Kinematic calibration of gantry hybrid machine tool based on estimation error and local measurement information

This paper presents the kinematic calibration of a four degrees-of-freedom (DOF) hybrid machine tool based on a novel planar 3-DOFs parallel mechanism and a long movement of the worktable. Closed-form solutions are developed for both the inverse and direct kinematics about the parallel mechanism. The error model is built and the mechanism accuracy is investigated. Two types of kinematic calibration method are proposed by a simple measurement device. The first type of calibration method is based on estimation error, and can easy improve the machine tool accuracy quickly by estimating the error trends. The second type of kinematic calibration method is based on local measurement information, which includes the position errors and does not include the pose errors of the machine tool. The calibration tests showed the effectiveness of the calibration methods, which can be useful for the similar types of parallel machine tool.     

基于球杆仪检测信息的并联机构运动学标定

由于并联构型装备难于实现全闭环反馈控制,使运动学标定成为一项具有显著经济价值并能非常有效提高并联构型装备精度的手段,运动学标定通常包括误差建模、测量、辨识和补偿4个环节。基于以上因素,以5自由度混联机械手TriVariant为对象,研究一种基于球杆仪检测信息的运动学标定方法。首先建立球杆仪测量值与影响末端可补偿位姿误差的几何误差源的映射关系,并给出可辨识条件。在此基础上,以误差参数辨识矩阵条件数为评价指标,探讨合理设置球杆仪安装位置和数目的方法。最后,计算机仿真和试验验证了所提出方法的可行性和有效性,并指出仍然需要解决的若干问题。     

利用正交位移测量系统进行六自由度并联机构参数标定

为了简化六自由度并联机构的参数标定过程,提高标定效率,降低标定成本,提出了基于正交位移测量系统的位姿测量装置及方法。首先,研究了该装置的位姿解算方法,利用空间解析几何的方法,求解其运动学正解与逆解。其次,利用微小位移合成法,建立了并联机构及正交位移测量系统组合体的误差模型。然后,基于误差模型,构建了组合体参数误差辨识的最优化问题数学模型,其中,传感器示值的平方和最小为目标函数,组合体的结构参数误差为设计变量。最后,利用正交位移测量系统对六自由度并联机构位姿进行测量,利用OASIS奥希思软件直接搜索出参数误差最优解,将其补偿到并联机构控制系统中,完成并联机构的参数标定。标定前后位姿误差对比表明:最大位置误差降低了58%~96%,最大姿态误差降低了92%~97%。利用正交位移测量系统进行并联机构参数标定,不仅可有效提升并联机构的定位精度,还可有效简化标定工作,提升标定效率,降低标定成本。     

3-RPS并联机构运动学标定方法的研究

针对六轴混联机床中因3-RPS并联机构结构参数误差引起的精度问题,分析了影响3-RPS并联机构几何精度的误差因素,给出了并联机构的误差模型;基于影响并联机构定平台运动精度较大的几何误差参数;建立了运动学标定模型.采用阻尼最小二乘法,经多次优化迭代实现了利用一组测量数据完成非线性超越矛盾标定方程组的求解.利用激光干涉仪完成了标定用数据的测量,通过3-RPS并联机构运动学逆解和各铰链的几何标定参数,得到动平台的实际位姿.通过对标定前后的Z轴定位精度的检测及实际零件加工试验,验证了3-RPS并联机构运动学标定模型和方法的正确性和有效性.     

Delta并联机构精度标定方法研究

以Delta并联机构为对象,研究一类含平行四边形支链的3自由度并联机构误差建模技术,所建模型可有效分离出影响末端姿态误差的几何误差源。在此基础上提出一种精度标定方法,该方法利用并联机构操作空间与关节空间非线性映射的性质,仅需检测末端沿z向的位置误差、以及在初始位形下的姿态误差便可识别出几何参数,并可通过修改系统输入实现末端位置误差补偿。给出算例以验证该方法的有效性。     

Modelling,kinematic parameter identification and sensitivity analysis of a Laser Tracker having the beam source in the rotating head

This paper presents a new kinematic model, a parameter identification procedure and a sensitivity analysis of a laser tracker having the beam source in the rotating head. This model obtains the kinematic parameters by the coordinate transformation between successive reference systems following the Denavit–Hartenberg method. One of the disadvantages of laser tracker systems is that the end-user cannot know when the laser tracker is working in a suitable way or when it needs an error correction. The ASME B89.4.19 Standard provides some ranging tests to evaluate the laser tracker performance but these tests take a lot of time and require specialized equipment. Another problem is that the end-user cannot apply the manufacturer’s model because he cannot measure physical errors. In this paper, first the laser tracker kinematic model has been developed and validated with a generator of synthetic measurements using different meshes with synthetic reflector coordinates and known error parameters. Second, the laser tracker has been calibrated with experimental data using the measurements obtained by a coordinate measuring machine as nominal values for different strategies, increasing considerably the laser tracker accuracy. Finally, a sensitivity analysis of the length measurement system tests is presented to recommend the more suitable positions to perform the calibration procedure.     

Analysis and evaluation of objective functions in kinematic calibration of parallel mechanisms

This paper analyses different objective functions for the parameter identification of parallel mechanisms and studies the influence in the position and orientation errors to improve their accuracy. A new objective function considering deviation terms is presented. This function is compared with other widely used functions and the advantages and disadvantages of each function are presented. The geometric parameter identification is performed by external calibration by means of the direct kinematic model. First, the objective functions are defined considering error position, error orientation and deviations in measurement. These functions compare the measured and calculated moving platform coordinates in order to obtain the identified model parameters that minimize this difference. The measured coordinates are obtained by measuring three sphere centres, fixed to the moving platform of a parallel mechanism, and the computed coordinates are given by the kinematic model. Second, the model is solved by the Levenberg–Marquardt algorithm for a number of identification positions. Finally, the calibration is verified in test positions. The results obtained show that the consideration of the deviations in measurement in the objective function with respect to classical approaches allows us to better identify those kinematic parameters corresponding with passive joints that cannot be measured. These findings confirm that a suitable objective function can improve the mechanism accuracy by more than one order of magnitude in both position and orientation errors.     

一种基于工具坐标系的机器人运动学参数标定方法

机器人末端执行器位姿误差在基础坐标系中表示时,误差模型中包含姿态误差与位置矢量的乘积项,影响了参数标定识别精度。以工具坐标系为参考系,给出一种基于指数积公式包含关节约束条件的机器人位姿误差标定模型,避免了姿态误差与位置矢量的乘积项对参数标定识别精度的影响。以UR5机器人为标定对象,采用LeciaAT960-MR激光跟踪仪为测量设备,进行参数标定试验。试验结果表明,经参数标定后UR5机器人位置误差模和姿态误差模的平均值分别减小了91.07%和89.16%。     

考虑测量参照物误差对VAMT1Y并联机床的运动标定仿真

采用间接测量对 VAMT1Y并联机床进行标定仿真时 ,需要引进标准测量参照物对动平台的位姿进行测量 ,但参照物本身可能存在一定的尺寸误差 ;另外间接测量时要不断变换标准测量参照物的位置 ,又会引进位置误差。为便于解决实际问题 ,将上述误差和待标定的机床的几何误差综合考虑对机床进行了标定仿真。仿真结果表明 ,适当地考虑一些测量系统的误差并不会影响最终的标定效果     

基于三坐标测量机的球面5R并联机构运动学标定研究

基于D-H参数建立了包含球面5R并联机构全部结构参数的标定用位置反解模型。建立了该机构位置和姿态运动学标定模型,结合实际样机进一步得到了标定简化模型,简化了参数辨识与补偿计算过程。通过三坐标测量机确定了球面机构的近似球心,并以此为原点建立了测量坐标系,从而实现了测量参考系与运动参考系的统一,便于末端执行器位姿的测量。通过标定实验,验证了该方法能够提高球面并联机构的绝对精度。     

Design of a Two-Step Calibration Method of Kinematic Parameters for Serial Robots

Serial robots are used to handle workpieces with large dimensions, and calibrating kinematic parameters is one of the most efficient ways to upgrade their accuracy. Many models are set up to investigate how many kinematic parameters can be identified to meet the minimal principle,but the base frame and the kinematic parameter are indistinctly calibrated in a one-step way. A two-step method of calibrating kinematic parameters is proposed to improve the accuracy of the robot's base frame and kinematic parameters.The forward kinematics described with respect to the measuring coordinate frame are established based on the productof-exponential(POE) formula. In the first step the robot's base coordinate frame is calibrated by the unit quaternion form. The errors of both the robot's reference configuration and the base coordinate frame's pose are equivalently transformed to the zero-position errors of the robot's joints. The simplified model of the robot's positioning error is established in second-power explicit expressions. Then the identification model is finished by the least square method, requiring measuring position coordinates only. The complete subtasks of calibrating the robot's 39 kinematic parameters are finished in the second step. It's proved by a group of calibration experiments that by the proposed two-step calibration method the average absolute accuracy of industrial robots is updated to 0.23 mm. This paper presents that the robot's base frame should be calibrated before its kinematic parameters in order to upgrade its absolute positioning accuracy.     

Elasto-geometrical error modeling and compensation of a five-axis parallel machining robot

Parallel manipulators have the potentials of high efficiency and high precision in the field of machining and manufacturing. However, accuracy improvement of the parallel manipulator is still an essential and challenging issue, encountering two important problems. Firstly, the ignorance of elastic deformation caused by gravity or deviations of static stiffness model restricts further improvement of accuracy. To solve this problem, an elasto-geometrical error modeling method is proposed. The comprehensive effects of structural errors, elastic deformation under gravity and compliance parameter errors on pose deviations are disclosed. On this basis, the identification equation of actual structural errors and compliance parameter errors can be established. Secondly, the ill-conditioned identification matrix and the identification equation with anisotropic residual error can lead to inaccurate identification results. To solve this problem, a weighted regularization method is proposed. The identification equation with isotropic residual error is built, and accurate identification can be realized with the regularization method. Based on the proposed methods, the error compensation experiment is conducted on the prototype of a five-axis parallel machining robot using a laser tracker. Experiment results show that the accuracy of the machining robot is significantly improved after compensation. An M1_160 test piece and an S-shaped test piece are machined and measured to further validate the effectiveness of the proposed methods. The elasto-geometrical error modeling method and the weighted regularization method can be applied to other parallel manipulators’ accuracy improvement.     

Apply fuzzy interpolation method to calibrate parallel machine tools

A novel and efficient fuzzy interpolation method is proposed to simplify the calibration process for parallel machine tools (PMTs). Either inverse or forward kinematic models must be used in the traditional PMT calibration methods to perform the identification and compensation of the pose errors for PMTs, which made the calibration process time consuming and inefficient in real applications. Instead of using a model, the proposed method presents a modeless technique combined with the fuzzy interpolation method to obtain high calibration accuracies when a small workspace is adopted. This new approach can significantly reduce the complex in traditional PMT calibration processes and greatly simplify the calibration procedures.     

基于改进遗传算法实现柔性三坐标测量机参数标定

针对柔性三坐标测量机测量精度低的弊端,提出了误差修正和参数标定的方法.应用Denavit-Hartenberg( DH)法建立了柔性三坐标测量系统的运动学模型和误差模型,考虑系统结构参数标定问题,提出了一种基于优化最小二乘法的改进遗传算法.首先,在最小二乘法中引入变化因子来衡量收敛速度;其次,当该因子趋于稳定时,将产生...     

面向精度评价的并联机床参数辨识技术

基于并联机床外部标定,推导出辨识方程的残差近似等于标定后的位姿误差。为克服最小二乘法存在较大残差的缺陷,面向精度评价,提出最小最大优化的参数辨识技术,以残差最大绝对值最小为优化目标,直接控制误差范围。标定实例验证了最小二乘法缺陷的实际存在和最小最大优化抑制较大残差的效果。该参数辨识技术直接联系运动学标定和标定后的精度评价,简单有效的提高并联机床的整体精度。     

Constraint operator for the kinematic calibration of a parallel mechanism

This paper introduces a constraint operator for the kinematic calibration of a parallel mechanism. By adopting the concept of a constraint operator, the movement between two poses is constrained. When the constrained movements are satisfied, the active joint displacements are taken and inputted into the kinematic model to compute the theoretical movements. A cost function is derived by the errors between the theoretical movement and the actual movement. The parameters that minimize the cost function are estimated and substituted into the kinematic model for a kinematic calibration. A single constraint plane is employed as a mechanical fixture to constrain the movement, and three digital indicators are used as the sensing devices to determine whether the constrained movement is satisfied. This calibration system represents an effective, low cost and feasible technique for a parallel mechanism. A calibration algorithm is developed with a constraint operator and implemented on a parallel manipulator constructed for a machining center tool.     

Variable speed compensation method of errors of probes for CNC machine tools

Systematic errors of kinematic touch-trigger probes for CNC machine tools may exceed errors of the machine tool itself. As a result, the machining accuracy is strongly dependent on the probe's accuracy. Numerical correction of probes’ systematic errors can be used. However, it requires executing calculations by the CNC machine tool controller. To avoid this troublesome requirement, a new method of errors compensation is proposed. In this approach, a modification of the probe's pre-travel in a given direction is achieved by modification of measurement speed in this direction. Because all measurement speeds can be calculated offline, the controller does not have to do any calculations. The proposed method has been tested for sample kinematic probes and the error reduction was at least 10-fold.     

A two-step calibration methodology of multi-actuated mechanical servo press with parallel topology

We present a two-step calibration methodology of multi-actuated mechanical press with parallel topology and illustrate the method with a case study of a dual-actuated servo press with parallel topology. The kinematic model of the servo press is established firstly. From the total differentials of the kinematic equations, the error sensitivity matrix is obtained to find out linear dependent parameters and the effects of kinematic parameters on the press accuracy are studied. It is found that the press mechanism has the advantage that the press accuracy at the working area is less sensitive to the kinematic parameter errors. The experiment is carried out to measure the motions of the moving platform and slider. By the kinematic error model, the kinematic parameters of the active and passive chains are identified, respectively. Experimental results show that the accuracy of the servo press improves by 82% after kinematic calibration.     

基于单目视觉的并联机器人末端位姿检测

高效、准确地检测机器人末端位姿误差是实现运动学标定的关键环节。提出一种基于单目摄像机拍摄立体靶标序列图像信息的末端执行器6维位姿误差辨识方法,构造具有平行四边形几何约束的四个空间特征点,并以平行四边形的两个消隐点为约束,建立空间刚体位姿与其二维图像映射关系模型,实现末端位姿的精确定位,然后以Delta高速并联机器人为对象,进行了运动学标定试验,验证该方法的有效性,为这类机器人低成本、快速、在线运动学标定提供重要的理论与技术基础。     

Review on the research of contact parameters calibration of particle system

With the widespread application of the discrete element method, research on accurate simulation of particle systems has attracted significant attention. However, there is no accurate process for the parameter calibration of particle systems. Most calibrations use a direct measurement method or test-simulation combined calibration method. Both methods have their advantages and disadvantages. This study reviews the calibration of contact parameters of particle systems, introduces the main calibration methods of different contact parameters, and summarizes the advantages and disadvantages of two main measurement methods. For the parameter measurement of particle systems, the accurate representation of particle shape and the reasonable optimization of simulation time are still not perfect. Furthermore, the correction of parameters after calibration applied to subsequent simulation needs further discussion.