CN113500585B - Robot measurement pose evaluation method and evaluation device for kinematics calibration - Google Patents
Robot measurement pose evaluation method and evaluation device for kinematics calibration Download PDFInfo
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Abstract
Description
技术领域technical field
本申请涉及机器人运动学标定技术领域,特别涉及一种用于运动学标定的机器人测量位姿评价方法及评价装置。The present application relates to the technical field of robot kinematics calibration, in particular to a robot measurement pose evaluation method and evaluation device for kinematics calibration.
背景技术Background technique
由于制造、装配等因素产生机器人的几何误差,会导致机器人的定位精度降低,进而导致机器人的工业应用受到限制,因此在出厂之前需要对机器人进行运动学标定。通常运动学标定方法是通过建立的几何误差模型,通过测量多组机器人末端执行器位姿,利用理论和实际的位姿偏差来进行辨识几何误差,进而修正机器人运动学模型来提高机器人末端定位位姿精度。Due to the geometric error of the robot due to factors such as manufacturing and assembly, the positioning accuracy of the robot will be reduced, which will limit the industrial application of the robot. Therefore, it is necessary to calibrate the kinematics of the robot before leaving the factory. Usually, the kinematic calibration method is to establish a geometric error model, measure the poses of multiple groups of robot end effectors, use the theoretical and actual pose deviations to identify geometric errors, and then correct the robot kinematics model to improve the end positioning of the robot. Attitude accuracy.
对于运动学标定而言,为了保证在整体任务空间内标定后的定位精度,同时兼顾测量位姿数目高导致的测量成本问题,需要对测量位姿进行优化。对测量位姿优化的前提是,对确定的一组测量位姿进行定量的指标评价。For kinematics calibration, in order to ensure the positioning accuracy after calibration in the overall task space, and at the same time take into account the measurement cost caused by the high number of measurement poses, it is necessary to optimize the measurement pose. The premise of optimizing the measurement pose is to perform quantitative index evaluation on a certain set of measurement poses.
目前针对评价方法的研究主要集中于误差辨识矩阵的分析,是针对几何误差可观测性进行的分析,包括参数方差最小化指标条件数倒数指标/>末端位姿不确定性最小化指标O3=σL、噪声方法指标/>以及A最优指标/> At present, the research on evaluation methods mainly focuses on the analysis of the error identification matrix, which is the analysis of the observability of geometric errors, including the parameter variance minimization index Condition number reciprocal index/> Terminal pose uncertainty minimization index O 3 =σ L , noise method index/> And the optimal index of A/>
在上述的现有技术中,目前的评价方法在统计学的各个方面对误差辨识方程进行全面的分析,但是其局限性在于只分析几何误差的观测性,而实际上几何误差的估计偏差对于末端执行器的位姿影响并不一致,因此几何误差的观测性和运动学标定后的残差并不严格一致。注意到运动学标定的目的是提高整体任务空间的定位精度,而几何误差的观测性是间接性反应这一点,因此一个直接反应运动学标定后整体任务空间定位精度的指标可以更直观体现测量位姿评价对运动学标定的影响。In the prior art mentioned above, the current evaluation method conducts a comprehensive analysis of the error identification equation in all aspects of statistics, but its limitation is that it only analyzes the observability of the geometric error. The pose effect of the actuator is not consistent, so the observation of the geometric error and the residual error after kinematic calibration are not strictly consistent. Note that the purpose of kinematics calibration is to improve the positioning accuracy of the overall task space, and the observability of geometric errors is an indirect reflection. Therefore, an index that directly reflects the positioning accuracy of the overall task space after kinematics calibration can more intuitively reflect the measurement position. The influence of posture evaluation on kinematic calibration.
发明内容Contents of the invention
本申请旨在至少在一定程度上解决相关技术中的技术问题之一。This application aims to solve one of the technical problems in the related art at least to a certain extent.
为此,本申请的一个目的在于提出一种用于运动学标定的机器人测量位姿评价方法,该方法解决了目前测量位姿评价方法侧重几何误差观测性而不能直接反应运动学标定效果的问题。For this reason, one purpose of this application is to propose a robot measurement pose evaluation method for kinematics calibration, which solves the problem that the current measurement pose evaluation method focuses on the observability of geometric errors and cannot directly reflect the effect of kinematics calibration .
本申请的另一个目的在于提出一种用于运动学标定的机器人测量位姿评价装置。Another object of the present application is to propose a robot measurement pose evaluation device for kinematics calibration.
为达到上述目的,本申请一方面实施例提出了一种用于运动学标定的机器人测量位姿评价方法,包括:In order to achieve the above purpose, an embodiment of the present application proposes a robot measurement pose evaluation method for kinematic calibration, including:
建立机器人的几何误差模型;Establish the geometric error model of the robot;
确定并离散化所述机器人的任务空间,确定所述机器人的测量噪声强度权值和位姿精度权值,对离散化的所述机器人的任务空间中的每一组位姿,根据所述位姿精度权值确定相应地误差传递矩阵集合并对其进行预处理;Determining and discretizing the task space of the robot, determining the measurement noise intensity weight and pose accuracy weight of the robot, and for each group of poses in the discretized task space of the robot, according to the position The attitude accuracy weight determines the corresponding error transfer matrix set and preprocesses it;
根据待评价位姿和所述几何误差模型确定误差辨识方程,根据所述测量噪声强度权值确定离散化后的所述机器人的任务空间中运动学标定后的位姿残差的均方根平方值期望均值,利用所述位姿残差的均方根平方值期望均值评价所述机器人的标定效果。Determine the error identification equation according to the pose to be evaluated and the geometric error model, and determine the root mean square square of the kinematically calibrated pose residual in the task space of the robot after discretization according to the measurement noise intensity weight value Value expected mean value, using the root mean square value expected mean value of the pose residual to evaluate the calibration effect of the robot.
为达到上述目的,本申请另一方面实施例提出了一种用于运动学标定的机器人测量位姿评价装置,包括:In order to achieve the above purpose, another embodiment of the present application proposes a robot measurement pose evaluation device for kinematic calibration, including:
建模模块,用于建立机器人的几何误差模型;A modeling module is used to establish a geometric error model of the robot;
计算模块,用于确定并离散化所述机器人的任务空间,确定所述机器人的测量噪声强度权值和位姿精度权值,对离散化的所述机器人的任务空间中的每一组位姿,根据所述位姿精度权值确定相应地误差传递矩阵集合并对其进行预处理;The calculation module is used to determine and discretize the task space of the robot, determine the measurement noise intensity weight and the pose accuracy weight of the robot, and calculate each group of poses in the discretized task space of the robot , determining a set of corresponding error transfer matrices according to the pose accuracy weights and preprocessing them;
评价模块,用于根据待评价位姿和所述几何误差模型确定误差辨识方程,根据所述测量噪声强度权值确定离散化后的所述机器人的任务空间中运动学标定后的位姿残差的均方根平方值期望均值,利用所述位姿残差的均方根平方值期望均值评价所述机器人的标定效果。An evaluation module, configured to determine an error identification equation according to the pose to be evaluated and the geometric error model, and determine a discretized kinematically calibrated pose residual in the task space of the robot according to the measured noise intensity weight The expected mean value of the root mean square value of , and the expected mean value of the root mean square value of the pose residual is used to evaluate the calibration effect of the robot.
本申请实施例的用于运动学标定的机器人测量位姿评价方法及评价装置,提出了考虑基于该组测量位姿进行运动学标定后的任务空间内的位姿残差的测量位姿评价方法,对于一组给定的测量位姿和机器人需要保证精度的任务空间,将预估的基于该组测量位姿进行运动学标定后的任务空间内的位姿残差均方根的平方值期望作为评价该组测量位姿的标准,并考虑测量分量的不同噪声强度和位姿精度不同权重给出相应的加权评价指标。提出的指标有别于以往表征运动学参数误差观测性的评价指标,而是用于表征机器人任务空间内运动学标定后残差的幅值,用于机器人的运动学标定领域,目的在于基于该方法最优化选取的测量位姿能提高机器人的精度或者降低运动学标定所需的测量位姿数目。由此,解决了目前测量位姿评价方法侧重几何误差观测性而不能直接反应运动学标定效果的问题,从而更准确、直观地将测量位姿评价和运动学标定联系起来,反应机器人任务空间内运动学标定后残差的幅值。The robot measurement pose evaluation method and evaluation device for kinematics calibration of the embodiment of the present application proposes a measurement pose evaluation method that considers the pose residual in the task space after kinematic calibration based on the group of measurement poses , for a given set of measured poses and a task space where the robot needs to ensure accuracy, the estimated square value of the root mean square of the pose residual error in the task space after kinematic calibration based on the set of measured poses is expected As a standard for evaluating the group of measured poses, and considering different noise intensities of the measured components and different weights of pose accuracy, the corresponding weighted evaluation indicators are given. The proposed index is different from the previous evaluation index that characterizes the observability of kinematic parameter errors, but is used to characterize the amplitude of the residual error after kinematic calibration in the robot task space, and is used in the field of robot kinematic calibration. The method optimizes the selected measurement poses to improve the accuracy of the robot or reduce the number of measurement poses required for kinematics calibration. As a result, the problem that the current measurement pose evaluation method focuses on the observability of geometric errors and cannot directly reflect the effect of kinematics calibration is solved, so that the measurement pose evaluation and kinematics calibration can be linked more accurately and intuitively, reflecting the robot's task space. The magnitude of the residual after kinematic calibration.
本申请附加的方面和优点将在下面的描述中部分给出,部分将从下面的描述中变得明显,或通过本申请的实践了解到。Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the application.
附图说明Description of drawings
本申请上述的和/或附加的方面和优点从下面结合附图对实施例的描述中将变得明显和容易理解,其中:The above and/or additional aspects and advantages of the present application will become apparent and easy to understand from the following description of the embodiments in conjunction with the accompanying drawings, wherein:
图1为根据本申请一个实施例的用于运动学标定的机器人测量位姿评价方法流程图;Fig. 1 is a flow chart of a robot measurement pose evaluation method for kinematics calibration according to an embodiment of the present application;
图2为根据本申请一个实施例的典型的混联机器人构型;Fig. 2 is a typical hybrid robot configuration according to an embodiment of the present application;
图3为一种典型的任务空间离散化示意图;Figure 3 is a schematic diagram of a typical task space discretization;
图4为根据本申请一个实施例的用于运动学标定的机器人测量位姿评价装置结构示意图。Fig. 4 is a schematic structural diagram of a robot measurement pose evaluation device for kinematics calibration according to an embodiment of the present application.
附图标记:1-第一分支;2-第二分支;3-第三分支;4-下定平台;5-C型构件;6-A型构件;7-动平台;8-上定平台。Reference signs: 1-first branch; 2-second branch; 3-third branch; 4-lower fixed platform; 5-C-shaped member; 6-A-shaped member; 7-moving platform; 8-upper fixed platform.
具体实施方式Detailed ways
下面详细描述本申请的实施例,所述实施例的示例在附图中示出,其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的,旨在用于解释本申请,而不能理解为对本申请的限制。Embodiments of the present application are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary, and are intended to explain the present application, and should not be construed as limiting the present application.
下面参照附图描述根据本申请实施例提出的用于运动学标定的机器人测量位姿评价方法及评价装置。The robot measurement pose evaluation method and evaluation device for kinematics calibration proposed according to the embodiments of the present application will be described below with reference to the accompanying drawings.
首先将参照附图描述根据本申请实施例提出的用于运动学标定的机器人测量位姿评价方法。Firstly, a robot measurement pose evaluation method for kinematics calibration proposed according to an embodiment of the present application will be described with reference to the accompanying drawings.
图1为根据本申请一个实施例的用于运动学标定的机器人测量位姿评价方法流程图。Fig. 1 is a flow chart of a robot measurement pose evaluation method for kinematics calibration according to an embodiment of the present application.
如图1所示,该用于运动学标定的机器人测量位姿评价方法包括以下步骤:As shown in Figure 1, the robot measurement pose evaluation method for kinematics calibration includes the following steps:
步骤S1,建立机器人的几何误差模型。Step S1, establishing a geometric error model of the robot.
可选地,在本申请的一个实施例中,建立机器人的几何误差模型为:Optionally, in one embodiment of the present application, the geometric error model of the robot is established as:
其中,δbE为机器人终端执行器的位置,ωE为机器人终端执行器的姿态误差,代表共有n项互不相关的几何误差,M是相应的误差传递矩阵,表示∈中的几何误差对机器人终端执行器的位置姿态误差的影响,为机器人驱动轴位移向量q的函数。Among them, δb E is the position of the robot end effector, ω E is the attitude error of the robot end effector, Represents a total of n uncorrelated geometric errors, and M is the corresponding error transfer matrix, which represents the influence of the geometric error in ∈ on the position and attitude error of the robot end effector, which is a function of the displacement vector q of the robot drive shaft.
步骤S2,确定并离散化机器人的任务空间,确定机器人的测量噪声强度权值和位姿精度权值,对离散化的机器人的任务空间中的每一组位姿,根据位姿精度权值确定相应地误差传递矩阵集合并对其进行预处理。Step S2, determine and discretize the robot's task space, determine the robot's measurement noise intensity weight and pose accuracy weight, for each group of poses in the discretized robot task space, determine according to the pose accuracy weight Correspondingly the set of error transfer matrices is preprocessed.
确定机器人的基础信息及进行预处理,首先,确定并离散化机器人的任务空间,机器人的任务空间指机器人实现任务需求的末端位姿构成的空间,通常需要保证定位精度。该任务空间是机器人末端位姿连续分布的空间,由于空间内具有无限元素,需要将其离散化来进行分析,离散化是指将空间内有限的元素作为整体空间的表征,可以通过对任务空间均匀采样实现。离散化后的任务空间可以表示为机器人驱动轴位移向量的集合Π={s1,s2,...,sm},也可以表示为其余能唯一表征该离散化任务空间的数学表达。Determine the basic information of the robot and perform preprocessing. First, determine and discretize the task space of the robot. The task space of the robot refers to the space formed by the end pose of the robot to achieve the task requirements, and usually needs to ensure the positioning accuracy. The task space is a space in which the robot's terminal pose is continuously distributed. Since there are infinite elements in the space, it needs to be discretized for analysis. Discretization refers to the representation of the overall space by using the limited elements in the space. Uniform sampling is achieved. The discretized task space can be expressed as a set Π={s 1 , s 2 , .
其次,确定机器人的测量噪声强度权值,对机器人的测量位姿处的末端位姿误差进行测量,测量精度会受到测量噪声的影响,测量噪声假定满足均值为0的独立正态分布,但由于不同分量强度的不同其正态分布的方差不一致,/>的方差矩阵归一化为对称正定矩阵W-1,归一化方法可以采用将其特定元素缩放为1或者其他方式,可以用于表征机器人的测量噪声强度权值,并通过测量仪器和测量方案先验确定。Secondly, determine the measurement noise intensity weight of the robot, and measure the end pose error at the measurement pose of the robot. The measurement accuracy will be affected by the measurement noise, and the measurement noise It is assumed that an independent normal distribution with a mean of 0 is satisfied, but the variance of the normal distribution is inconsistent due to the different component strengths, /> The variance matrix of is normalized to a symmetric positive definite matrix W -1 , and the normalization method can be used to scale its specific elements to 1 or other methods, which can be used to characterize the measurement noise intensity weight of the robot, and through the measurement instrument and measurement scheme determined a priori.
再次,确定机器人的位姿精度权值:机器人的位置和姿态的表达单位不相同,实际机器人对位置和姿态精度的要求也不同,其位姿精度权值可以表达为对角矩阵C,特别地,在位置和姿态精度要求的比值是r(rad-1)时,C可以确定为C=diag(1,1,1,r,r,r)。Thirdly, determine the weight of the robot’s pose accuracy: the robot’s position and attitude are expressed in different units, and the actual robot’s requirements for position and attitude accuracy are also different. The pose accuracy weight can be expressed as a diagonal matrix C, especially , when the required ratio of position and attitude accuracy is r(rad −1 ), C can be determined as C=diag(1, 1, 1, r, r, r).
最后进行数据预处理:对离散化任务空间Π中的每一组位姿,确定相应地误差传递矩阵集合记为ΠA={A1,A2,...,Am},其中Ai=M(si),预处理矩阵对于特定结构参数、任务空间和几何误差模型的机器人只需要计算一次。Finally, data preprocessing: For each group of poses in the discretized task space Π, determine the corresponding set of error transfer matrices and write it as Π A ={A 1 , A 2 ,...,A m }, where A i =M(s i ), preconditioning matrix The robot needs to be calculated only once for a specific structural parameter, task space and geometric error model.
步骤S3,根据待评价位姿和几何误差模型确定误差辨识方程,根据测量噪声强度权值确定离散化后的机器人的任务空间中运动学标定后的位姿残差的均方根平方值期望均值,利用位姿残差的均方根平方值期望均值评价机器人的标定效果。Step S3, determine the error identification equation according to the pose to be evaluated and the geometric error model, and determine the expected mean value of the root mean square value of the kinematically calibrated pose residual in the discretized task space of the robot according to the weight of the measurement noise intensity , using the expected mean value of the root mean square value of the pose residual to evaluate the calibration effect of the robot.
可选地,在本申请的一个实施例中,S3进一步包括:Optionally, in one embodiment of the present application, S3 further includes:
根据待评价位姿和几何误差模型确定误差辨识方程为:According to the pose to be evaluated and the geometric error model, the error identification equation is determined as:
δ=Ma∈δ=M a ∈
其中,Mi为误差传递矩阵,δ为相应的位姿误差测值;in, M i is the error transfer matrix, and δ is the corresponding pose error measurement;
基于机器人的测量噪声强度权值,根据加权最小二乘法确定几何误差的估计值其中,W为测量噪声方差矩阵的逆矩阵;Based on the robot's measurement noise intensity weights, an estimate of the geometric error is determined according to a weighted least squares method Among them, W is the inverse matrix of the measurement noise variance matrix;
确定几何误差的估计值和实际值,在离散化后的机器人的任务空间中的运动学标定后归一化位姿残差其中,/>为几何误差估计值,∈*为几何误差实际值,C为位姿精度权值对应的矩阵,Ai为位姿si对应的误差传递矩阵;Determine the estimated and actual values of the geometric error, and normalize the pose residual after kinematic calibration in the task space of the discretized robot where, /> is the estimated value of the geometric error, ∈ * is the actual value of the geometric error, C is the matrix corresponding to the pose accuracy weight, A i is the error transfer matrix corresponding to the pose s i ;
根据估计值和位姿残差确定离散化后的机器人的任务空间中运动学标定后的位姿残差的均方根其中,m为离散化任务空间中的总位姿数;Determine the root mean square of the kinematically calibrated pose residual in the task space of the discretized robot based on the estimated value and the pose residual where m is the total number of poses in the discretized task space;
根据统计学知识确定均方根平方值期望均值其中,A为预处理矩阵。Determining the expected mean value of root mean square value based on statistical knowledge Among them, A is the preprocessing matrix.
具体地,对于任一测量位姿进行评价,首先,基于待评价的测量位姿组合Ω和几何误差模型,可以确定误差辨识方程为δ=Ma∈,其中为由误差传递矩阵Mi=M(qi)堆叠确定,δ是相应的位姿误差测量值。Specifically, to evaluate any measurement pose, first, based on the measurement pose combination Ω to be evaluated and the geometric error model, the error identification equation can be determined as δ=M a ∈, where As determined by stacking of the error transfer matrix M i =M(q i ), δ is the corresponding pose error measurement.
基于机器人的测量噪声强度权值,可以根据加权最小二乘法确定∈的估计值 被广泛应用的最小二乘法∈=MaTMa-1MaTδ可以认为是取噪声强度各分量上均等的一个特例。Based on the robot's measurement noise intensity weights, an estimate of ∈ can be determined according to weighted least squares The widely used least squares method ∈=MaTMa-1MaTδ can be considered as a special case of equalizing the components of the noise intensity.
对于∈的估计值和实际值∈*,在任务空间si处的运动学标定后归一化位姿残差可以表示为/>其中机器人的位姿精度权值矩阵C将位姿误差转化为相同单位而实现归一化,直接考虑/>作为归一化误差则是权值矩阵C作为单位矩阵的一个特例。Estimated value for ∈ and the actual value ∈ * , the normalized pose residual after kinematic calibration at the task space si can be expressed as /> Among them, the pose accuracy weight matrix C of the robot converts the pose error into the same unit to achieve normalization, and directly considers As a normalized error, it is a special case of the weight matrix C as an identity matrix.
基于上述估计值,在离散化任务空间Π中运动学标定后的位姿残差的均方根表示为通过统计学知识的分析可以确定其平方值期望均值将η作为本方法提出的位姿评价数值,其数值越大,说明运动学标定后的位姿残差越大,运动学标定效果越差。Based on the above estimates, the root mean square of the kinematically calibrated pose residual in the discretized task space Π is expressed as Through the analysis of statistical knowledge, the expected mean value of its square value can be determined Taking η as the pose evaluation value proposed by this method, the larger the value is, the larger the pose residual after kinematic calibration is, and the worse the kinematic calibration effect is.
需要说明的是,对于位姿评价指标中,由于矩阵的性质,η也可以表达为/>等其余等价形式。It should be noted that for the pose evaluation index In , due to the nature of the matrix, η can also be expressed as /> and other equivalent forms.
图2所示为一种典型的混联机器人构型,该五自由度混联机器人包括一个三自由度并联机构和一个与并联机构串接的两自由度串联机构。三自由度并联机构包括上定平台8、下定平台4、并联动平台7和三个分支组件1、2、3。三个分支组件中结构相同的第一分支组件1和第二分支组件2处于同一平面并穿过上定平台8,与上定平台8通过转动铰链连接。第三分支组件3穿过下定平台4并与下定平台4用转动铰链连接。第一分支组件1、第二分支组件2的前端与并联动平台7通过转动铰链连接,第三分支组件3的前端与并联动平台7固连。两自由度姿态串联机构包括C型构件5和A型构件6。C型构件5与并联动平台7用转动铰链连接。A型构件6的第一端设有与刀柄连接的配合孔,该孔所在平面作为机器人的终端动平台,第二端与C型构件通过转动铰链连接。C型构件5、A型构件6和三个分支组件1、2、3作为机器人的五个驱动轴。将所提出的一种用于运动学标定的机器人测量位姿评价方法的流程图应用于该混联机器人,具体方法步骤如下:Figure 2 shows a typical configuration of a hybrid robot. The five-degree-of-freedom hybrid robot includes a three-degree-of-freedom parallel mechanism and a two-degree-of-freedom serial mechanism connected in series with the parallel mechanism. The three-degree-of-freedom parallel mechanism includes an upper fixed platform 8 , a lower fixed platform 4 , a parallel linkage platform 7 and three branch components 1 , 2 , 3 . Among the three branch assemblies, the first branch assembly 1 and the second branch assembly 2 with the same structure are on the same plane and pass through the upper fixed platform 8, and are connected with the upper fixed platform 8 by a rotary hinge. The third branch assembly 3 passes through the fixed platform 4 and is connected with the fixed platform 4 with a rotary hinge. The front ends of the first branch assembly 1 and the second branch assembly 2 are connected to the parallel linkage platform 7 through rotating hinges, and the front ends of the third branch assembly 3 are fixedly connected to the parallel linkage platform 7 . The two-degree-of-freedom attitude series mechanism includes a C-shaped member 5 and an A-shaped member 6 . The C-shaped member 5 is connected with the parallel linkage platform 7 with a rotary hinge. The first end of the A-shaped component 6 is provided with a matching hole connected to the knife handle, and the plane where the hole is located is used as the terminal moving platform of the robot, and the second end is connected with the C-shaped component through a rotary hinge. The C-shaped member 5, the A-shaped member 6 and the three branch assemblies 1, 2, 3 are used as five drive shafts of the robot. The proposed flow chart of a robot measurement pose evaluation method for kinematics calibration is applied to the hybrid robot, and the specific method steps are as follows:
1)针对机器人的构型进行分析,可以建立机器人的几何误差模型:1) By analyzing the configuration of the robot, the geometric error model of the robot can be established:
其中δbE、ωE分别代表机器人终端执行器的位置和姿态误差,代表共有38项互不相关的几何误差,可以表示为:where δb E and ω E represent the position and attitude errors of the robot end effector respectively, Represents a total of 38 uncorrelated geometric errors, which can be expressed as:
M是相应的误差传递矩阵,表示∈中的几何误差对机器人终端执行器的位置姿态误差的影响,是机器人驱动轴位移向量q=[l1,l2,l3,θC,θA]T的函数,其中l1、l2和l3分别是三个分支的长度,θC和θA是C型和A型构件相对于初始位姿的旋转角度。M is the corresponding error transfer matrix, which represents the influence of the geometric error in ∈ on the position and attitude error of the robot end effector, and is the robot drive axis displacement vector q=[l 1 , l 2 , l 3 , θ C , θ A ] A function of T , where l 1 , l 2 and l 3 are the lengths of the three branches, respectively, and θ C and θ A are the rotation angles of the C-type and A-type members relative to the initial pose.
2)确定机器人的基础信息及预处理,主要包括:2) Determine the basic information and preprocessing of the robot, mainly including:
2-1)确定并离散化机器人的任务空间:以图3所示的2维空间为例,其中矩形范围表示机器人的任务空间,那么图3的均匀分布在矩形范围内的菱形点的集合可以作为机器人的离散化任务空间,其中省略号表示之间的菱形点。对于具体实施的五自由度混联机器人,采用图3中5维空间下的离散方式即可,离散化后的任务空间可以表示为机器人驱动轴位移向量的集合Π={s1,s2,...,sm}。2-1) Determine and discretize the task space of the robot: Take the 2-dimensional space shown in Figure 3 as an example, where the rectangular range represents the task space of the robot, then the set of diamond-shaped points uniformly distributed in the rectangular range in Figure 3 can be as a discretized task space for the robot, where ellipses represent diamond-shaped points in between. For the specific implementation of the five-degree-of-freedom hybrid robot, the discretization method in the 5-dimensional space shown in Figure 3 can be used. The discretized task space can be expressed as a set of robot drive axis displacement vectors Π={s 1 , s 2 , ..., sm }.
2-2)确定机器人的测量噪声强度权值:通过五自由度混联机器人运动学标定中的测量仪器和测量方案可以先验确定位姿测量噪声的方差矩阵为对称正定矩阵P,将作为归一化方差矩阵,其中P(1,1)是矩阵P的第1行第1列的数值。2-2) Determine the weight of the robot's measurement noise intensity: the pose measurement noise can be determined a priori through the measuring instruments and measurement schemes in the kinematic calibration of the five-degree-of-freedom hybrid robot The variance matrix of is a symmetric positive definite matrix P, and the As a normalized variance matrix, where P(1, 1) is the value in row 1, column 1 of matrix P.
2-3)确定机器人的位姿精度权值:五自由度混联机器人对位置和姿态精度的要求不同,其位姿精度权值可以表达为对角矩阵C,特别地,在位置和姿态精度要求的比值是r(rad-1)时,C可以确定为C=diag(1,1,1,r,r,r),r可以根据机器人需求调整。2-3) Determining the pose accuracy weight of the robot: the five-DOF hybrid robot has different requirements for position and attitude accuracy, and its pose accuracy weight can be expressed as a diagonal matrix C. In particular, the position and attitude accuracy When the required ratio is r(rad −1 ), C can be determined as C=diag(1, 1, 1, r, r, r), and r can be adjusted according to the requirements of the robot.
2-4)数据预处理:对Π中的每一组位姿,确定相应地误差传递矩阵集合记为ΠA={A1,A2,...,Am},其中Ai=M(si),预处理矩阵 2-4) Data preprocessing: For each group of poses in Π, determine the corresponding set of error transfer matrices as Π A ={A 1 , A 2 ,...,A m }, where A i =M (s i ), the preconditioning matrix
3)对于任何一组待评价的测量位姿,表示为机器人驱动轴位移向量的集合Ω={q1,q2,...,qn}。3) For any set of measured poses to be evaluated, it is expressed as a set of displacement vectors of the robot's drive shaft Ω={q 1 , q 2 , . . . , q n }.
4)确定该组测量位姿的评价数值:基于待评价的测量位姿组合Ω和几何误差模型,可以确定误差辨识方程为:δ=Ma∈,其中为由误差传递矩阵Mi=M(qi)堆叠确定,δ是相应的位姿误差测量值,通过统计学知识的分析可以确定离散化任务空间中运动学标定后的位姿残差的均方根平方值期望均值/>η即为根据本方法计算的该组位姿的评价数值。4) Determine the evaluation value of this group of measurement poses: based on the measurement pose combination Ω to be evaluated and the geometric error model, the error identification equation can be determined as: δ=M a ∈, where is determined by stacking the error transfer matrix M i =M(q i ), and δ is the corresponding measurement value of the pose error. Through the analysis of statistical knowledge, it can be determined that the mean square root square expected mean /> η is the evaluation value of this group of poses calculated according to this method.
根据本申请实施例提出的用于运动学标定的机器人测量位姿评价方法,提出了考虑基于该组测量位姿进行运动学标定后的任务空间内的位姿残差的测量位姿评价方法,对于一组给定的测量位姿和机器人需要保证精度的任务空间,将预估的基于该组测量位姿进行运动学标定后的任务空间内的位姿残差均方根的平方值期望作为评价该组测量位姿的标准,并考虑测量分量的不同噪声强度和位姿精度不同权重给出相应的加权评价指标。提出的指标有别于以往表征运动学参数误差观测性的评价指标,而是用于表征机器人任务空间内运动学标定后残差的幅值,用于机器人的运动学标定领域,目的在于基于该方法最优化选取的测量位姿能提高机器人的精度或者降低运动学标定所需的测量位姿数目。由此,解决了目前测量位姿评价方法侧重几何误差观测性而不能直接反应运动学标定效果的问题,从而更准确、直观地将测量位姿评价和运动学标定联系起来,反应机器人任务空间内运动学标定后残差的幅值。According to the robot measurement pose evaluation method for kinematic calibration proposed in the embodiment of the present application, a measurement pose evaluation method considering the pose residual in the task space after kinematic calibration based on the group of measurement poses is proposed, For a given set of measurement poses and a task space where the robot needs to ensure accuracy, the estimated square value of the root mean square of the pose residual error in the task space after kinematic calibration based on the set of measurement poses is taken as Evaluate the standard of this group of measurement poses, and give corresponding weighted evaluation indexes considering different noise strengths of measurement components and different weights of pose accuracy. The proposed index is different from the previous evaluation index that characterizes the observability of kinematic parameter errors, but is used to characterize the amplitude of the residual error after kinematic calibration in the robot task space, and is used in the field of robot kinematic calibration. The method optimizes the selected measurement poses to improve the accuracy of the robot or reduce the number of measurement poses required for kinematics calibration. As a result, the problem that the current measurement pose evaluation method focuses on the observability of geometric errors and cannot directly reflect the effect of kinematics calibration is solved, so that the measurement pose evaluation and kinematics calibration can be linked more accurately and intuitively, reflecting the robot's task space. The magnitude of the residual after kinematic calibration.
其次参照附图描述根据本申请实施例提出的用于运动学标定的机器人测量位姿评价装置。Next, a robot measurement pose evaluation device for kinematics calibration proposed according to an embodiment of the present application will be described with reference to the accompanying drawings.
图4为根据本申请一个实施例的用于运动学标定的机器人测量位姿评价装置结构示意图。Fig. 4 is a schematic structural diagram of a robot measurement pose evaluation device for kinematics calibration according to an embodiment of the present application.
如图4所示,该用于运动学标定的机器人测量位姿评价装置包括:建模平模块100、计算模块200和评价模块300。As shown in FIG. 4 , the robot measurement pose evaluation device for kinematic calibration includes: a modeling module 100 , a calculation module 200 and an evaluation module 300 .
建模模块100,用于建立机器人的几何误差模型。The modeling module 100 is used to establish a geometric error model of the robot.
计算模块200,用于确定并离散化机器人的任务空间,确定机器人的测量噪声强度权值和位姿精度权值,对离散化的机器人的任务空间中的每一组位姿,根据位姿精度权值确定相应地误差传递矩阵集合并对其进行预处理。The calculation module 200 is used to determine and discretize the task space of the robot, determine the measurement noise intensity weight and the pose accuracy weight of the robot, and for each group of poses in the discretized robot task space, according to the pose accuracy The weights determine the set of corresponding error transfer matrices and preprocess them.
评价模块300,用于根据待评价位姿和几何误差模型确定误差辨识方程,根据测量噪声强度权值确定离散化后的机器人的任务空间中运动学标定后的位姿残差的均方根平方值期望均值,利用位姿残差的均方根平方值期望均值评价机器人的标定效果。The evaluation module 300 is used to determine the error identification equation according to the pose to be evaluated and the geometric error model, and determine the root mean square square of the kinematically calibrated pose residual in the task space of the discretized robot according to the measurement noise intensity weight The expected mean value of the value is used, and the expected mean value of the root mean square value of the pose residual is used to evaluate the calibration effect of the robot.
可选地,在本申请的一个实施例中,几何误差模型为:Optionally, in one embodiment of the present application, the geometric error model is:
其中,δbE为机器人终端执行器的位置,ωE为机器人终端执行器的姿态误差,代表共有n项互不相关的几何误差,M是相应的误差传递矩阵,表示∈中的几何误差对机器人终端执行器的位置姿态误差的影响,为机器人驱动轴位移向量q的函数。Among them, δb E is the position of the robot end effector, ω E is the attitude error of the robot end effector, Represents a total of n uncorrelated geometric errors, and M is the corresponding error transfer matrix, which represents the influence of the geometric error in ∈ on the position and attitude error of the robot end effector, which is a function of the displacement vector q of the robot drive shaft.
可选地,在本申请的一个实施例中,对离散化的机器人的任务空间中的每一组位姿,确定相应地误差传递矩阵集合并对其进行预处理包括:Optionally, in one embodiment of the present application, for each group of poses in the task space of the discretized robot, determining a corresponding set of error transfer matrices and preprocessing it includes:
对离散化的机器人的任务空间中的每一组位姿,确定相应地误差传递矩阵集合为:ΠA={A1,A2,...,Am},其中,其中Ai=M(si),预处理矩阵C为位姿精度权值对应的矩阵,si为离散化任务空间中的第i个驱动轴位移向量,m为离散化任务空间中的总位姿数。For each group of poses in the discretized task space of the robot, determine the corresponding error transfer matrix set as: Π A ={A 1 , A 2 ,...,A m }, where A i =M (s i ), the preconditioning matrix C is the matrix corresponding to the pose accuracy weights, s i is the displacement vector of the ith drive axis in the discretized task space, and m is the total number of poses in the discretized task space.
可选地,在本申请的一个实施例中,评价模块300具体用于,根据待评价位姿和几何误差模型确定误差辨识方程为:Optionally, in one embodiment of the present application, the evaluation module 300 is specifically configured to determine the error identification equation according to the pose to be evaluated and the geometric error model as:
δ=Ma∈δ=M a ∈
其中,Mi为误差传递矩阵,δ为相应的位姿误差测值;in, M i is the error transfer matrix, and δ is the corresponding pose error measurement;
基于机器人的测量噪声强度权值,根据加权最小二乘法确定几何误差的估计值其中,W为测量噪声方差矩阵的逆矩阵;Based on the robot's measurement noise intensity weights, an estimate of the geometric error is determined according to a weighted least squares method Among them, W is the inverse matrix of the measurement noise variance matrix;
确定几何误差的估计值和实际值,在离散化后的机器人的任务空间中的运动学标定后归一化位姿残差其中,/>为几何误差估计值,∈*为几何误差实际值,C为位姿精度权值对应的矩阵,Ai为位姿si对应的误差传递矩阵;Determine the estimated and actual values of the geometric error, and normalize the pose residual after kinematic calibration in the task space of the discretized robot where, /> is the estimated value of the geometric error, ∈ * is the actual value of the geometric error, C is the matrix corresponding to the pose accuracy weight, A i is the error transfer matrix corresponding to the pose s i ;
根据估计值和位姿残差确定离散化后的机器人的任务空间中运动学标定后的位姿残差的均方根其中,m为离散化任务空间中的总位姿数;Determine the root mean square of the kinematically calibrated pose residual in the task space of the discretized robot based on the estimated value and the pose residual where m is the total number of poses in the discretized task space;
根据统计学知识确定均方根平方值期望均值其中,A为预处理矩阵。Determining the expected mean value of root mean square value based on statistical knowledge Among them, A is the preprocessing matrix.
可选地,在本申请的一个实施例中,利用位姿残差的均方根平方值期望均值评价机器人的标定效果,包括:Optionally, in one embodiment of the present application, the expected mean value of the root mean square value of the pose residual is used to evaluate the calibration effect of the robot, including:
位姿残差的均方根平方值期望均值越大,则机器人的标定效果越差。The larger the expected mean value of the root mean square value of the pose residual, the worse the calibration effect of the robot.
需要说明的是,前述对方法实施例的解释说明也适用于该实施例的装置,此处不再赘述。It should be noted that the foregoing explanations of the method embodiment are also applicable to the device of this embodiment, and details are not repeated here.
根据本申请实施例提出的用于运动学标定的机器人测量位姿评价装置,提出了考虑基于该组测量位姿进行运动学标定后的任务空间内的位姿残差的测量位姿评价方法,对于一组给定的测量位姿和机器人需要保证精度的任务空间,将预估的基于该组测量位姿进行运动学标定后的任务空间内的位姿残差均方根的平方值期望作为评价该组测量位姿的标准,并考虑测量分量的不同噪声强度和位姿精度不同权重给出相应的加权评价指标。提出的指标有别于以往表征运动学参数误差观测性的评价指标,而是用于表征机器人任务空间内运动学标定后残差的幅值,用于机器人的运动学标定领域,目的在于基于该方法最优化选取的测量位姿能提高机器人的精度或者降低运动学标定所需的测量位姿数目。由此,解决了目前测量位姿评价方法侧重几何误差观测性而不能直接反应运动学标定效果的问题,从而更准确、直观地将测量位姿评价和运动学标定联系起来,反应机器人任务空间内运动学标定后残差的幅值。According to the robot measurement pose evaluation device for kinematic calibration proposed in the embodiment of the present application, a measurement pose evaluation method considering the pose residual in the task space after kinematic calibration based on the group of measurement poses is proposed, For a given set of measurement poses and a task space where the robot needs to ensure accuracy, the estimated square value of the root mean square of the pose residual error in the task space after kinematic calibration based on the set of measurement poses is taken as Evaluate the standard of this group of measurement poses, and give corresponding weighted evaluation indexes considering different noise strengths of measurement components and different weights of pose accuracy. The proposed index is different from the previous evaluation index that characterizes the observability of kinematic parameter errors, but is used to characterize the amplitude of the residual error after kinematic calibration in the robot task space, and is used in the field of robot kinematic calibration. The method optimizes the selected measurement poses to improve the accuracy of the robot or reduce the number of measurement poses required for kinematics calibration. As a result, the problem that the current measurement pose evaluation method focuses on the observability of geometric errors and cannot directly reflect the effect of kinematics calibration is solved, so that the measurement pose evaluation and kinematics calibration can be linked more accurately and intuitively, reflecting the robot's task space. The magnitude of the residual after kinematic calibration.
此外,术语“第一”、“第二”仅用于描述目的,而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此,限定有“第一”、“第二”的特征可以明示或者隐含地包括至少一个该特征。在本申请的描述中,“多个”的含义是至少两个,例如两个,三个等,除非另有明确具体的限定。In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be interpreted as indicating or implying relative importance or implicitly specifying the quantity of indicated technical features. Thus, the features defined as "first" and "second" may explicitly or implicitly include at least one of these features. In the description of the present application, "plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.
在本说明书的描述中,参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本申请的至少一个实施例或示例中。在本说明书中,对上述术语的示意性表述不必须针对的是相同的实施例或示例。而且,描述的具体特征、结构、材料或者特点可以在任一个或多个实施例或示例中以合适的方式结合。此外,在不相互矛盾的情况下,本领域的技术人员可以将本说明书中描述的不同实施例或示例以及不同实施例或示例的特征进行结合和组合。In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the described specific features, structures, materials or characteristics may be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples and features of different embodiments or examples described in this specification without conflicting with each other.
尽管上面已经示出和描述了本申请的实施例,可以理解的是,上述实施例是示例性的,不能理解为对本申请的限制,本领域的普通技术人员在本申请的范围内可以对上述实施例进行变化、修改、替换和变型。Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limitations on the present application, and those skilled in the art can make the above-mentioned The embodiments are subject to changes, modifications, substitutions and variations.
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Citations (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4763276A (en) * | 1986-03-21 | 1988-08-09 | Actel Partnership | Methods for refining original robot command signals |
CN107443382A (en) * | 2017-09-12 | 2017-12-08 | 清华大学 | Industrial robot structure parameter error recognizes and compensation method |
CN108015808A (en) * | 2017-12-07 | 2018-05-11 | 天津大学 | A kind of Kinematic Calibration method of series-parallel robot |
CN110842927A (en) * | 2019-11-30 | 2020-02-28 | 天津大学 | A Multiple Regression-Based Geometric Error Compensation Method for Robot Joints |
CN110977940A (en) * | 2019-11-28 | 2020-04-10 | 清华大学 | Geometric error modeling method and device for parallel-hybrid robots |
CN112197770A (en) * | 2020-12-02 | 2021-01-08 | 北京欣奕华数字科技有限公司 | Robot positioning method and positioning device thereof |
-
2021
- 2021-07-16 CN CN202110807852.1A patent/CN113500585B/en active Active
Patent Citations (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4763276A (en) * | 1986-03-21 | 1988-08-09 | Actel Partnership | Methods for refining original robot command signals |
CN107443382A (en) * | 2017-09-12 | 2017-12-08 | 清华大学 | Industrial robot structure parameter error recognizes and compensation method |
CN108015808A (en) * | 2017-12-07 | 2018-05-11 | 天津大学 | A kind of Kinematic Calibration method of series-parallel robot |
CN110977940A (en) * | 2019-11-28 | 2020-04-10 | 清华大学 | Geometric error modeling method and device for parallel-hybrid robots |
CN110842927A (en) * | 2019-11-30 | 2020-02-28 | 天津大学 | A Multiple Regression-Based Geometric Error Compensation Method for Robot Joints |
CN112197770A (en) * | 2020-12-02 | 2021-01-08 | 北京欣奕华数字科技有限公司 | Robot positioning method and positioning device thereof |
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