CN103231375A

CN103231375A - Industrial robot calibration method based on distance error models

Info

Publication number: CN103231375A
Application number: CN2013101561155A
Authority: CN
Inventors: 王振华; 许辉; 陈国栋; 孙荣川; 任子武; 孙立宁; 洪云波
Original assignee: Suzhou University
Current assignee: Suzhou University
Priority date: 2013-04-28
Filing date: 2013-04-28
Publication date: 2013-08-07

Abstract

The invention discloses an industrial robot calibration method based on a distance error model, comprising: establishing a robot MDH kinematics model; the error of a homogeneous transformation matrix; establishing a robot distance error calibration model; measuring the actual pose of the robot end; Calibration of rod geometric parameter errors; experimental verification. The industrial robot calibration method based on the distance error model provided by the present invention has the advantages of simplicity, practicality, high efficiency and quickness, is applicable to any series joint robot, has strong versatility, and can improve the positioning accuracy and distance accuracy of the industrial robot at the same time.

Description

Calibration method of industrial robot based on distance error model

技术领域technical field

本发明涉及机器人标定技术领域，特别是涉及一种基于距离误差模型的工业机器人标定方法。The invention relates to the technical field of robot calibration, in particular to an industrial robot calibration method based on a distance error model.

背景技术Background technique

现代制造业对工业机器人性能的要求在不断地提高，机器人的性能的两个主要评价指标为：重复定位精度和绝对定位精度。现今机器人重复定位精度比较高，绝对定位精度却很低，一般相差一个数量级以上，因此无法达到高精度加工的要求。研究发现，绝对定位精度主要受到机器人运动学模型中连杆参数精度的影响，而标定技术能够通过对机器人运动学参数的修正提高机器人的绝对定位精度。因此，在机器人使用前需要对其进行标定。所谓标定就是应用先进的测量手段和基于模型的参数识别方法辨识出机器人模型的准确参数，从而提高机器人绝对精度的过程。The performance requirements of industrial robots in modern manufacturing industry are constantly improving. The two main evaluation indicators of robot performance are: repeated positioning accuracy and absolute positioning accuracy. Nowadays, the repetitive positioning accuracy of robots is relatively high, but the absolute positioning accuracy is very low, generally differing by more than one order of magnitude, so it cannot meet the requirements of high-precision machining. The study found that the absolute positioning accuracy is mainly affected by the accuracy of the connecting rod parameters in the robot kinematics model, and the calibration technology can improve the absolute positioning accuracy of the robot through the correction of the robot kinematics parameters. Therefore, it needs to be calibrated before the robot is used. The so-called calibration is the process of using advanced measurement methods and model-based parameter identification methods to identify the exact parameters of the robot model, thereby improving the absolute accuracy of the robot.

但在应用传统的方法进行位置误差的标定和补偿时，要涉及到测量系统坐标系与机器人基础坐标系间的变换，由于这一过程很难精确完成，而且操作复杂，容易引入外界误差，使得标定结果不准确，不能满足实际应用的要求。However, when using the traditional method to calibrate and compensate the position error, it involves the transformation between the coordinate system of the measurement system and the basic coordinate system of the robot. Because this process is difficult to complete accurately, and the operation is complicated, it is easy to introduce external errors. The calibration results are inaccurate and cannot meet the requirements of practical applications.

因此，针对上述技术问题，有必要提供一种基于距离误差模型的工业机器人标定方法。Therefore, in view of the above technical problems, it is necessary to provide an industrial robot calibration method based on a distance error model.

发明内容Contents of the invention

有鉴于此，本发明提供了一种基于距离误差模型的工业机器人标定方法，其有效提高了工业机器人的定位精度和距离精度。In view of this, the present invention provides an industrial robot calibration method based on a distance error model, which effectively improves the positioning accuracy and distance accuracy of the industrial robot.

为了实现上述目的，本发明实施例提供的技术方案如下：In order to achieve the above object, the technical solutions provided by the embodiments of the present invention are as follows:

一种基于距离误差模型的工业机器人标定方法，所述方法包括以下步骤：A kind of industrial robot calibration method based on distance error model, described method comprises the following steps:

S1、建立机器人MDH运动学模型；S1, establish the robot MDH kinematics model;

S2、齐次变换矩阵的误差；S2, the error of the homogeneous transformation matrix;

S3、建立机器人距离误差标定模型；S3. Establishing a robot distance error calibration model;

S4、机器人末端实际位姿的测量；S4. Measurement of the actual pose of the end of the robot;

S5、机器人各连杆几何参数误差的标定；S5. Calibration of the geometric parameter error of each connecting rod of the robot;

S6、实验验证，判断是否满足精度要求，若是，则标定结束，若否，返回步骤S4，将实验结果迭代，再次进行标定实验。S6. Experimental verification, judging whether the accuracy requirement is met, if yes, the calibration ends, if not, return to step S4, iterate the experimental results, and perform the calibration experiment again.

作为本发明的进一步改进，所述步骤S1中MDH运动学模型中连杆i-1和连杆i固连坐标系的齐次变换矩阵定义为：As a further improvement of the present invention, the homogeneous transformation matrix of the fixed coordinate system of the connecting rod i-1 and the connecting rod i in the MDH kinematics model in the step S1 is defined as:

A_i＝Trans(Z,d_i)Rot(Z,θ_i)Trans(X,a_i)Rot(X,α_i)Rot(Y,β_i)，A _i =Trans(Z,d _i )Rot(Z,θ _i )Trans(X,a _i )Rot(X,α _i )Rot(Y,β _i ),

其中，a为连杆长度，α为连杆转角，d为连杆偏距，θ为关节角，β为绕Y轴旋转角；Among them, a is the length of the connecting rod, α is the rotation angle of the connecting rod, d is the offset distance of the connecting rod, θ is the joint angle, and β is the rotation angle around the Y axis;

机器人的基础坐标系B和末端连杆坐标系N之间的总变换为：The total transformation between the base coordinate system B of the robot and the end link coordinate system N is:

${T T}_{N N}^{B B} = = {A A}_{11} {A A}_{22} {A A}_{33} \cdot \cdot \cdot \cdot \cdot \cdot {A A}_{N N} . .$

作为本发明的进一步改进，所述步骤S2具体包括：As a further improvement of the present invention, the step S2 specifically includes:

计算实际的相邻连杆变换矩阵为：Calculate the actual adjacent link transformation matrix as:

${A A}_{i i}^{* *} = = {A A}_{i i} + + d d {A A}_{i i};;$

误差矩阵dA_i以微分形式表示为：The error matrix dA _i is expressed in differential form as:

${A A}_{i i} = = \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {α α}_{i i}} Δ Δ {α α}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {a a}_{i i}} Δ Δ {a a}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {d d}_{i i}} Δ Δ {d d}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {θ θ}_{i i}} Δ Δ {θ θ}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {β β}_{i i}} Δ Δ {β β}_{i i};;$

计算机器人末端连杆相对于基础坐标系的实际变换矩阵：Calculate the actual transformation matrix of the end link of the robot relative to the base coordinate system:

${T T}_{N N}^{B B * *} = = {T T}_{N N}^{B B} + + d d {T T}_{N N}^{B B} = = {T T}_{N N}^{B B} + + {T T}_{N N}^{B B} δ δ {T T}_{N N}^{B B}$

$= = {A A}_{11}^{* *} {A A}_{22}^{* *} \cdot \cdot \cdot &Center Dot; \cdot \cdot {A A}_{N N}^{* *}$

计算

的误差矩阵

calculate

The error matrix of

$δ δ {T T}_{N N}^{B B} = = (\begin{matrix} 00 & - - {δ δ}_{z z}^{N N} & {δ δ}_{y the y}^{N N} & {d d}_{x x}^{N N} \\ {δ δ}_{z z}^{N N} & 00 & - - {δ δ}_{x x}^{N N} & {d d}_{y the y}^{N N} \\ - - {δ δ}_{y the y}^{N N} & {δ δ}_{x x}^{N N} & 00 & {d d}_{z z}^{N N} \\ 00 & 00 & 00 & 00 \end{matrix});;$

计算机器人末端位置误差向量 $dP = {(\begin{matrix} d_{x}^{N} & d_{y}^{N} & d_{z}^{N} \end{matrix})}^{T}$ 的矩阵。Calculation of robot end position error vector $dP = {(\begin{matrix} d_{x}^{N} & d_{the y}^{N} & d_{z}^{N} \end{matrix})}^{T}$ matrix.

作为本发明的进一步改进，所述步骤S3中机器人距离误差标定模型的公式为：As a further improvement of the present invention, the formula of the robot distance error calibration model in the step S3 is:

$Δl Δl ((i i,, j j)) = = ((\frac{{x x}_{B B} ((j j)) - - {x x}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))},, \frac{{y the y}_{B B} ((j j)) - - {y the y}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))},, \frac{{z z}_{B B} ((j j)) - - {z z}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))})) (({B B}_{j j} - - {B B}_{i i})) Δq Δq;;$

i和j为机器人在三维空间中任意的点，l_B(i,j)、l_L(i,j)分别为两点在机器人基坐标系B和测量坐标系L中的距离，Δl(i,j)为距离误差。i and j are arbitrary points of the robot in three-dimensional space, l _B (i, j) and l _L (i, j) are the distances between two points in the robot base coordinate system B and the measurement coordinate system L respectively, Δl(i ,j) is the distance error.

作为本发明的进一步改进，所述步骤S4具体为：As a further improvement of the present invention, the step S4 is specifically:

在机器人工作空间内，任意指定n个点，记录所述n个点的笛卡尔坐标值，当机器人末端运动到指定点时，记录下相应的关节转角值，同时用激光跟踪仪测量出对应的机器人末端的实际位姿坐标值。In the robot workspace, arbitrarily specify n points, record the Cartesian coordinate values of the n points, when the end of the robot moves to the specified point, record the corresponding joint rotation angle value, and measure the corresponding joint angle with the laser tracker The actual pose coordinate value of the robot end.

作为本发明的进一步改进，所述步骤S5具体为：As a further improvement of the present invention, the step S5 is specifically:

将步骤S4中的每一个指定点对应的一组关节转角值及其对应的由激光跟踪仪测量得到的机器人末端的实际位姿坐标值代入到步骤S3中的机器人距离误差标定模型的公式；Substituting a group of joint rotation angle values corresponding to each specified point in step S4 and the corresponding actual pose coordinates of the robot end measured by the laser tracker into the formula of the robot distance error calibration model in step S3;

由n个点得到n-1个方程，组成一个方程组；Obtain n-1 equations from n points to form an equation system;

将方程组改写成矩阵形式，采用广义逆矩阵的基本理论求得最小二乘解，即机器人各连杆几何参数误差值Δα₁,Δa₁,Δd₁,Δθ₁,Δβ₁,Δα₂,…,Δβ_N；Rewrite the equations into a matrix form, and use the basic theory of generalized inverse matrices to obtain the least squares solution, that is, the error values of the geometric parameters of the robot's connecting rods Δα ₁ , Δa ₁ , Δd ₁ , Δθ ₁ , Δβ ₁ , Δα ₂ ,… ,Δβ _N ;

根据求得的机器人各连杆几何参数误差值，求出相应的距离误差Δl(i,j)和位置误差dP。According to the error values of geometric parameters of each link of the robot obtained, the corresponding distance error Δl(i, j) and position error dP are obtained.

作为本发明的进一步改进，所述步骤S6中的实验验证具体为：As a further improvement of the present invention, the experimental verification in the step S6 is specifically:

根据步骤S5中计算出的Δq对机器人各连杆几何参数进行修正，运用修正的连杆几何参数进行实验验证，将步骤S4中n个点的坐标值再次输入到机器人控制器中，记录下对应的一组关节转角值及其对应的由激光跟踪仪测量得到的机器人末端的实际位姿坐标值，对实验后的结果分析计算，求得此次实验的距离误差Δl(i,j)和位置误差dP。According to the Δq calculated in step S5, correct the geometric parameters of the connecting rods of the robot, use the corrected geometric parameters of the connecting rods for experimental verification, input the coordinate values of n points in step S4 into the robot controller again, and record the corresponding A set of joint rotation angle values and the corresponding actual position and orientation coordinates of the robot end measured by the laser tracker are analyzed and calculated after the experiment, and the distance error Δl(i,j) and position of the experiment are obtained. Error dP.

本发明的有益效果是：本发明提供的基于距离误差模型的工业机器人标定方法具有简单、实用、高效、快捷的优点，适用于任何串联关节型机器人，通用性强，可以同时提高工业机器人定位精度和距离精度。The beneficial effects of the present invention are: the calibration method of industrial robots based on the distance error model provided by the present invention has the advantages of simplicity, practicality, high efficiency, and quickness, and is suitable for any serially articulated robots, has strong versatility, and can improve the positioning accuracy of industrial robots at the same time and distance accuracy.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明中记载的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments described in the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

图1为本发明基于距离误差模型的工业机器人标定方法的具体流程图；Fig. 1 is the specific flowchart of the industrial robot calibration method based on distance error model of the present invention;

图2为本发明一具体实施方式中六轴工业机器人的MDH运动学模型坐标系图；Fig. 2 is the coordinate system diagram of the MDH kinematics model of the six-axis industrial robot in a specific embodiment of the present invention;

图3为本发明一具体实施方式中机器人的距离误差描述图；Fig. 3 is a description diagram of the distance error of the robot in a specific embodiment of the present invention;

图4为本发明一具体实施方式中机器人的位置误差图。Fig. 4 is a position error diagram of the robot in a specific embodiment of the present invention.

具体实施方式Detailed ways

为了使本技术领域的人员更好地理解本发明中的技术方案，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都应当属于本发明保护的范围。In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described The embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

参图1所示，图1为本发明一具体实施方式中基于距离误差模型的工业机器人标定方法包括以下步骤：Referring to shown in Fig. 1, Fig. 1 is the industrial robot calibration method based on distance error model in a specific embodiment of the present invention and comprises the following steps:

DH模型是目前最基本运动学模型，它是按照一定的规则把构件坐标系嵌入机器人的每一个连杆机构中，从而建立机器人各连杆的空间坐标系。DH运动学模型包含4个几何参数：连杆长度a，连杆转角α，连杆偏距d和关节角θ。DH模型的不足之处是，当相邻两关节轴线平行时，平行度的微小偏差将导致实际公法线的位置与理论公法线的位置存在极大偏差。因此，在DH模型的基础上，修正的MDH运动学模型增加了绕Y轴旋转的β参数。The DH model is the most basic kinematics model at present. It embeds the component coordinate system into each link mechanism of the robot according to certain rules, so as to establish the space coordinate system of each link of the robot. The DH kinematics model contains four geometric parameters: the length of the connecting rod a, the rotation angle of the connecting rod α, the offset distance of the connecting rod d and the joint angle θ. The disadvantage of the DH model is that when the axes of two adjacent joints are parallel, a slight deviation in parallelism will lead to a large deviation between the position of the actual public normal and the position of the theoretical public normal. Therefore, on the basis of the DH model, the modified MDH kinematics model adds the β parameter of the rotation around the Y axis.

参图2所示，本实施方式采用MDH运动学模型，按照一定的规则把构件坐标系嵌入机器人的每一个连杆机构中，从而建立机器人各连杆的空间坐标系。MDH运动学模型包含5个几何参数：α,a,d,θ,β。把连杆i-1和连杆i固连坐标系的齐次变换矩阵定义为：As shown in Fig. 2, this embodiment adopts the MDH kinematics model, and embeds the component coordinate system into each link mechanism of the robot according to certain rules, so as to establish the space coordinate system of each link of the robot. The MDH kinematic model contains five geometric parameters: α, a, d, θ, β. The homogeneous transformation matrix of the fixed coordinate system of connecting rod i-1 and connecting rod i is defined as:

A_i=Trans(Z,d_i)Rot(Z,θ_i)Trans(X,a_i)Rot(X,α_i)Rot(Y,β_i)，A _i =Trans(Z,d _i )Rot(Z,θ _i )Trans(X,a _i )Rot(X,α _i )Rot(Y,β _i ),

由于制造和安装过程中机器人关节的实际几何参数与理论参数值之间存在偏差，故实际的相邻连杆变换矩阵为：Due to the deviation between the actual geometric parameters of the robot joints and the theoretical parameter values during the manufacturing and installation process, the actual adjacent link transformation matrix is:

${A A}_{i i}^{* *} = = {A A}_{i i} + + d d {A A}_{i i};;$

的误差主要是由各连杆的几何参数误差引起的，同时由于各个参数误差比较小，所以误差矩阵dA_i以微分形式表示为：

The error of is mainly caused by the geometric parameter error of each connecting rod, and because the error of each parameter is relatively small, the error matrix dA _i is expressed in differential form as:

${A A}_{i i} = = \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {α α}_{i i}} Δ Δ {α α}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {a a}_{i i}} Δ Δ {a a}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {d d}_{i i}} Δ Δ {d d}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {θ θ}_{i i}} Δ Δ {θ θ}_{i i} + + \frac{&PartialD; &PartialD; {A A}_{i i}}{&PartialD; &PartialD; {β β}_{i i}} Δ Δ {β β}_{i i}$

机器人末端连杆相对于基础坐标的实际变换矩阵为：The actual transformation matrix of the end link of the robot relative to the base coordinates is:

${= = {A A}_{11}}^{* *} {A A}_{22}^{* *} \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {A A}_{N N}^{* *};;$

是

的误差矩阵，其表达式为：

yes

The error matrix of , its expression is:

根据上面所述公式，可以推导出机器人末端位置误差向量 $dP = {(\begin{matrix} d_{x}^{N} & d_{y}^{N} & d_{z}^{N} \end{matrix})}^{T}$ 的矩阵表示公式。According to the above formula, the robot end position error vector can be deduced $dP = {(\begin{matrix} d_{x}^{N} & d_{the y}^{N} & d_{z}^{N} \end{matrix})}^{T}$ The matrix representation formula of .

参图3所示，对于机器人在三维空间中任意的点i和点j，虽然它们在机器人基坐标系B和测量坐标系L中的坐标值是不同的，但是这两点在机器人基坐标系B中的距离l_B(i,j)和在测量坐标系L中的距离l_L(i,j)是相同的。利用这一特点，建立了机器人距离误差标定模型。参图4所示，在此模型中机器人末端位置误差向量dP与距离误差Δl(i,j)的关系式为：As shown in Figure 3, for any point i and point j of the robot in three-dimensional space, although their coordinate values in the robot base coordinate system B and the measurement coordinate system L are different, these two points are in the robot base coordinate system The distance l _B (i,j) in B is the same as the distance l _L (i,j) in the measurement coordinate system L. Taking advantage of this feature, a robot distance error calibration model is established. As shown in Figure 4, the relationship between the robot end position error vector dP and the distance error Δl(i,j) in this model is:

$Δl Δl ((i i,, j j)) = = {l l}_{L L} ((i i,, j j)) - - {l l}_{B B} ((i i,, j j))$

$= = ((\frac{{x x}_{B B} ((j j)) - - {x x}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))},, \frac{{y the y}_{B B} ((j j)) - - {y the y}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))},, \frac{{z z}_{B B} ((j j)) - - {z z}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))})) ((d d {P P}_{j j} - - d d {P P}_{i i}));;$

机器人末端位置误差向量dP_i可以进一步表示为：The robot end position error vector dP _i can be further expressed as:

dP_i=B_iΔq，dP _i =B _i Δq,

其中，Δq=(Δα₁,Δa₁,Δd₁,Δθ₁,Δβ₁,Δα₂,…,Δβ_N)^T是机器人各连杆参数固有系统误差所构成的误差向量，是需要求解的未知量；B_i是3×5N(N为自由度数)系数矩阵，根据步骤S2中的公式确定具体数值。Among them, Δq=(Δα ₁ ,Δa ₁ ,Δd ₁ ,Δθ ₁ ,Δβ ₁ ,Δα ₂ ,…,Δβ _N ) ^T is the error vector formed by the inherent system error of each link parameter of the robot, and is the unknown quantity to be solved ; _Bi is a 3*5N (N is the number of degrees of freedom) coefficient matrix, and the specific value is determined according to the formula in step S2.

按照上述各公式，机器人距离误差标定模型的公式可以表示为：According to the above formulas, the formula of the robot distance error calibration model can be expressed as:

$Δl Δl ((i i,, j j)) = = ((\frac{{x x}_{B B} ((j j)) - - {x x}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))},, \frac{{y the y}_{B B} ((j j)) - - {y the y}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))},, \frac{{z z}_{B B} ((j j)) - - {z z}_{B B} ((i i))}{{l l}_{B B} ((i i,, j j))})) (({B B}_{j j} - - {B B}_{i i})) Δq Δq . .$

在机器人工作空间内，任意指定n个点，将这n个点的笛卡尔坐标值输入机器人的控制面板，当机器人末端运动到指定点时，记录下相应的关节转角值，同时用激光跟踪仪测量出对应的机器人末端的实际位姿坐标值。In the robot workspace, specify n points arbitrarily, and input the Cartesian coordinates of these n points into the control panel of the robot. Measure the actual pose coordinates of the corresponding robot end.

本步骤中方程个数要足以解出待修正的参数。The number of equations in this step should be enough to solve the parameters to be corrected.

根据步骤S5中计算出的Δq对机器人各连杆几何参数进行修正，运用修正的连杆几何参数进行实验验证，将步骤S4中n个点的坐标值再次输入到机器人控制器中，记录下对应的一组关节转角值及其对应的由激光跟踪仪测量得到的机器人末端的实际位姿坐标值，对实验后的结果分析计算，求得此次实验的距离误差Δl(i,j)和位置误差dP。与要求的精度标准进行比较，如未达到精度要求，则将此次实验的数据代入距离误差标定模型公式中，进行二次标定，直至达到精度要求。According to the Δq calculated in step S5, correct the geometric parameters of the connecting rods of the robot, use the corrected geometric parameters of the connecting rods for experimental verification, input the coordinate values of n points in step S4 into the robot controller again, and record the corresponding A set of joint rotation angle values and the corresponding actual position and orientation coordinates of the robot end measured by the laser tracker are analyzed and calculated after the experiment, and the distance error Δl(i,j) and position of the experiment are obtained. Error dP. Compare with the required accuracy standard, if the accuracy requirement is not met, then substitute the data of this experiment into the distance error calibration model formula, and perform secondary calibration until the accuracy requirement is met.

与现有技术相比，本发明具有以下有益效果：Compared with the prior art, the present invention has the following beneficial effects:

本发明中的验证步骤可进行多次，如定位精度未达到要求，将参数修正值代替理论参数值代入步骤S3中的机器人距离误差标定模型的公式，重复进行步骤S4～S6，使标定的定位精度和距离精度更高；The verification step in the present invention can be carried out multiple times, as the positioning accuracy does not meet the requirements, the parameter correction value is substituted into the formula of the robot distance error calibration model in step S3 instead of the theoretical parameter value, and steps S4～S6 are repeated to make the positioning of the calibration Higher accuracy and distance accuracy;

工业机器人定位精度及距离精度的标定方法采用修正的5参数MDH运动学模型，克服了DH运动学模型中当相邻两关节轴线平行时出现奇异现象的不足之处，使运动学模型更准确；The calibration method of positioning accuracy and distance accuracy of industrial robots adopts the revised 5-parameter MDH kinematics model, which overcomes the insufficiency of the singular phenomenon in the DH kinematics model when the axes of two adjacent joints are parallel, and makes the kinematics model more accurate;

该标定方法基于距离误差标定模型，避免了机器人坐标系与测量坐标系转换带来的误差，引入外界误差小。实验操作简单，直接向机器人控制器输入工作空间中的点坐标值控制机器人末端运动到指定点，不需要预先规划特定的轨迹。The calibration method is based on the distance error calibration model, which avoids the error caused by the conversion between the robot coordinate system and the measurement coordinate system, and introduces little external error. The experimental operation is simple, and the point coordinate value in the workspace is directly input to the robot controller to control the end of the robot to move to the specified point, without pre-planning a specific trajectory.

该标定方法的实验数据的处理过程简单，将实验数据代入公式中，得到多元一次方程组，运用Matlab等数学分析软件，可以快速得到实验结果。The processing process of the experimental data of this calibration method is simple, and the experimental data is substituted into the formula to obtain a multivariate linear equation system, and the experimental results can be quickly obtained by using Matlab and other mathematical analysis software.

综上所述，本发明提供的基于距离误差模型的工业机器人标定方法具有简单、实用、高效、快捷的优点，适用于任何串联关节型机器人，通用性强，可以同时提高工业机器人定位精度和距离精度。In summary, the calibration method for industrial robots based on the distance error model provided by the present invention has the advantages of simplicity, practicality, high efficiency, and quickness. precision.

对于本领域技术人员而言，显然本发明不限于上述示范性实施例的细节，而且在不背离本发明的精神或基本特征的情况下，能够以其他的具体形式实现本发明。因此，无论从哪一点来看，均应将实施例看作是示范性的，而且是非限制性的，本发明的范围由所附权利要求而不是上述说明限定，因此旨在将落在权利要求的等同要件的含义和范围内的所有变化囊括在本发明内。不应将权利要求中的任何附图标记视为限制所涉及的权利要求。It will be apparent to those skilled in the art that the invention is not limited to the details of the above-described exemplary embodiments, but that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Accordingly, the embodiments should be regarded in all points of view as exemplary and not restrictive, the scope of the invention being defined by the appended claims rather than the foregoing description, and it is therefore intended that the scope of the invention be defined by the appended claims rather than by the foregoing description. All changes within the meaning and range of equivalents of the elements are embraced in the present invention. Any reference sign in a claim should not be construed as limiting the claim concerned.

此外，应当理解，虽然本说明书按照实施方式加以描述，但并非每个实施方式仅包含一个独立的技术方案，说明书的这种叙述方式仅仅是为清楚起见，本领域技术人员应当将说明书作为一个整体，各实施例中的技术方案也可以经适当组合，形成本领域技术人员可以理解的其他实施方式。In addition, it should be understood that although this specification is described according to implementation modes, not each implementation mode only contains an independent technical solution, and this description in the specification is only for clarity, and those skilled in the art should take the specification as a whole , the technical solutions in the various embodiments can also be properly combined to form other implementations that can be understood by those skilled in the art.

Claims

1. the industrial robot scaling method based on the range error model is characterized in that, said method comprising the steps of:

S1, set up the MDH of robot kinematics model;

The error of S2, homogeneous transformation matrix;

S3, set up robot range error peg model;

The measurement of S4, robot end's attained pose;

The demarcation of S5, each connecting rod geometric parameter error of robot;

S6, experimental verification judge whether to satisfy required precision, if, then demarcate and finish, if not, return step S4, with the experimental result iteration, carry out calibration experiment again.

2. method according to claim 1 is characterized in that, among the described step S1 in the MDH kinematics model the be connected homogeneous transformation defined matrix of coordinate system of connecting rod i-1 and connecting rod i be:

A _i=Trans(Z,d _i)Rot(Z,θ _i)Trans(X,a _i)Rot(X,α _i)Rot(Y,β _i)，

Wherein, a is length of connecting rod, and α is the connecting rod corner, and d is the connecting rod offset distance, and θ is joint angle, and β is around the Y-axis anglec of rotation;

The base coordinate of robot is always being transformed between B and the tail end connecting rod coordinate system N:

T_{N}^{B} = A_{1} A_{2} A_{3} \cdot \cdot \cdot A_{N} .

3. method according to claim 2 is characterized in that, described step S2 specifically comprises:

Calculating actual adjacent connecting rod transformation matrix is:

{A_{i}}^{*} = A_{i} + d A_{i};

Error matrix dA _iBe expressed as with differential form:

d A_{i} = \frac{&PartialD; A_{i}}{&PartialD; α_{i}} Δ α_{i} + \frac{&PartialD; A_{i}}{&PartialD; a_{i}} Δ a_{i} + \frac{&PartialD; A_{i}}{&PartialD; d_{i}} Δ d_{i} + \frac{&PartialD; A_{i}}{&PartialD; θ_{i}} Δ θ_{i} + \frac{&PartialD; A_{i}}{&PartialD; β_{i}} Δ β_{i};

The real transform matrix that calculating robot's tail end connecting rod with respect to base coordinate is:

T_{N}^{B *} = T_{N}^{B} + d T_{N}^{B} = T_{N}^{B} + T_{N}^{B} δ T_{N}^{B}

= {A_{1}}^{*} {A_{2}}^{*} \cdot \cdot \cdot {A_{N}}^{*}

Calculate

Error matrix

δ T_{N}^{B} = (\begin{matrix} 0 & - δ_{z}^{N} & δ_{y}^{N} & d_{x}^{N} \\ δ_{z}^{N} & 0 & - δ_{x}^{N} & d_{y}^{N} \\ - δ_{y}^{N} & δ_{x}^{N} & 0 & d_{z}^{N} \\ 0 & 0 & 0 & 0 \end{matrix});

Calculating robot's terminal position error vector

{dP = (\begin{matrix} d_{x}^{N} & d_{y}^{N} & d_{z}^{N} \end{matrix})}^{T}

Matrix.

4. method according to claim 3 is characterized in that, the formula of robot range error peg model is among the described step S3:

Δl (i, j) = (\frac{x_{B} (j) - x_{B} (i)}{l_{B} (i, j)}, \frac{y_{B} (j) - y_{B} (i)}{l_{B} (i, j)}, \frac{z_{B} (j) - z_{B} (i)}{l_{B} (i, j)}) (B_{j} - B_{i}) Δq;

I and j are robot point arbitrarily in three dimensions, l _B(i, j), l _L(i, j) being respectively at 2 is B and the distance of measuring among the coordinate system L in the robot basis coordinates, (i j) is range error to Δ l.

5. method according to claim 4 is characterized in that, described step S4 is specially:

In the robot working space, specify n point arbitrarily, record the cartesian coordinate value of described n point, when the robot end moves to specified point, note corresponding joint rotation angle value, measure corresponding robot end's attained pose coordinate figure simultaneously with laser tracker.

6. method according to claim 5 is characterized in that, described step S5 is specially:

One group of joint rotation angle value of each the specified point correspondence among the step S4 and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure is updated to the formula of the robot range error peg model among the step S3;

Obtain n-1 equation by n point, form an equation group;

Equation group is rewritten into matrix form, adopts the basic theories of generalized inverse matrix to try to achieve least square solution, i.e. each connecting rod geometric parameter error amount Δ α of robot ₁, Δ a ₁, Δ d ₁, Δ θ ₁, Δ β ₁, Δ α ₂..., Δ β _N

According to each connecting rod geometric parameter error amount of the robot of trying to achieve, (i is j) with site error dP to obtain corresponding range error Δ l.

7. method according to claim 6 is characterized in that, the experimental verification among the described step S6 is specially:

Revise according to each the connecting rod geometric parameter of the robot of Δ q that calculates among the step S5, the connecting rod geometric parameter of use the revising checking that experimentizes, be input to the coordinate figure of n point among the step S4 in the robot controller again, note corresponding one group of joint rotation angle value and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure, interpretation of result after the experiment is calculated, (i is j) with site error dP to try to achieve the range error Δ l that this time tests.