技术领域Technical Field
本发明涉及基于连续运动测量的工业机器人快速标定方法，属于机器人标定技术领域。The invention relates to a rapid calibration method for an industrial robot based on continuous motion measurement, and belongs to the technical field of robot calibration.
背景技术Background technique
对于工业机器人而言，绝对定位精度是其完成复杂精密任务的重要标准。构成工业机器人的零部件数量多、组合复杂，部件的加工误差和部件之间的装配误差是影响绝对定位精度的主要因素。工业机器人的运动学标定通过测量来辨识运动学参数误差，是提升工业机器人绝对定位精度的一种有效的且可降低成本的手段。For industrial robots, absolute positioning accuracy is an important criterion for completing complex and precise tasks. Industrial robots are composed of many parts and components with complex combinations. The processing errors of the parts and the assembly errors between the parts are the main factors affecting the absolute positioning accuracy. The kinematic calibration of industrial robots is an effective and cost-effective means to improve the absolute positioning accuracy of industrial robots by identifying the kinematic parameter errors through measurement.
但现阶段，工业机器人标定的测量阶段的时间成本仍太高而且不够灵活。其中，经典的位形采集可以描述为一个循环测量过程，首先控制机器人运动至第一个测量位形处，待末端稳定静止之后，开启测量仪器(程序)以获得末端位姿和关节位移的数据，之后在控制机器人运动至下一个测量位形，如此循环直至所有测量位形下的数据都被获取。这是一种循环执行“移动-稳定-测量”的测量策略(Loop of Move-Settle-Measure,LMSM)。该策略的特点在于不必考虑测量过程中的运动误差和测量延时问题，测量过程中机器人处于静止状态，仪器获取数据之后，机器人再执行运动程序。然而，执行该测量策略下的测量时间随位形的增多呈线性增长，不是一种高效的标定方式。而对生产线中的机器人因碰撞、传动部件磨损、更换末端执行器，以及在产线中新增同类型机器人等因素，而产生的在线标定或定期重标定需求，期望标定系统具有更高的效率。因此，一种能够减少标定中位形测量的时间且同时还能满足原有误差建模、辨识等技术条件下保证工业机器人定位精度要求的标定方法，能对工业机器人生产的精度和效率提升方面具有重要意义。However, at present, the time cost of the measurement phase of industrial robot calibration is still too high and not flexible enough. Among them, the classic configuration acquisition can be described as a cyclic measurement process. First, the robot is controlled to move to the first measurement configuration. After the end is stable and stationary, the measuring instrument (program) is turned on to obtain the data of the end posture and joint displacement. Then the robot is controlled to move to the next measurement configuration, and the cycle is repeated until the data under all measurement configurations are acquired. This is a measurement strategy of "Move-Settle-Measure" (Loop of Move-Settle-Measure, LMSM) that executes a loop. The characteristic of this strategy is that there is no need to consider the motion error and measurement delay problems during the measurement process. The robot is in a stationary state during the measurement process. After the instrument acquires the data, the robot executes the motion program. However, the measurement time under this measurement strategy increases linearly with the increase of configurations, which is not an efficient calibration method. For the online calibration or regular recalibration needs of robots in the production line due to collisions, wear of transmission components, replacement of end effectors, and addition of robots of the same type in the production line, it is expected that the calibration system will have higher efficiency. Therefore, a calibration method that can reduce the time of calibration mid-position measurement and at the same time meet the original error modeling, identification and other technical conditions to ensure the positioning accuracy of the industrial robot can be of great significance to improving the accuracy and efficiency of industrial robot production.
发明内容Summary of the invention
本发明提供基于连续运动测量的工业机器人快速标定方法，旨在至少解决现有技术中存在的技术问题之一。The present invention provides an industrial robot rapid calibration method based on continuous motion measurement, aiming to solve at least one of the technical problems existing in the prior art.
本发明的技术方案涉及基于连续运动测量的工业机器人快速标定方法，根据本发明的方法包括以下步骤：The technical solution of the present invention relates to a rapid calibration method for an industrial robot based on continuous motion measurement. The method according to the present invention comprises the following steps:
S100、基于工业机器人工作空间的备选位形池，选择获得最优的测量位形，以确定工业机器人运动所经过的路点；S100, based on the candidate configuration pool of the industrial robot workspace, selecting the optimal measurement configuration to determine the waypoints through which the industrial robot moves;
S200、基于路点的分布，确定时间最优的光滑连续运动的规划轨迹；S200, determining a planning trajectory of a smooth continuous motion with optimal time based on the distribution of waypoints;
S300、测量工业机器人的实际轨迹，将规划轨迹与实测轨迹对齐，以确定被选的测量位形的实际数据；S300, measuring the actual trajectory of the industrial robot, aligning the planned trajectory with the measured trajectory to determine actual data of the selected measurement configuration;
S400、构建工业机器人运动学模型，采用基于连续运动测量策略的快速标定方法，对工业机器人进行标定。S400, construct a kinematic model of the industrial robot, and calibrate the industrial robot using a fast calibration method based on a continuous motion measurement strategy.
进一步，所述步骤S100包括：Further, the step S100 includes:
S110、在工业机器人的工作空间中准备备选位形，并初始化一定数量的测量位形；S110, preparing alternative configurations in the workspace of the industrial robot and initializing a certain number of measurement configurations;
S120、采用DETMAX加模拟退火的搜索方法，在备选位形中搜索以确定最优的测量位形。S120, using a search method of DETMAX plus simulated annealing to search among candidate configurations to determine the optimal measurement configuration.
进一步，对于所述步骤S200包括：Further, the step S200 includes:
S210、采用样条插值方法连接路点，以规划经过路点的光滑路径，并获得任意两个相邻路点之间的运动距离；S210, connecting the waypoints using a spline interpolation method to plan a smooth path passing through the waypoints, and obtaining a movement distance between any two adjacent waypoints;
S220、根据任意两个相邻路点之间的运动距离，使用分段S模型规划每两个路点之间的轨迹，获得两个相邻路点之间与时间相关的运动参数以及运动时间；S220, according to the movement distance between any two adjacent waypoints, use the segmented S model to plan the trajectory between every two waypoints, and obtain the time-related movement parameters and movement time between the two adjacent waypoints;
S230、根据任意相邻路点之间的运动时间，基于遗传算法确定运动时间最短的路点经过顺序。S230, determining the passing order of the waypoints with the shortest moving time based on a genetic algorithm according to the moving time between any adjacent waypoints.
进一步，所述步骤S300中，根据速度曲线的波谷特征，对齐速度的测量曲线与规划曲线，以从测量曲线中获得标定所需的测量位形的测量数据。Furthermore, in step S300, the measured velocity curve and the planned velocity curve are aligned according to the trough characteristics of the velocity curve, so as to obtain measurement data of the measurement configuration required for calibration from the measured velocity curve.
进一步，所述步骤S400包括：Further, the step S400 includes:
S410、构建工业机器人的运动学模型，以建立误差映射模型；S410, constructing a kinematic model of the industrial robot to establish an error mapping model;
S420、建立工业机器人的逆运动学误差模型；S420, establish an inverse kinematics error model for industrial robots;
S430、搭建测量的数据采集平台，分别采集CMM策略与“移动-稳定-测量”(Loop ofMove-Settle-Measure,LMSM)策略中所需的标定位形集；S430, building a measurement data acquisition platform to respectively collect the calibration geometry sets required in the CMM strategy and the “Loop of Move-Settle-Measure, LMSM” strategy;
S440、分别利用CMM策略与LMSM策略获取的标定位形数据辨识运动学误差参数，并补偿工业机器人运动学参数。S440, respectively using the calibration positioning data obtained by the CMM strategy and the LMSM strategy to identify kinematic error parameters and compensate for the kinematic parameters of the industrial robot.
进一步，所述工业机器人为SPM-RP并联机器人，所述步骤S410中，Furthermore, the industrial robot is a SPM-RP parallel robot, and in step S410,
基于动平台坐标系{rm}在基坐标系{rb}的变换关系中旋转矩阵R和平移向量p，所述SPM-RP并联机器人的单个支链Zi的误差等式表示如下：Based on the rotation matrix R and the translation vector p in the transformation relationship between the moving platform coordinate system {rm} and the base coordinate system {rb}, the error equation of a single branch chainZi of the SPM-RP parallel robot is expressed as follows:
式中，i＝1,2,3,4，表示支链的序列号；In the formula, i = 1, 2, 3, 4, indicating the sequence number of the branch chain;
si表示支链i的PRPaR结构中的下部旋转关节R中心相对于{rm}坐标系的位置，是si的位置误差向量，且si represents the position of the center of the lower revolute joint R in thePRPaR structure of branch i relative to the {rm} coordinate system, is the position error vector ofsi , and
qi表示SPM-RP处于零位状态下，支链i的PRPaR结构中的上部旋转关节R中心相对于{rb}坐标系的位置，是qi的位置误差向量，且di表示支链i的PRPaR结构中的平移关节P的位移量；Δdi表示关节位移偏差量，表征了运动学误差参数在关节位移方向测量值与计算值之间的偏差；qi represents the position of the center of the upper rotation joint R in thePRPaR structure of branch i relative to the {rb} coordinate system when SPM-RP is in the zero position. is the position error vector ofqi , and di represents the displacement of the translation joint P in thePRPaR structure of branch i; Δdi represents the joint displacement deviation, which characterizes the deviation between the measured value and the calculated value of the kinematic error parameter in the joint displacement direction;
RQ,i表示支链i上固连于Qi点的关节坐标系{rqi}相对于{rb}的旋转矩阵，与移动副的轴线方向相关；ΔRQ,i表示微分旋转矩阵，轴线角度参数被包含于且由固连于Qi点的关节坐标系{rqi}相对于基坐标系{rb}绕z轴旋转角度而得到的；RQ,i represents the rotation matrix of the joint coordinate system {rqi } fixed to pointQi on branch i relative to {rb}, which is related to the axis direction of the moving pair; ΔRQ,i represents the differential rotation matrix, and the axis angle parameters are included in and The joint coordinate system {rqi } fixed to pointQi rotates around the z axis relative to the base coordinate system {rb} obtained by angle;
li表示支链i的PRPaR结构中的平行四边形结构Pa的等效杆长，等效杆长的误差且ηi表示中间变量ηi＝p+Rsi-qi，Δηi表示中间变量ηi的误差项。ez表示z方向上的单位向量ez＝[0,0,1]T；li represents the equivalent rod length of the parallelogram structure Pa in thePRPaR structure of branch i, and the error of the equivalent rod length and ηi represents the intermediate variable ηi =p+Rsi -qi , Δηi represents the error term of the intermediate variable ηi . ez represents the unit vector ez =[0,0,1]T in thez direction;
式中，上标n表示运动学参数名义项。Wherein, the superscript n represents the nominal term of kinematic parameters.
进一步，所述步骤S420中，将工业机器人末端位姿信息作为输入量，工业机器人关节位移偏差量作为输出量，误差映射模型表示为：Furthermore, in step S420, the end position information of the industrial robot is used as input, and the joint displacement deviation of the industrial robot is used as output. The error mapping model is expressed as:
其中，in,
式中，下标i表示SPM-RP并联机器人的第i个支链序列，下标j表示第j个测量位形序列，Aj表示第j个测量位形下的误差映射矩阵，pm和Rm表示工业机器人被测量的末端位姿；Wherein, subscript i represents the i-th branch sequence of the SPM-RP parallel robot, subscript j represents the j-th measurement configuration sequence,Aj represents the error mapping matrix under the j-th measurement configuration,pm andRm represent the measured end poses of the industrial robot;
其中，根据测量末端位姿计算得到的第i关节的关节位移表示如下：Among them, the joint displacement of the i-th joint calculated according to the measured end posture is expressed as follows:
根据关节编码器测量得到的第i关节的关节位移为获得关节位移偏差量Δdi表示如下：The joint displacement of the i-th joint measured by the joint encoder is The joint displacement deviation Δdi is obtained as follows:
进一步，所述步骤S440包括：Further, the step S440 includes:
S441、根据建立的逆运动学误差模型和采集的基于CMM策略的测量位形的实际数据，获得运动学参数辨识的方程组；S441, obtaining a set of equations for kinematic parameter identification according to the established inverse kinematics error model and the actual data of the measurement configuration collected based on the CMM strategy;
S442、采用扩展卡尔曼滤波法获得得到CMM策略下的运动学参数误差的估计值，并以参数误差的估计值更新名义运动学参数。S442. Use the extended Kalman filter method to obtain an estimated value of the kinematic parameter error under the CMM strategy, and update the nominal kinematic parameters with the estimated value of the parameter error.
本发明的技术方案还涉及计算机可读存储介质，其上储存有程序指令，所述程序指令被处理器执行时实施上述的方法。The technical solution of the present invention also relates to a computer-readable storage medium on which program instructions are stored, and the above-mentioned method is implemented when the program instructions are executed by a processor.
本发明的技术方案还涉及基于连续运动测量的工业机器人快速标定系统，所述系统包括计算机装置，该计算机装置包含上述计算机可读存储介质。The technical solution of the present invention also relates to a rapid calibration system for an industrial robot based on continuous motion measurement, wherein the system comprises a computer device, and the computer device comprises the above-mentioned computer-readable storage medium.
本发明的有益效果如下：The beneficial effects of the present invention are as follows:
本发明基于连续运动测量(Continuous-Moving Measurement,CMM)策略的工业机器人快速标定方法，可消除测量的等待时间，使得标定测量的工作在机器人运动过程中完成。在CMM测量策略中，系统从机器人一次连续运动中获取标定所需位形数据，且获取的数据质量与利用传统“移动-稳定-测量”(Loop of Move-Settle-Measure,LMSM)测量策略获取的数据质量基本相当。从而采用本发明的基于CMM的快速标定方法，既能够提升工业机器人的绝对定位精度，又能够减少工业机器人运动学标定的数据采集的时间，提高了实际生产线机器人的标定效率。The present invention discloses a rapid calibration method for industrial robots based on a continuous-moving measurement (CMM) strategy, which can eliminate the waiting time for measurement and complete the calibration measurement work during the robot's movement. In the CMM measurement strategy, the system obtains the required configuration data for calibration from a continuous movement of the robot, and the quality of the obtained data is basically equivalent to the quality of the data obtained using the traditional "movement-stabilization-measurement" (Loop of Move-Settle-Measure, LMSM) measurement strategy. Therefore, the CMM-based rapid calibration method of the present invention can not only improve the absolute positioning accuracy of the industrial robot, but also reduce the data acquisition time for the kinematic calibration of the industrial robot, thereby improving the calibration efficiency of the actual production line robot.
将本发明方法应用于SPM-RM并联机器人，验证了基于连续运动测量的快速标定方案的高效性和精确性，相较于基于经典LMSM测量策略的传统标定方法，基于CMM策略的快速标定比传统标定方法以仅仅1.77％的定位精度上的牺牲却获得了93.13％标定效率方面的提升。The method of the present invention is applied to the SPM-RM parallel robot, and the efficiency and accuracy of the rapid calibration scheme based on continuous motion measurement are verified. Compared with the traditional calibration method based on the classic LMSM measurement strategy, the rapid calibration based on the CMM strategy achieves a 93.13% improvement in calibration efficiency at the expense of only 1.77% of positioning accuracy.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1是根据本发明方法的基于CMM测量策略的总体流程图。FIG. 1 is an overall flow chart of a CMM-based measurement strategy according to the method of the present invention.
图2是根据本发明方法的标定优化测量的位形选择流程图。FIG. 2 is a flow chart of configuration selection for calibration optimization measurement according to the method of the present invention.
图3是根据本发明方法的分段S型模型的加加速度、加速度、速度和位移的曲线示意图。FIG. 3 is a schematic diagram of curves of jerk, acceleration, velocity and displacement of a segmented S-shaped model according to the method of the present invention.
图4是根据本发明方法的SPM-RP机器人的3D模型结构示意图。FIG. 4 is a schematic diagram of the 3D model structure of the SPM-RP robot according to the method of the present invention.
图5(a)是根据本发明方法的SPM-RP机器人的整体结构简图。FIG. 5( a ) is a schematic diagram of the overall structure of the SPM-RP robot according to the method of the present invention.
图5(b)是根据本发明方法的SPM-RP机器人的单支链结构简图。FIG5( b ) is a schematic diagram of a single-branched chain structure of a SPM-RP robot according to the method of the present invention.
图6(a)是根据本发明方法的标定的数据采集的模型实物示意图。FIG. 6( a ) is a schematic diagram of a physical model of data acquisition for calibration according to the method of the present invention.
图6(b)是根据本发明方法的标定的数据采集的结构简图。FIG. 6( b ) is a simplified structural diagram of calibration data acquisition according to the method of the present invention.
图7(a)是根据本发明方法标定获得的SPM-RP连续轨迹的空间曲线图。FIG. 7( a ) is a spatial curve diagram of the SPM-RP continuous trajectory calibrated according to the method of the present invention.
图7(b)是根据本发明方法标定获得的SPM-RP连续轨迹的规划速度曲线图和测量速度曲线图。FIG. 7( b ) is a planned speed curve diagram and a measured speed curve diagram of the SPM-RP continuous trajectory calibrated according to the method of the present invention.
图8是在SPM-RP工作空间内随机采集的用于验证本发明快速标定方法与传统标定方法的100个独立验证位形数据集的示意图。FIG8 is a schematic diagram of 100 independent verification configuration data sets randomly collected in the SPM-RP workspace for verifying the fast calibration method of the present invention and the traditional calibration method.
图9(a)是根据本发明方法的SPM-RP在标定前的绝对定位误差值。FIG9( a ) is an absolute positioning error value of the SPM-RP before calibration according to the method of the present invention.
图9(b)是根据本发明方法的SPM-RP分别使用CMM策略与LMSM策略标定后的绝对定位误差值。FIG9( b ) shows the absolute positioning error values of the SPM-RP after calibration using the CMM strategy and the LMSM strategy respectively according to the method of the present invention.
具体实施方式Detailed ways
以下将结合实施例和附图对本发明的构思、具体结构及产生的技术效果进行清楚、完整的描述，以充分地理解本发明的目的、方案和效果。The concept, specific structure and technical effects of the present invention will be clearly and completely described below in combination with the embodiments and drawings to fully understand the purpose, scheme and effect of the present invention.
需要说明的是，如无特殊说明，当某一特征被称为“固定”、“连接”在另一个特征，它可以直接固定、连接在另一个特征上，也可以间接地固定、连接在另一个特征上。本文所使用的单数形式的“一种”、“所述”和“该”也旨在包括多数形式，除非上下文清楚地表示其他含义。此外，除非另有定义，本文所使用的所有的技术和科学术语与本技术领域的技术人员通常理解的含义相同。本文说明书中所使用的术语只是为了描述具体的实施例，而不是为了限制本发明。本文所使用的术语“和/或”包括一个或多个相关的所列项目的任意的组合。It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to another feature, or it may be indirectly fixed or connected to another feature. The singular forms "a", "said" and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art. The terms used in this specification are intended only to describe specific embodiments and are not intended to limit the invention. The term "and/or" used herein includes any combination of one or more related listed items.
应当理解，尽管在本公开可能采用术语第一、第二、第三等来描述各种元件，但这些元件不应限于这些术语。这些术语仅用来将同一类型的元件彼此区分开。例如，在不脱离本公开范围的情况下，第一元件也可以被称为第二元件，类似地，第二元件也可以被称为第一元件。本文所提供的任何以及所有实例或示例性语言(“例如”、“如”等)的使用仅意图更好地说明本发明的实施例，并且除非另外要求，否则不会对本发明的范围施加限制。It should be understood that, although the term first, second, third etc. may be adopted to describe various elements in the present disclosure, these elements should not be limited to these terms. These terms are only used to distinguish the same type of elements from each other. For example, without departing from the scope of the present disclosure, the first element may also be referred to as the second element, and similarly, the second element may also be referred to as the first element. The use of any and all examples or exemplary language ("for example", "such as" etc.) provided herein is only intended to better illustrate embodiments of the present invention, and unless otherwise required, the scope of the present invention will not be limited.
参照图1至图3，在一些实施例中，根据本发明的基于连续运动测量的工业机器人快速标定方法，至少包括以下步骤：1 to 3, in some embodiments, the rapid calibration method of an industrial robot based on continuous motion measurement according to the present invention comprises at least the following steps:
S100、基于工业机器人工作空间的备选位形池，选择获得最优的测量位形，以确定工业机器人运动所经过的路点；S100, based on the candidate configuration pool of the industrial robot workspace, selecting the optimal measurement configuration to determine the waypoints through which the industrial robot moves;
S200、基于路点的分布，确定时间最优的光滑连续运动的规划轨迹；S200, determining a planning trajectory of a smooth continuous motion with optimal time based on the distribution of waypoints;
S300、测量工业机器人的实际轨迹，将规划轨迹与实测轨迹对齐，以确定被选的测量位形的实际数据；S300, measuring the actual trajectory of the industrial robot, aligning the planned trajectory with the measured trajectory to determine actual data of the selected measurement configuration;
S400、构建工业机器人运动学模型，采用基于CMM策略的快速标定方法，对工业机器人进行标定。S400, construct the kinematic model of the industrial robot and calibrate the industrial robot using a fast calibration method based on the CMM strategy.
本发明方法可实现CMM策略下的快速标定，是标定测量位形的优化选择方法，其采用从机器人一次连续运动中获取标定所需位形数据的CMM测量策略，可应用于新型SPM-RP并联机器人的运动学标定平台。The method of the invention can realize rapid calibration under the CMM strategy and is an optimal selection method for calibration measurement configuration. It adopts a CMM measurement strategy for obtaining configuration data required for calibration from one continuous motion of the robot and can be applied to the kinematic calibration platform of the new SPM-RP parallel robot.
需要说明的是，本发明上述步骤S100至S300属于从机器人一次连续运动中获取标定所需位形数据的通用策略，适用于一般工业机器人运动学标定中的测量，连续运动测量的流程如图1所示，其中步骤S100至S300分别对应于图中Part 1至Part 3。而步骤S400属于为基于步骤S100至S300的连续运动测量的工业机器人快速标定方法，其利用一款SPM-RP并联工业机器人作为具体实施例，对步骤S100至S300中的连续运动测量的标定方法开展验证工作。It should be noted that the above steps S100 to S300 of the present invention belong to a general strategy for obtaining the configuration data required for calibration from a continuous motion of the robot, which is applicable to the measurement in the kinematic calibration of general industrial robots. The process of continuous motion measurement is shown in Figure 1, wherein steps S100 to S300 correspond to Part 1 to Part 3 in the figure respectively. Step S400 belongs to a rapid calibration method for industrial robots based on the continuous motion measurement of steps S100 to S300, which uses an SPM-RP parallel industrial robot as a specific embodiment to carry out verification work on the calibration method of continuous motion measurement in steps S100 to S300.
步骤S100的具体实施方式Specific implementation of step S100
本发明在工业机器人的工作空间的备选位形池中选择一组能尽可能提高运动学参数误差辨识精度的最优位形，所选择的最优位形是机器人运动所经过的路点。参见图2，最优位形的选择流程包括至少以下子步骤：The present invention selects a set of optimal configurations that can improve the accuracy of kinematic parameter error identification as much as possible from the pool of candidate configurations of the workspace of the industrial robot. The selected optimal configurations are the waypoints that the robot moves through. Referring to FIG. 2 , the selection process of the optimal configuration includes at least the following sub-steps:
S110、准备备选位形池，并确定初始测量位形。S110, preparing a candidate configuration pool and determining an initial measurement configuration.
具体地，在工业机器人的工作空间内，等间隔或随机准备N数量的备选位形，需要说明的是，上述备选位形既可以用末端笛卡尔空间的位姿表示，也可以用关节空间的位移表示。初始测量位形是从位形池中的备选位形随机选择而来。具体地，测量位形为备选位形的子集，从备选位形中随即选择一组一定数量的测量位形作为初始化测量位形。在确定了一组初始的测量位形后，DETMAX方法开始展开迭代，从备选位形中选出最优的测量位形。进一步地，为了获得更高精度的辨识效果，测量位形数量M至少等于运动学误差参数的数目除以单个位形的维度所述获得商值的整数部分的2至3倍。因此，测量位形是从位形池中的备选位形选择而来，且数量上N＞＞M。Specifically, in the working space of the industrial robot, N number of alternative configurations are prepared at equal intervals or randomly. It should be noted that the above-mentioned alternative configurations can be represented by the posture of the end Cartesian space or the displacement of the joint space. The initial measurement configuration is randomly selected from the alternative configurations in the configuration pool. Specifically, the measurement configuration is a subset of the alternative configurations, and a certain number of measurement configurations are randomly selected from the alternative configurations as the initialization measurement configurations. After determining a set of initial measurement configurations, the DETMAX method begins to iterate and selects the optimal measurement configuration from the alternative configurations. Furthermore, in order to obtain a higher precision identification effect, the number of measurement configurations M is at least equal to 2 to 3 times the integer part of the quotient obtained by dividing the number of kinematic error parameters by the dimension of a single configuration. Therefore, the measurement configuration is selected from the alternative configurations in the configuration pool, and the number N>>M.
S120、DETMAX配合模拟退火方法的搜索最优位形。S120 and DETMAX are used in combination with simulated annealing method to search for the optimal configuration.
本发明采用的DETMAX(DETerminant MAXimization method,行列式最大化问题求解方法)从备选位形池中迭代搜索最优位形以替代相同数量的初始测量位形，其每次迭代依次包括一个AddConfiguration子程序和一个MinusConfiguration子程序。经过多次AddConfiguration和MinusConfiguration迭代流程，当可观测性指标趋于稳定或收敛，可得到最优的测量位形集合。进一步地，为了防止迭代陷入局部最优，本发明在上述AddConfiguration和MinusConfiguration迭代中加入了模拟退火，使得测量位形具有跳出局部最优的概率。The DETMAX (DETerminant MAXimization method) used in the present invention iteratively searches for the optimal configuration from the candidate configuration pool to replace the same number of initial measurement configurations, and each iteration includes an AddConfiguration subroutine and a MinusConfiguration subroutine in turn. After multiple AddConfiguration and MinusConfiguration iterations, when the observability index tends to be stable or converged, the optimal set of measurement configurations can be obtained. Furthermore, in order to prevent the iteration from falling into the local optimum, the present invention adds simulated annealing to the above-mentioned AddConfiguration and MinusConfiguration iterations, so that the measurement configuration has the probability of jumping out of the local optimum.
此处以一个具体实施例加以说明。譬如，1)在DETMAX方法中增加一个先入先出(FIFO)的位形堆栈，其容量为t；2)每一次DETMAX搜索迭代中，在AddConfiguration子程序执行之后，将AddConfiguration子程序所得到最优的位形放入位形堆栈中，由于迭代次数远大于堆栈容量，t次迭代之后，堆栈执行FIFO规则；3)每一次DETMAX搜索迭代中，MinusConfiguration子程序通过引入模拟退火算法，增加一定的随机性和接受删除堆栈中前n次最优位形的可能性，重新计算该子程序所得到最优的位形结果。4)最终帮助DETMAX方法在迭代优化过程中跳出局部最优测量位形，以提高找到全局最优测量位形的几率A specific embodiment is used here to illustrate. For example, 1) a first-in, first-out (FIFO) configuration stack is added to the DETMAX method, and its capacity is t; 2) in each DETMAX search iteration, after the AddConfiguration subroutine is executed, the optimal configuration obtained by the AddConfiguration subroutine is placed in the configuration stack. Since the number of iterations is much larger than the stack capacity, after t iterations, the stack executes the FIFO rule; 3) in each DETMAX search iteration, the MinusConfiguration subroutine introduces a simulated annealing algorithm to increase a certain degree of randomness and the possibility of accepting the deletion of the firstn optimal configurations in the stack, and recalculates the optimal configuration result obtained by the subroutine. 4) Finally, it helps the DETMAX method to jump out of the local optimal measurement configuration during the iterative optimization process to increase the probability of finding the global optimal measurement configuration.
步骤S200的具体实施方式Specific implementation of step S200
基于上述步骤S100获得的路点分布，本发明自动规划一条光滑的空间路径曲线，该曲线同时满足速度规划的连续性以及整体曲线的时间最优。针对两个路点之间的曲线开展分段S-型速度轨迹规划，确定每个分段的运动参数以及运动时间，其中确定的运动参数包括加加速度、加速度、速度和位移等。基于遗传算法重组路点的穿越序列，保证空间路径曲线的时间最优。其时间最优的光滑连续运动的规划轨迹的确定，至少包括以下步骤：Based on the waypoint distribution obtained in step S100, the present invention automatically plans a smooth spatial path curve that satisfies both the continuity of speed planning and the time optimization of the overall curve. Segmented S-shaped velocity trajectory planning is carried out for the curve between two waypoints, and the motion parameters and motion time of each segment are determined, wherein the determined motion parameters include jerk, acceleration, velocity, and displacement. The crossing sequence of the waypoints is reorganized based on a genetic algorithm to ensure the time optimization of the spatial path curve. The determination of the planning trajectory of the time-optimal smooth continuous motion includes at least the following steps:
S210、经过路点的光滑路径规划。S210: smooth path planning passing through waypoints.
利用样条插值方法连接路点，可实现相邻两个路点之间的连接，即Using the spline interpolation method to connect waypoints, the connection between two adjacent waypoints can be achieved, that is,
式中，fj(u)表示第j段曲线(位于第j与第j+1路点之间)的插值函数，u是位置变量，表示第j段曲线插值点的x，y或z的变量，而Uj+1是第j+1路点的x，y或z的值。而插值函数的形状由参数控制，通过函数积分易得路点j和路点j+1之间插值路径的绝对距离Lc,j。Wherefj (u) represents the interpolation function of the jth curve (between the jth and j+1th waypoints), u is the position variable, representing the x, y, or z variable of the jth curve interpolation point, and Uj+1 is the x, y, or z value of the j+1th waypoint. The shape of the interpolation function is determined by the parameters Control, the absolute distance Lc,j of the interpolation path between waypoint j and waypoint j+1 can be easily obtained by function integration.
需要说明的是，本发明的上述路径规划，可确定从起始测量位形到目标测量位形的可行路线，其不直接考虑时间因素。该路径规划既生成了一条平滑的路径，用于连续运动且穿过所有路点，确保机器人在测量位形处的速度不会发生剧烈变化，又为下一步规划确定了轨迹规划时每对相邻路点之间的距离。It should be noted that the above path planning of the present invention can determine the feasible route from the starting measurement configuration to the target measurement configuration, which does not directly consider the time factor. The path planning not only generates a smooth path for continuous movement and passing through all waypoints, ensuring that the speed of the robot does not change drastically at the measurement configuration, but also determines the distance between each pair of adjacent waypoints during trajectory planning for the next step of planning.
S220、路点之间的分段S型轨迹规划。S220: Segmented S-shaped trajectory planning between waypoints.
为了削弱路点之间和过路点的颤振问题，保证路径速度曲线的一阶可导，本发明设计关于时间的每两个路点之间的分段S型轨迹，同时在已知最大速度、最大加速度和最大加加速度以及距离约束的条件下，优化计算轨迹运动的时间。In order to weaken the chattering problem between waypoints and at crossing points and ensure the first-order differentiability of the path velocity curve, the present invention designs a segmented S-shaped trajectory between every two waypoints with respect to time, and optimizes the time for calculating the trajectory motion under the conditions of known maximum speed, maximum acceleration, maximum jerk and distance constraints.
具体地，参见图3所示的对称7段S型轨迹，对于路点j和路点j+1之间的轨迹的加加速度、加速度、速度和位移的曲线变化，它们的最小值和最大值分别对应被定义为[-jm,jm]，[-am,am]，[v0,vm]和[0,Lj]。其中，S型速度的前3段t1～t3为加速段，t4为匀速段，后3段t5～t7为减速段。由于是对称曲线，其各个时间段具有以下关系：Specifically, referring to the symmetrical 7-segment S-shaped trajectory shown in FIG3 , for the curve changes of the jerk, acceleration, velocity and displacement of the trajectory between waypoint j and waypoint j+1, their minimum and maximum values are defined as [-jm ,jm ], [-am ,am ], [v0 ,vm ] and [0,Lj ], respectively. Among them, the first three segments t1 to t3 of the S-shaped velocity are acceleration segments, t4 is a uniform speed segment, and the last three segments t5 to t7 are deceleration segments. Because it is a symmetrical curve, its various time segments have the following relationship:
以及，其各段时间t1～t7所对应的运动距离的关系如下：And, the relationship between the movement distances corresponding to each time segment t1 to t7 is as follows:
则路点j和路点j+1之间的轨迹的运动距离为：Then the moving distance of the trajectory between waypoint j and waypoint j+1 is:
其中，因上述各段时间t1～t7不是机器人控制器的运动规划周期ts的整数倍，若按照上述时间段直接计算规划，将会引入的圆整误差，对路点的准确判和运动的平滑性造成影响。本发明利用路点j和路点j+1之间的轨迹的距离约束，即通过适当增大规划总时间以及调整加加速度参数、加速度参数和速度参数，开展对t1～t7时间的圆整规划：Among them, because the above-mentioned time periods t1 to t7 are not integer multiples of the motion planning cycle ts of the robot controller, if the planning is directly calculated according to the above-mentioned time periods, rounding errors will be introduced, which will affect the accurate judgment of the waypoints and the smoothness of the motion. The present invention uses the distance constraint of the trajectory between waypoint j and waypoint j+1, that is, by appropriately increasing the total planning time and adjusting the acceleration parameter, acceleration parameter and speed parameter, to carry out rounding planning for the time period t1 to t7 :
min eL＝||Lc,j-Lj||min eL ＝||Lc,j -Lj ||
s.t.st
S230、时间最少的路点顺序优化S230, Optimization of the waypoint sequence with the least time
在已知任意路点相连的路径和任意两个相邻路点之间的运动距离，以及任意两个相邻路点之间的运动时间的条件下，本发明使用遗传算法选择路点的经过顺序，使得最终的运动时间最短。参见图1，由于路点之间的运动时间需要根据连续路径的变化而重新计算，参见图1的“更新被选位形的遍历序列”模块中，S230将根据样条路径的总体规划时间是否减少来判断停止迭代S210和S220，即随着一定次数的迭代之后，样条路径的总体规划时间没有减少时，则停止迭代，并进入下一步骤。Under the condition that the path connecting any waypoints and the moving distance between any two adjacent waypoints and the moving time between any two adjacent waypoints are known, the present invention uses a genetic algorithm to select the passing order of the waypoints so that the final moving time is the shortest. Referring to FIG1 , since the moving time between the waypoints needs to be recalculated according to the change of the continuous path, referring to the "update the traversal sequence of the selected configuration" module of FIG1 , S230 will determine whether to stop iteration S210 and S220 according to whether the overall planning time of the spline path is reduced, that is, after a certain number of iterations, if the overall planning time of the spline path is not reduced, the iteration is stopped and the next step is entered.
步骤S300的具体实施方式Specific implementation of step S300
根据测量位形之间S型曲线t1～t7时间分段的规划数值，可以得到工业机器人末端的规划速度曲线，作为规划轨迹数据。其中，工业机器人末端的最大速度是一系列速度曲线的波峰，而最小速度是它们之间的波谷。以及，使用测量仪器对工业机器人末端进行跟踪测量，再通过坐标变换采集获取工业机器人末端的速度数据，作为实际轨迹数据。根据测量的速度曲线与规划的速度曲线的一致性特征，速度的最高处(即波峰)的持续时间相对较长，最高处的速度与最低处(即波谷)的速度区别明显，且速度曲线在波谷的持续时间短暂。利用速度曲线的波谷特征对齐速度的测量曲线与规划曲线，最终从连续运动测量曲线中得到标定所需的测量位形的实际测量数据。需要说明的是，虽然由于仪器的测量误差、坐标变换误差以及伺服控制误差的影响，速度曲线的一致性存在一定的波动，本发明方法可忽略上述影响。According to the planning values of the S-curve t1 ~ t7 time segments between the measured configurations, the planned speed curve of the industrial robot terminal can be obtained as the planned trajectory data. Among them, the maximum speed of the industrial robot terminal is the peak of a series of speed curves, and the minimum speed is the trough between them. And, the industrial robot terminal is tracked and measured using a measuring instrument, and then the speed data of the industrial robot terminal is acquired through coordinate transformation acquisition as the actual trajectory data. According to the consistency characteristics of the measured speed curve and the planned speed curve, the duration of the highest point of the speed (i.e., the peak) is relatively long, the speed at the highest point is significantly different from the speed at the lowest point (i.e., the trough), and the duration of the speed curve in the trough is short. The trough characteristics of the speed curve are used to align the speed measurement curve and the planning curve, and finally the actual measurement data of the measurement configuration required for calibration is obtained from the continuous motion measurement curve. It should be noted that although there is a certain fluctuation in the consistency of the speed curve due to the influence of the measurement error, coordinate transformation error and servo control error of the instrument, the above influence can be ignored by the method of the present invention.
步骤S400的具体实施方式Specific implementation of step S400
本发明中所提出的基于CMM的快速标定方法既能够提升工业机器人的绝对定位精度，又能够减少工业机器人运动学标定的数据采集的时间，提高了实际生产线机器人的标定效率。本发明的基于上述测量的快速标定方法至少包括以下步骤：The CMM-based rapid calibration method proposed in the present invention can not only improve the absolute positioning accuracy of industrial robots, but also reduce the data acquisition time of kinematic calibration of industrial robots, thereby improving the calibration efficiency of actual production line robots. The rapid calibration method based on the above measurement of the present invention at least comprises the following steps:
S410、构建工业机器人的运动学模型，以建立误差映射模型；S410, constructing a kinematic model of the industrial robot to establish an error mapping model;
S420、建立工业机器人的逆运动学误差模型；S420, establish an inverse kinematics error model for industrial robots;
S430、搭建测量的数据采集平台，采集CMM策略中所需的标定位形集；S430, build a measurement data collection platform to collect the calibration geometry set required in the CMM strategy;
S440、利用CMM策略获取的标定位形数据辨识运动学误差参数，并补偿工业机器人运动学参数。S440, using the calibration positioning data obtained by the CMM strategy to identify kinematic error parameters and compensate for the kinematic parameters of the industrial robot.
进一步地，将本发明应用新型SPM-RM并联工业机器人，通过搭建测量的数据采集平台，分别采集CMM策略与LMSM策略中所需的末端位姿数据集以及验证数据集，再分别利用CMM策略与LMSM策略获取的标定位形数据辨识运动学误差参数，并补偿SPM-RP并联机器人运动学参数，利用验证数据集来验证本发明快速标定方法的有效性。相较于基于经典LMSM测量策略的传统标定方法，基于CMM策略的快速标定比传统标定方法以仅仅1.77％的定位精度上的牺牲却获得了93.13％标定效率方面的提升。具体地，本发明应用SPM-RM并联机器人的快速标定方法及其验证至少包括以下步骤：Furthermore, the present invention is applied to a new type of SPM-RM parallel industrial robot. By building a measurement data acquisition platform, the terminal posture data set and verification data set required in the CMM strategy and LMSM strategy are respectively collected, and then the calibration positioning data obtained by the CMM strategy and the LMSM strategy are used to identify the kinematic error parameters, and the kinematic parameters of the SPM-RP parallel robot are compensated. The verification data set is used to verify the effectiveness of the rapid calibration method of the present invention. Compared with the traditional calibration method based on the classic LMSM measurement strategy, the rapid calibration based on the CMM strategy has achieved a 93.13% improvement in calibration efficiency at the expense of only 1.77% of positioning accuracy over the traditional calibration method. Specifically, the rapid calibration method of the SPM-RM parallel robot used in the present invention and its verification include at least the following steps:
S410、SPM-RP并联机器人结构模型构建和运动学参数误差的确定：S410, SPM-RP parallel robot structure model construction and kinematic parameter error determination:
参见图4，本发明方法可应用于如图4所示的Schonflies-motion parallelmanipulator with rotational pitch motion，SPM-RP并联机器人的模型。SPM-RP并联机器人包含了一个末端动平台、两条PRPaRR支链(图4所示Z2和Z4)和两条PRPaR支链(图4所示Z1和Z3)，其中P，R，和Pa分别表示主动平移关节、被动旋转关节和被动的平行四边形结构。四条支链的PRPaR部分的拓扑结构是一致的且对称的。P的关节轴线与上部旋转关节R的轴线相交且轴线方向相互垂直，下部旋转关节R与末端动平台相连。Z2和Z4支链的两个上部旋转关节R的轴线平行，Z2和Z4支链的两个下部旋转关节R的轴线平行的，同样地，Z1和Z3支链的两个上部旋转关节R的轴线平行，Z1和Z3支链的两个下部旋转关节R的轴线也是平行的。其中参见图4右侧的动平台，不管SPM-RP并联机器人如何运动，其下部四个旋转关节R的轴线始终保持共面的，且Z2，Z3和Z4支链的下部旋转关节R的中心点共线。Referring to FIG4 , the method of the present invention can be applied to the model of the Schonflies-motion parallel manipulator with rotational pitch motion, SPM-RP parallel robot as shown in FIG4 . The SPM-RP parallel robot comprises a terminal moving platform, twoPRPaRR branches (Z2 and Z4 shown in FIG4 ) and twoPRPaR branches (Z1 and Z3 shown in FIG4 ), whereinP , R, and Pa represent active translation joints, passive rotation joints and passive parallelogram structures, respectively. The topological structures ofthe PRPaR parts of the four branches are consistent and symmetrical. The joint axis of P intersects with the axis of the upper rotation joint R and the axis directions are perpendicular to each other, and the lower rotation joint R is connected to the terminal moving platform. The axes of the two upper rotation joints R of theZ2 andZ4 branches are parallel, and the axes of the two lower rotation joints R of theZ2 andZ4 branches are parallel. Similarly, the axes of the two upper rotation joints R of theZ1 andZ3 branches are parallel, and the axes of the two lower rotation joints R of theZ1 andZ3 branches are also parallel. Referring to the moving platform on the right side of FIG4 , no matter how the SPM-RP parallel robot moves, the axes of its four lower rotation joints R always remain coplanar, and the center points of the lower rotation joints R of theZ2 ,Z3 andZ4 branches are collinear.
利用SPM-RP并联机器人的闭环矢量运动学模型建立误差映射模型。具体地，参见图5的SPM-RP整体与任一单个支链Zi结构简图，动平台坐标系{rm}在基坐标系{rb}的变换关系中旋转矩阵R和平移向量p可以表示为：The error mapping model is established using the closed-loop vector kinematic model of the SPM-RP parallel robot. Specifically, referring to the schematic diagram of the SPM-RP structure as a whole and any single branch chainZi in Figure 5, the rotation matrix R and the translation vector p of the moving platform coordinate system {rm} in the transformation relationship of the base coordinate system {rb} can be expressed as:
p+Rsi＝qi+diRQ,iez+linip+Rsi ＝qi +di RQ,i ez +li ni
根据第Zi支链的结构特征，PRPaR结构中平行四边形结构Pa的等效杆长li是固定的，上式变换为：According to the structural characteristics of the Zi -th branch chain, the equivalent rod length li of the parallelogram structure Pa in thePRPaR structure is fixed, and the above formula is transformed into:
误差映射模型可基于一阶摄动原理得到任一单个支链Zi的误差等式：The error mapping model can obtain the error equation of any single branch chainZi based on the first-order perturbation principle:
式中，i＝1,2,3,4，表示支链的序列号。si表示支链i的PRPaR结构中的下部旋转关节R中心相对于{rm}坐标系的位置，是si的位置误差向量，且qi表示SPM-RP处于零位状态下，支链i的PRPaR结构中的上部旋转关节R中心相对于{rb}坐标系的位置，是qi的位置误差向量，且di表示支链i的PRPaR结构中的平移关节P的位移量；Δdi表示关节位移偏差量，表征了运动学误差参数在关节位移方向测量值与计算值之间的偏差。RQ,i表示支链i上固连于Qi点的关节坐标系{rqi}相对于{rb}的旋转矩阵，与移动副的轴线方向相关；ΔRQ,i表示微分旋转矩阵，轴线角度参数被包含于且由固连于Qi点的关节坐标系{rqi}相对于基坐标系{rb}绕z轴旋转角度而得到的。li表示支链i的PRPaR结构中的平行四边形结构Pa的等效杆长，等效杆长的误差且ηi表示中间变量ηi＝p+Rsi-qi，Δηi表示中间变量ηi的误差项。ez表示z方向上的单位向量ez＝[0,0,1]T。式中，上标n表示运动学参数名义项。Where i = 1, 2, 3, 4, represents the serial number of the branch.si represents the position of the center of the lower revolute joint R in thePRPaR structure of branch i relative to the {rm} coordinate system, is the position error vector ofsi , and qi represents the position of the center of the upper rotation joint R in thePRPaR structure of branch i relative to the {rb} coordinate system when SPM-RP is in the zero position. is the position error vector ofqi , and di represents the displacement of the translation joint P in thePRPaR structure of branch i; Δdi represents the joint displacement deviation, which characterizes the deviation between the measured value and the calculated value of the kinematic error parameter in the joint displacement direction.R Q,i represents the rotation matrix of the joint coordinate system {rqi } fixed to pointQi on branch i relative to {rb}, which is related to the axis direction of the moving pair; ΔRQ,i represents the differential rotation matrix, and the axis angle parameters are included in and The joint coordinate system {rqi } fixed to pointQi rotates around the z axis relative to the base coordinate system {rb} The angle is obtained.l i represents the equivalent rod length of the parallelogram structure Pa in thePRPaR structure of branch i, and the error of the equivalent rod length and ηi represents the intermediate variable ηi = p + Rsi - qi , Δηi represents the error term of the intermediate variable ηi .ez represents the unit vectorez = [0, 0, 1]T in thez direction. Wherein, the superscript n represents the nominal term of the kinematic parameter.
其中，运动学参数误差包括：Among them, the kinematic parameter errors include:
1)运动副(R副)的位置误差。是si的位置误差向量，且是qi零位的位置参数误差向量，且1) Position error of the kinematic pair (R pair). is the position error vector ofsi , and is the position parameter error vector of the zero position ofqi , and
2)运动副(P副)的轴线误差。轴线角度参数被包含于且由固连于Qi点的关节坐标系{rqi}相对于基坐标系{rb}绕z轴旋转角度而得到的。微分旋转矩阵ΔRQ,i为：2) Axis error of the kinematic pair (P pair). The axis angle parameters are included in and The joint coordinate system {rqi } fixed to pointQi rotates around the z axis relative to the base coordinate system {rb} The differential rotation matrix ΔRQ,i is obtained by:
因此，轴线的角度误差参数表示为并根据反对称矩阵变换理论，单支链的误差等式中的项diRQ,iΔRQ,iez可重写为操作因子×表示向量的反对称操作——对于任意3维向量v＝[v1,v2,v3]T，存在Therefore, the angular error parameter of the axis is expressed as According to the antisymmetric matrix transformation theory, the term di RQ,i ΔRQ,i ez in the error equation for a single branch can be rewritten as The operation factor × represents the antisymmetric operation of the vector - for any 3-dimensional vector v = [v1 ,v2 ,v3 ]T , there exists
式中，v1，v2，v3分别表示3维向量v中的三个标量元素。Wherein, v1 , v2 , and v3 represent three scalar elements in the three-dimensional vector v.
3)长度误差，即等效杆长参数的误差且3) Length error, that is, the error of the equivalent rod length parameter and
上述运动学误差参数可以集中表示为误差参数向量上标n表示运动学参数名义(标称)值，同样可表示为The above kinematic error parameters can be collectively expressed as the error parameter vector The superscript n represents the nominal value of the kinematic parameter, which can also be expressed as
S420、建立SPM-RP并联机器人逆运动学误差模型：S420. Establish the inverse kinematics error model of the SPM-RP parallel robot:
建立逆运动学参数误差方程，被测量的位置p和被测量的含有姿态信息的旋转矩阵R，以pm和Rm来标注工业机器人被测量的末端位姿。在逆运动学误差模型中，将工业机器人末端位姿信息为输入量而工业机器人关节位移偏差量为输出量。根据测量末端位姿计算得到的第i关节的关节位移为：Establish the inverse kinematics parameter error equation, the measured position p and the measured rotation matrix R containing the posture information, and use pm and Rm to mark the measured end posture of the industrial robot. In the inverse kinematics error model, the end posture information of the industrial robot is used as the input and the joint displacement deviation of the industrial robot is used as the output. The joint displacement of the i-th joint calculated according to the measured end posture is:
根据关节编码器测量得到的第i关节的关节位移为因此关节位移偏差量Δdi可表示为：The joint displacement of the i-th joint measured by the joint encoder is Therefore, the joint displacement deviation Δdi can be expressed as:
可得到误差映射模型，下标j表示第j个测量位形序列为The error mapping model can be obtained, and the subscript j represents the jth measurement configuration sequence:
其中，in,
式中，Aj第j个测量位形下的误差映射矩阵。WhereAj is the error mapping matrix under the jth measurement configuration.
S430、搭建测量的数据采集平台，分别采集CMM策略与LMSM策略中所需的标定位形集。S430, build a measurement data collection platform to collect the calibration geometry sets required in the CMM strategy and the LMSM strategy respectively.
具体地，参见图6(a)和图6(b)所示的SPM-RP并联机器人的数据采集平台，利用Leica AT960激光跟踪仪测量安装于动平台表面的球型反射器(SMR)并计算获取末端位姿pm和Rm的数据。图7(a)是运动的空间轨迹，图中蓝色点为轨迹中测量位形之间的位置点，绿色点为测量位形的位置点，并以红色方向箭头表示该测量位形下的姿态方向。图7(b)是连续运动下沿运动方向的速度标量曲线，在对齐速度规划曲线图之后的圆形交叉点即为CMM策略中的标定所需的测量位形实际数据。采用LMSM策略分别在图7(b)的规划速度曲线波谷所对应的测量位形处，停稳SPM-RP后采集的测量位形数据。Specifically, referring to the data acquisition platform of the SPM-RP parallel robot shown in FIG6(a) and FIG6(b), the Leica AT960 laser tracker is used to measure the spherical reflector (SMR) installed on the surface of the moving platform and calculate the data of the terminal posture pm and Rm . FIG7(a) is the spatial trajectory of the motion, in which the blue points are the position points between the measurement configurations in the trajectory, the green points are the position points of the measurement configurations, and the red direction arrows indicate the posture direction under the measurement configuration. FIG7(b) is the velocity scalar curve along the motion direction under continuous motion, and the circular intersection after aligning the velocity planning curve diagram is the actual measurement configuration data required for calibration in the CMM strategy. The LMSM strategy is used to collect the measurement configuration data after the SPM-RP is stopped at the measurement configuration corresponding to the trough of the planning velocity curve in FIG7(b).
其中，CMM策略相对于LMSM策略的测量效率提升为：Among them, the measurement efficiency improvement of CMM strategy compared with LMSM strategy is:
其中，表示每相邻测量位形之间的运动测量时间，而表示在测量位形的等待测量时间。CMM策略下的M个测量位形的运动测量时间为10.7s，而LMSM策略下测量位形的等待测量时间取实验的平均值5s，进而LMSM的整体运动与等待测量时间为155.7s，即测量效率提升率r＝93.13％。in, represents the motion measurement time between each adjacent measurement configuration, and = represents the waiting measurement time in the measurement configuration. The motion measurement time of M measurement configurations under the CMM strategy The waiting time for measuring the configuration under the LMSM strategy is 10.7s, and the average value of the experimental waiting time is 5s. It is 155.7s, that is, the measurement efficiency improvement rate r = 93.13%.
S440、分别利用CMM策略与LMSM策略获取的标定位形数据辨识运动学误差参数，并补偿SPM-RP并联机器人运动学参数，利用验证数据集来验证快速标定方法的有效性。S440. Use the calibration positioning data obtained by the CMM strategy and the LMSM strategy to identify the kinematic error parameters, compensate the kinematic parameters of the SPM-RP parallel robot, and use the verification data set to verify the effectiveness of the fast calibration method.
首先，利用步骤S420中的误差模型，以及利用步骤S430中分别基于CMM策略与LMSM策略采集的测量位形数据，得到如下两组运动学参数辨识的方程组，上标L表示LMSM策略采集的数据，而上标C表示CMM策略采集的数据。First, using the error model in step S420 and the measurement configuration data collected based on the CMM strategy and the LMSM strategy in step S430, the following two sets of equations for kinematic parameter identification are obtained, where the superscript L represents the data collected by the LMSM strategy, and the superscript C represents the data collected by the CMM strategy.
然后，对两组辨识方程组使用相同的辨识方法——扩展卡尔曼滤波法，得到CMM策略与LMSM策略下的运动学参数误差的估计值和并以参数误差的估计值更新名义运动学参数Then, the same identification method, the extended Kalman filter method, is used for the two sets of identification equations to obtain the estimated values of the kinematic parameter errors under the CMM strategy and the LMSM strategy. and And update the nominal kinematic parameters with the estimated values of the parameter errors
参见图8，利用SPM-RP工作空间内随机采集的100个独立验证位形数据集，分别验证和的准确性，其名义运动学参数下的末端x，y和z方向上的绝对定位误差如图9(a)所示。而使用更新后的运动学参数和后的绝对定位误差如图9(b)所示，其中红色点线表示CMM策略辨识的蓝色点线表示辨识的As shown in Figure 8, 100 independent validation configuration data sets randomly collected in the SPM-RP workspace are used to verify and The accuracy of the end position in thex , y andz directions under the nominal kinematic parameters is shown in Figure 9(a). and The absolute positioning error after 3D is shown in Figure 9(b), where the red dotted line indicates the absolute positioning error after 3D CMM strategy identification. The blue dotted line indicates the identified
本发明通过统计100个验证位形的绝对定位误差数据得到：The present invention obtains the following by statistically analyzing the absolute positioning error data of 100 verification configurations:
1)采用LMSM测量策略，标定后末端定位误差的最大值“Maximum”、平均值“Mean”和标准差“STD”，相比于标定前精度提升了92.03％、95.76％和87.78％；所对应的末端姿态精度的提升率分别为92.19％、97.12％和79.33％。1) Using the LMSM measurement strategy, the maximum value "Maximum", average value "Mean" and standard deviation "STD" of the terminal positioning error after calibration are improved by 92.03%, 95.76% and 87.78% compared with the accuracy before calibration; the corresponding improvement rates of the terminal posture accuracy are 92.19%, 97.12% and 79.33% respectively.
2)采用CMM策略，标定后末端定位误差的最大值“Maximum”、平均值“Mean”和标准差“STD”，相比于标定前精度提升了90.30％、93.99％、和84.44％，所对应的末端姿态精度的提升率分别为85.97％，94.76％，和65.33％。与LMSM策略相比，CMM策略的平均位置精度损失为1.77％，平均姿态精度损失为2.36％。2) Using the CMM strategy, the maximum value "Maximum", average value "Mean" and standard deviation "STD" of the terminal positioning error after calibration are improved by 90.30%, 93.99%, and 84.44% compared with the accuracy before calibration, and the corresponding terminal posture accuracy improvement rates are 85.97%, 94.76%, and 65.33%, respectively. Compared with the LMSM strategy, the average position accuracy loss of the CMM strategy is 1.77%, and the average posture accuracy loss is 2.36%.
应当认识到，本发明实施例中的方法步骤可以由计算机硬件、硬件和软件的组合、或者通过存储在非暂时性计算机可读存储器中的计算机指令来实现或实施。所述方法可以使用标准编程技术。每个程序可以以高级过程或面向对象的编程语言来实现以与计算机系统通信。然而，若需要，该程序可以以汇编或机器语言实现。在任何情况下，该语言可以是编译或解释的语言。此外，为此目的该程序能够在编程的专用集成电路上运行。It should be appreciated that the method steps in the embodiments of the present invention can be implemented or implemented by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The method can use standard programming techniques. Each program can be implemented in a high-level process or object-oriented programming language to communicate with a computer system. However, if necessary, the program can be implemented in an assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, the program can be run on a programmed ASIC for this purpose.
此外，可按任何合适的顺序来执行本文描述的过程的操作，除非本文另外指示或以其他方式明显地与上下文矛盾。本文描述的过程(或变型和/或其组合)可在配置有可执行指令的一个或多个计算机系统的控制下执行，并且可作为共同地在一个或多个处理器上执行的代码(例如，可执行指令、一个或多个计算机程序或一个或多个应用)、由硬件或其组合来实现。所述计算机程序包括可由一个或多个处理器执行的多个指令。Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and/or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) that is executed collectively on one or more processors, by hardware, or a combination thereof. The computer program includes a plurality of instructions that may be executed by one or more processors.
进一步，所述方法可以在可操作地连接至合适的任何类型的计算平台中实现，包括但不限于个人电脑、迷你计算机、主框架、工作站、网络或分布式计算环境、单独的或集成的计算机平台、或者与带电粒子工具或其它成像装置通信等等。本发明的各方面可以以存储在非暂时性存储介质或设备上的机器可读代码来实现，无论是可移动的还是集成至计算平台，如硬盘、光学读取和/或写入存储介质、RSM、ROM等，使得其可由可编程计算机读取，当存储介质或设备由计算机读取时可用于配置和操作计算机以执行在此所描述的过程。此外，机器可读代码，或其部分可以通过有线或无线网络传输。当此类媒体包括结合微处理器或其他数据处理器实现上文所述步骤的指令或程序时，本文所述的发明包括这些和其他不同类型的非暂时性计算机可读存储介质。当根据本发明所述的方法和技术编程时，本发明还可以包括计算机本身。Further, the method can be implemented in any type of computing platform that is operably connected to a suitable computer, including but not limited to a personal computer, a minicomputer, a mainframe, a workstation, a network or distributed computing environment, a separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, etc. Various aspects of the present invention can be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, an optical read and/or write storage medium, an RSM, a ROM, etc., so that it can be read by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the process described herein. In addition, the machine-readable code, or portions thereof, can be transmitted via a wired or wireless network. When such media includes instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor, the invention described herein includes these and other different types of non-transitory computer-readable storage media. When programmed according to the methods and techniques of the present invention, the present invention can also include the computer itself.
计算机程序能够应用于输入数据以执行本文所述的功能，从而转换输入数据以生成存储至非易失性存储器的输出数据。输出信息还可以应用于一个或多个输出设备如显示器。在本发明优选的实施例中，转换的数据表示物理和有形的对象，包括显示器上产生的物理和有形对象的特定视觉描绘。The computer program can be applied to input data to perform the functions described herein, thereby converting the input data to generate output data stored in a non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present invention, the converted data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on the display.
以上所述，只是本发明的较佳实施例而已，本发明并不局限于上述实施方式，只要其以相同的手段达到本发明的技术效果，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明保护的范围之内。在本发明的保护范围内其技术方案和/或实施方式可以有各种不同的修改和变化。The above is only a preferred embodiment of the present invention. The present invention is not limited to the above implementation. As long as the technical effect of the present invention is achieved by the same means, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of protection of the present invention. Within the scope of protection of the present invention, its technical scheme and/or implementation method may have various modifications and changes.
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202410499700.3ACN118386232B (en) | 2024-04-24 | 2024-04-24 | Industrial robot rapid calibration method based on continuous motion measurement |
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202410499700.3ACN118386232B (en) | 2024-04-24 | 2024-04-24 | Industrial robot rapid calibration method based on continuous motion measurement |
| Publication Number | Publication Date |
|---|---|
| CN118386232Atrue CN118386232A (en) | 2024-07-26 |
| CN118386232B CN118386232B (en) | 2025-04-29 |
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202410499700.3AActiveCN118386232B (en) | 2024-04-24 | 2024-04-24 | Industrial robot rapid calibration method based on continuous motion measurement |
| Country | Link |
|---|---|
| CN (1) | CN118386232B (en) |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101556137A (en)* | 2008-04-07 | 2009-10-14 | 莱卡地球系统公开股份有限公司 | Articulated arm coordinate measuring machine |
| WO2023170166A1 (en)* | 2022-03-11 | 2023-09-14 | Renishaw Plc | System and method for calibration of an articulated robot arm |
| CN116810786A (en)* | 2023-07-17 | 2023-09-29 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Robot kinematics calibration method based on truncated total least square regularization |
| CN117091470A (en)* | 2017-10-13 | 2023-11-21 | 瑞尼斯豪公司 | Coordinate positioning machine |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101556137A (en)* | 2008-04-07 | 2009-10-14 | 莱卡地球系统公开股份有限公司 | Articulated arm coordinate measuring machine |
| CN117091470A (en)* | 2017-10-13 | 2023-11-21 | 瑞尼斯豪公司 | Coordinate positioning machine |
| WO2023170166A1 (en)* | 2022-03-11 | 2023-09-14 | Renishaw Plc | System and method for calibration of an articulated robot arm |
| CN116810786A (en)* | 2023-07-17 | 2023-09-29 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Robot kinematics calibration method based on truncated total least square regularization |
| Publication number | Publication date |
|---|---|
| CN118386232B (en) | 2025-04-29 |
| Publication | Publication Date | Title |
|---|---|---|
| CN110815206B (en) | Kinematics calibration method for Stewart parallel robot | |
| CN111702762B (en) | A method for optimizing the working attitude of an industrial robot | |
| CN111897216A (en) | A Multi-segment Velocity Planning and Interpolation Method | |
| CN109397292B (en) | A 7-DOF manipulator control method and system based on analytical solution | |
| CN115616983B (en) | A five-axis linkage synchronous tool path interpolation method and system | |
| CN109202904A (en) | A kind of the determination method and determining system in manipulator motion path | |
| CN104020665A (en) | Minimum saltus trajectory optimization method of mechanical arm based on multi-objective particle swarm optimization algorithm | |
| CN113650011B (en) | Method and device for planning splicing path of mechanical arm | |
| CN115570565B (en) | Multi-objective trajectory optimization method for industrial robots based on improved particle swarm optimization algorithm | |
| CN109176487A (en) | A kind of cooperating joint section scaling method, system, equipment, storage medium | |
| CN118163112B (en) | Mechanical arm inverse solution control method and device based on diffusion model | |
| CN114995431A (en) | An Improved A-RRT Path Planning Method for Mobile Robots | |
| CN115464653B (en) | Time optimal asymmetric S-type acceleration and deceleration control method | |
| CN114879678A (en) | Distance weight-based global path smoothing method for mobile robot | |
| CN116661377A (en) | Multi-axis track smoothing and interpolation method and device based on travel space | |
| CN118386232A (en) | Industrial robot rapid calibration method based on continuous motion measurement | |
| CN115179291A (en) | Industrial robot motion planning optimization method based on performance constraint term phase dimension reduction | |
| CN113778082B (en) | A method and system for unmanned vehicle trajectory tracking control based on self-triggering mechanism | |
| CN118682780A (en) | A robot arm execution path planning method for complex spatial measurement tasks | |
| CN104908030A (en) | SCARA robot accurate positioning method based on granularity model | |
| Szczepanski et al. | Optimal Path Planning Algorithm with Built-In Velocity Profiling for Collaborative Robot | |
| CN114407006B (en) | Control method for repairing and three-dimensional reconstructing aero-engine blade disc and application thereof | |
| CN116880209B (en) | Robot time-energy optimal smooth track planning method | |
| CN118493413B (en) | Material moving manipulator for fire-fighting pipeline production line, control method and related products | |
| Wan et al. | Robotic Arm Path Planning in Intelligent Warehousing and Logistics Based on Multiple Optimisation Algorithms |
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |