a plurality of cubic regions. For an operating task in a certain machining region, different loads are applied to an end effector at multiple positions and multiple postures in the region, and robot joint stiffness in this section is identified and acquired according to the relationship between the loads and an end deformation, thereby realizing accurate stiffness control of the robot in different operating sections during a machining process.

Claims

1. A variable-parameter stiffness identification and modeling method for an industrial robot, comprising the following steps: Step 1: within an effective working range of a given type of industrial robot, dividing a whole operating space into a series of cubic grids according to a given maximum step length; Step 2: using theoretical coordinates of eight vertices of one cubic grid divided in Step 1 and a center point of a grid space for controlling the robot for positioning, selecting at least 3 robot accessible postures in each position, measuring a magnitude and direction of a load attached by a six-dimensional force sensor mounted on a flange, and using a laser tracker to measure position and posture changes of a robot end before and after loading in all positions and postures; Step 3: by collecting end loads and deformations in different positions and postures, realizing identification of robot joint stiffness satisfying an operating task of the grid space; and Step 4: according to the identification method in the grid space in Step 3 above, realizing the identification of joint stiffness of all the grids in the whole space, and establishing a stiffness model of the whole operating space.

2. The variable-parameter stiffness identification and modeling method for the industrial robot according to claim 1, wherein in Step 1, the effective operating space of the robot end is divided into three-dimensional grids to serve as a planning benchmark of robot sampling points.

3. The variable-parameter stiffness identification and modeling method for the industrial robot according to claim 1, wherein in Step 2, the laser tracker is used to measure positions of a group of target balls mounted on the flange of the robot to obtain the position and posture changes of the robot end by fitting, and the six-dimensional force sensor mounted on the flange of the robot is used to realize real-time collection of the end loads.

4. The variable-parameter stiffness identification and modeling method for the industrial robot according to claim 1, wherein in Step 2, by selecting a rotation axial direction of the robot around the end according to an operating type, an actual operating posture of the robot is simulated.

5. The variable-parameter stiffness identification and modeling method for the industrial robot according to claim 1, wherein in Step 3, a conversion relationship of the position and posture of the flange before and after loading is obtained by fitting through a least square method based on singular value decomposition.

6. The variable-parameter stiffness identification and modeling method for the industrial robot according to claim 1, wherein in Step 3, structural transformation of a static stiffness model of the robot is made to obtain a relationship between end deformations and the end loads of the robot in the given posture, and a Jacobian matrix of the robot is solved by differential transformation.

7. The variable-parameter stiffness identification and modeling method for the industrial robot according to claim 1, wherein in Step 4, the joint stiffness of each grid space is identified respectively, and the robot stiffness modeling in the whole operating space is realized by using an identification result in each grid space.

8. The variable-parameter stiffness identification and modeling method for the industrial robot according to claim 1, wherein Step 3 specifically comprises: (31) recording position changes of three target balls on the flange under the different postures of the robot at each vertex of the grid space before and after stressing; (32) fitting a position and posture change matrix of a plane in which the three target balls are located by a least square method, and regarding the matrix as a position and posture change matrix of the flange; (33) establishing a kinematics model and a Jacobian matrix of the robot; and (34) realizing stiffness identification in the grid space by combining the position and posture change matrix, readings of the force sensor and the kinematics model of the robot.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] FIG. 1 is a schematic diagram of division of an operating grid space of a robot;

[0034] FIG. 2 is a schematic diagram of sampling positions and postures of robot stiffness identification in a grid space; and

[0035] FIG. 3 is a schematic diagram of a positioning compensation effect for 25 test points.

DETAILED DESCRIPTION OF THE DISCLOSURE

[0036] In order to facilitate the understanding of the skilled in the art, the disclosure is further described in combination with an embodiment and accompanying drawings below. The content mentioned in the implementation is not a limitation to the disclosure.

[0037] According to the technical scheme of the disclosure, required stiffness identification equipment mainly includes: an industrial robot, a laser tracker (or other positioning acquisition sensors) and a six-dimensional force sensor.

[0038] Referring to FIG. 1, a variable-parameter stiffness identification and modeling method for an industrial robot includes the following steps.

[0039] Step 1: the laser tracker is placed in a suitable position to facilitate measurement. The laser tracker is used for measurement, a coordinate system including a robot base coordinate system Base, a flange coordinate system Flange, a tool coordinate system Tool and a six-dimensional force sensor coordinate system Force is established, and the effective operating space of the robot is divided into a series of cubic grids according to a given maximum step length.

[0040] Step 2: theoretical position coordinates of eight vertices of one cubic grid divided in Step 1 and a center point of a grid space (as shown by Tag1 to Tag9 in FIG. 2, where X.sub.i, Y.sub.i, Z.sub.i are three directional axes of the tool coordinate system Tool under postures corresponding to end positions) are used for controlling the robot for positioning. The initial posture of each vertex position is shown in FIG. 2. The directions of three cubic edges intersecting at the point Tag5 are respectively defined as the axis direction X, the axis direction Y and the axis direction Z of an initial target position and posture, namely they are parallel to the three axis directions of the coordinate system Base.

[0041] Three other postures are selected respectively in each position. In order to simplify the operation, an appropriate angle and an appropriate step length are selected to rotate along an axis direction (e.g., the direction of an operation axis, i.e. the direction X of coordinates of a target point) of the tool coordinate system for a certain number of times to obtain a series of an appropriate number of postures at the acting position. The rotation angle of the position and posture of a new target point relative to the initial position and posture is defined as θ=j*Δθ, j=1, 2, 3, where Δθ is as a selected step length of a sample. A new robot posture is generated by rotating by an angle θ about a selected axis direction, and a rotation change matrix Rot(x,θ) is introduced by taking the X axis as an example:

[00001]$\mathrm{Rot}\left(x,\theta \right)=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \theta & -s\mathrm{in}\theta & 0\\ 0& \sin \theta & \cos \theta & 0\\ 0& 0& 0& 1\end{array}\right)$

[0042] Information of a new end position and posture in the position under a Cartesian coordinate system is obtained by calculating through Tag.sub.now=Rot(x,θ)Tag, where Tag and Tag.sub.now are respectively information of the end position and posture after rotation. Finally, information of all the target position and postures at the 9 target positions is obtained. The rotation changes along the axis Y and axis Z are shown below:

[00002]$\mathrm{Rot}\left(y,\theta \right)=\left(\begin{array}{cccc}\cos \theta & 0& \sin \theta & 0\\ 0& 1& 0& 0\\ -s\mathrm{in}\theta & 0& \cos \theta & 0\\ 0& 0& 0& 1\end{array}\right)Rot\left(z,\theta \right)=\left(\begin{array}{cccc}\cos \theta & -s\mathrm{in}\theta & 0& 0\\ \sin \theta & \cos \theta & 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right)$

[0043] Step 3: for identifying the robot joint stiffness in the grid space, the six-dimensional force sensor is mounted on an end flange, a rigid load of a certain weight is hung on the force sensor, and the load magnitude and direction of each target position and posture in the force sensor coordinate system are obtained.

[0044] Through 3 targets mounted on the flange of the robot, the laser tracker is used to measure and indirectly obtain the reading of the deformation of a robot end before and after stressing, and position coordinate information of the two groups of targets before and after loading is read. A conversion relationship of the positions and postures of the flange before and after loading is obtained by fitting through a least square method based on singular value decomposition:

p′=R*p+t

[0045] where p and p′ respectively represent the coordinate information of a point group read before and after stressing, and R and t respectively represent a rotation matrix and a translation matrix,

[00003]$p_m=\frac{1}{3}\underset{{}^{i=1}}{\overset{3}{.Math.}}{p}_i,{p^{\prime }}_m=\frac{1}{3}\underset{{}^{i=1}}{\overset{3}{.Math.}}{p}^{\prime },H=\underset{{}^{i=1}}{\overset{3}{.Math.}}\left(p_i-p_m\right){\left(p_i^{\prime }-p_m^{\prime }\right)}^T$

[0046] where p.sub.i and p.sub.i′ are respectively the position coordinates of each target ball before and after stressing, and p.sub.m and p.sub.m′ are averages; singular value decomposition is conducted on H, and H=UDV.sup.T is obtained, where D is a diagonal matrix, and U and V are orthogonal matrixes; and therefore the rotation matrix and translation matrix of stressing deformation of the flange are obtained:

R=VU.sup.T,t=p.sub.m′−R*p.sub.m.

[0047] The robot joint stiffness is identified by using a static stiffness model of the robot, and a calculating formula is:

[0048] F=KD=J.sup.−T K.sub.θJ.sup.−1D, where F and D are a generalized load matrix and an end deformation matrix of the flange of the robot end, K and K.sub.θ are respectively a robot end stiffness matrix and a robot joint stiffness matrix, and J is a robot Jacobian matrix. A load vector measured at the robot end is converted to the flange coordinate system by a transformation matrix of the tool coordinate system and the flange coordinate system, the above formula is modified to: D=JK.sub.xJ.sup.TF=AK.sub.x, where K.sub.x=[k.sub.θ.sub.1.sup.−1,k.sub.θ.sub.2.sup.−1,k.sub.θ.sub.3.sup.−1,k.sub.θ.sub.4.sup.−1,k.sub.θ.sub.5.sup.−1,k.sub.θ.sub.6.sup.−1].sup.T, k.sub.θ.sub.1.sup.−1 to k.sub.θ.sub.6.sup.−1 are reciprocals of the stiffness of the 6 joints of the robot, and A is the matrix associated with a force matrix and the Jacobian matrix, represented as:

[00004]$A=\left[\begin{array}{ccc}{J}_{11}\underset{i=1}{\overset{6}{.Math.}}{J}_{i1}{F}_i& L& J_{16}\underset{i=1}{\overset{6}{.Math.}}{J}_{i6}{F}_i\\ M& O& M\\ J_{61}\underset{i=1}{\overset{6}{.Math.}}{J}_{i1}{F}_i& L& J_{66}\underset{i=1}{\overset{6}{.Math.}}{J}_{i6}{F}_i\end{array}\right]$

where Fi is the i.sup.th line of external force F, through the establishment of a robot kinematics D-H model and a method of differential transformation, the Jacobian matrix of the robot is established. Since the joints of the industrial robot are rotational joints, the i.sup.th column of the Jacobian matrix J is calculated according to the formula below:

[00005]$J_{\mathrm{li}}=\left[\begin{array}{c}{\left(p\times n\right)}_z\\ {\left(p\times o\right)}_z\\ {\left(p\times a\right)}_z\end{array}\right]J_{\mathrm{ai}}=\left[\begin{array}{c}{n}_z\\ o_z\\ a_z\end{array}\right]$

where J.sub.li is the rotation transformation of the i.sup.th column of the Jacobian matrix of the robot, J.sub.ai is the movement transformation of the i.sup.th column of the Jacobian matrix of the robot, n, o, a and P are respectively four column vectors of the transformation .sub.n.sup.iT from each link to an end link, and n.sub.z, o.sub.z, a.sub.z are respectively third line values of column matrixes of n, o, and a.

[0049] The joint stiffness identification of the robot in one grid space is realized through the above calculation process.

[0050] Step 4: according to the above operation process, joint stiffness identification in each grid of the robot operating space is realized, a stiffness identification result of each grid space is selected for stiffness modeling, when the operating positions of the robot end are distributed in different grid sections, robot stiffness models matching with them are selected, and accurate control of robot operating stiffness with high operating adaptability is realized.

[0051] The specific implementation method of the disclosure will be illustrated by taking a KUKA-KR500 industrial robot as an example:

[0052] firstly, the robot is used to establish a coordinate system, and in a space of 600 mm×1200 mm×600 mm, the robot operating space is divided into 128 spatial three-dimensional grids according to a grid step length of 150 mm;

[0053] secondly, position and posture coordinate information of the robot in 9 target positions in all the grids is planned and determined in offline programming software; and as shown in FIG. 2, three different positions and postures are obtained by rotating the initial posture by ±10° around the axis Y of the tool coordinate system, so as to simulate a machining task of a curved surface within a certain range;

[0054] thirdly, the target positions and postures are sampled under a no-load state, and the positions of the target balls on the flange are recorded by the laser tracker; a 50 KG load is mounted at the end in a fixed connection mode to simulate the force at the robot end in the operating process; and the target position and posture sampling is completed again under a load state, and the position information of the target balls on the flange under the load state of the robot is recorded by the laser tracker; and finally, the load information and position and posture information collected are processed, and the robot stiffness in each grid space is calculated through a stiffness identification algorithm, so as to realize the variable-parameter joint stiffness identification in the whole operating space and accurate stiffness modeling for the robot.

[0055] Based on the stiffness modeling, in the process of machining, the six-dimensional force sensor is combined to measure a sensor on-line, and on-line prediction and compensation of positioning errors of the robot in a machining state can be realized. 25 positions and postures of the robot end are randomly selected, the distribution grid spaces in which these points exist are determined, and positioning compensation of the positions and postures of the robot in the load state is realized. The results are shown in FIG. 3, after compensation, the errors are improved from 2-3 mm to 1 mm or less, and the accuracy is improved to 60% or more.

[0056] There are many specific application ways of the disclosure, and the above is only a preferred implementation of the disclosure. It should be noted that, for those of ordinary skill in the art, without deviating from the principle of the disclosure, several improvements can be made, and the improvements shall also be regarded as the protection scope of the disclosure.