A two-step method for kinematic parameters calibration based on complete pose measurement—Verification on a heavy-duty robot

The poor pose accuracy of industrial robots restricts their further application in aviation manufacturing. Kinematic calibration based on position errors is a traditional method to improve robot accuracy. However, due to the difference between length errors and angle errors in the order of magnitude, it is difficult to accurately calibrate these geometric parameters together. In this paper, a two-step method for robot kinematic parameters calibration and a novel method for position and orientation measurement are proposed and combined to identify these two kinds of errors respectively. The redundant parameter errors that affect the identification are also analyzed and eliminated to further improve the accuracy of this two-step method. Taking the Levenberg-Marquardt algorithm as the underlying algorithm, simulation results indicate that the proposed two-step calibration method has faster iteration speed and higher identification accuracy than the traditional one. On this basis, the calibration and measurement methods proposed in this paper are verified on a heavy-duty robot used for fiber placement. Experimental results show that the mean absolute position error decreases from 0.9906 mm to 0.3703 mm after calibration by the proposed two-step calibration method with redundancy elimination. The absolute position accuracy has increased by 41.81% compared with the traditional method based on position errors only and 14.97% compared with the two-step calibration method without redundancy elimination. At the same time, the orientation errors after calibration are not more than 0.1485°, and the average of absolute errors is 0.0447.     

Kinematic calibration of a 5-axis parallel machining robot based on dimensionless error mapping matrix

Accuracy problem is one of the most challenging issues for the application of parallel robots in manufacturing industry, and kinematic calibration is a feasible approach to solve it. Although lots of researches have brought up a diversity of calibration methods, there are still rooms for the improvement of the accuracy, efficiency and robustness of these calibration effects. In this paper, an improved method for kinematic calibration of a 5-axis parallel machining robot is proposed, which includes a new forward kinematic solution (FKS) based on dual quaternion and a modified error modeling process leading to dimensionless error mapping matrixes (EMMs). On this basis, an iterative identification procedure is schemed, and the kinematics and identification simulations are carried out. The kinematics simulation results show that the proposed FKS has wider convergence range and faster computation speed than Levenberg-Marquardt algorithm, while the identification simulation results show that the residual pose errors with the proposed dimensionless EMMs are lower than that with the conventional EMM in various units. Additionally, the procedure of the full pose measurement with a laser tracker and an auxiliary tool is introduced, and thereby the contrast experiments of kinematic calibration on the prototype are conducted. The experiment results indicate that the residual position and orientation errors based on the dimensionless EMM decrease by 97.67% and 86.85% of the original values, respectively, at least, and by 76.77% and 38.65% of that based on the conventional EMM, respectively, at most. Consequently, it is further confirmed that the proposed calibration method is effective in enhancing the identification accuracy of the geometric errors and improving the positioning accuracy of the studied parallel robot.     

排爆机器人机械臂定位精度误差自动补偿方法研究

针对于排爆机器人在进行排除爆破物质时,机械臂不能满足绝对准确的定位要求,位置检测精度与实际距离之间存在一定的误差。为了解决这一问题,提出排爆机器人机械臂定位精度误差自动补偿方法。基于D-H运动模型和微分变换法创建排爆机器人机械臂位姿误差模型,对误差模型进行重复参数分析,去除重复参数获得可辨识的线性方程;在可辨识的运动学参数误差模型线性方程中加入一个增量进行误差补偿。最后通过仿真实验结果表明,所提方法通过对机械臂位姿误差模型进行有效补偿,使排爆机器人机械臂绝对定位精度均值提升1.3mm。     

Analysis of unified error model and simulated parameters calibration for robotic machining based on Lie theory

In robotic machining process, the kinematic errors of serial structure and compliance errors caused by external cutter-workpiece interactions can result in considerable deviation of the desired trajectory. Therefore, this paper proposes an efficient calibration methodology by establishing a unified error model about kinematic errors and compliance errors based on Lie theory, which simultaneously calibrates the kinematic parameters and joint compliances of a serial machining robot. In this methodology, the propagation law of kinematic errors is investigated by analysis of the kinematic error model, and the corresponding equivalent kinematic error model is thus obtained, in which the joint offset errors are regarded as one source of twist (joint twist and reference configuration twist) errors. On this basis, with the segmentation and modelling of the joint compliance errors caused by the link self-weight and cutting payloads, the unified error model is developed by linear superposition of configuration errors of the robotic end-cutter, calculated from the kinematic errors and compliance errors respectively. Meanwhile, to improve the accuracy of parameters calibration, the observability index is adopted to optimize the calibration configurations so as to eliminate the twist error constraints. The calibrated kinematic parameters and joint compliances are obtained eventually, and used to compensate the kinematic and compliance errors of the serial machining robot. Finally, to validate the effectiveness of the proposed unified error model, simulation analysis is performed using a 6-DOF serial machining robot, namely KUKA KR500. The comparisons among calibrated parameters show that the unified error model is more computationally efficient with optimal calibration configurations, rendering it suitable for the calibration of kinematic parameters and joint compliances in actual machining applications.     

基于雷达测距的飞行器交会对接误差补偿控制技术

为解决由视线倾角、视线偏角过大造成的飞行器对接存在误差的问题,实现飞行器交会轨迹的精准对接,提出基于雷达测距的飞行器交会对接误差补偿控制技术。建立空间参考坐标系,根据轨道根数计算结果,推导动力学状态方程,实现对飞行器交会对接过程中的动力学作用分析。按照雷达测距原理,计算飞行器的理论飞行时长及雷达装置作用距离,再联合相关参数指标,确定精度极限的取值范围,实现基于雷达测距的对接误差控制。在三坐标测量机结构模型中,定义飞行位姿拟合条件,再根据位姿误差求解结果,实现对误差参数的补偿修正处理,完成基于雷达测距的飞行器交会对接误差补偿控制方法的设计。对比实验结果表明,应用所提方法可以同时将视线倾角、视线偏角的取值控制在0°-45.0°的数值范围之内,能够较好解决飞行器错误对接的问题,符合精准对接飞行器交会轨迹的实际应用需求。     

Accurate error compensation for a MR-compatible surgical robot based on a novel kinematic calibration method

Kinematic calibration is an effective and economical way to improve the accuracy of surgical robot, and in most cases, it is a necessary procedure before the robot is put into operation. This study investigates a novel kinematic calibration method where the effect of controller error is taken into account when formulating the model based on screw theory, which is applied to the kinematic control of magnetic resonance compatible surgical robot. Based on screw theory, the kinematic error model is established for the relationship between error of controller and the deviation of the measured pose of the end-effector. Therefore, the error of controller can be figured out and parameters of controller can be adjusted accordingly. Control strategy based on the kinematic calibration framework is proposed. According to artificial neural network, the deviation of end-effector in arbitrary configuration can be effectively obtained. Comparative experiments are carried out to show the validity and effectiveness of the proposed framework with the help of commercial visual system and joint encoders.     

Kinematic Calibration and Pose Measurement of a Medical Parallel Manipulator by Optical Position Sensors

In the applications of parallel manipulators, kinematic calibration is required to eliminate the errors resulting from the manufacturing and assembly of both base and tools. In this paper, a calibration method of base and tool transformation is developed by virtue of optical position sensors. An error model for calibration is constructed using differential geometry method. The pose error is obtained based on pose measurement results of OPTOTRAK 3020, a commercial 3D position measurement system. An iterative least squares procedure is used to identify the error parameters in the base and tool transformations. Simulation and experiment results are presented to demonstrate the effectiveness of the method for transformation matrices calibration. © 2003 Wiley Periodicals, Inc.     

基于共面圆的距离传感器与相机的相对位姿标定

近年来, 距离传感器与摄像机的组合系统标定在无人车环境感知中得到了广泛的研究与应用, 其中基于平面特征的方法简单易行而被广泛采用. 然而, 目前多数方法基于点匹配进行, 易错且鲁棒性较低. 本文提出了一种基于共面圆的距离传感器与相机的组合系统相对位姿估计方法. 该方法使用含有两个共面圆的标定板, 可以获取相机与标定板间的位姿, 以及距离传感器与标定板间的位姿. 此外, 移动标定板获取多组数据, 根据计算得到两个共面圆的圆心在距离传感器和相机下的坐标, 优化重投影误差与3D对应点之间的误差, 得到距离传感器与相机之间的位姿关系. 该方法不需要进行特征点的匹配, 利用射影不变性来获取相机与三维距离传感器的位姿. 仿真实验与真实数据实验结果表明, 本方法对噪声有较强的鲁棒性, 得到了精确的结果.     

Elasto-geometrical calibration of a hybrid mobile robot considering gravity deformation and stiffness parameter errors

Hybrid mobile robots, which combine the advantages of serial and parallel robots and have the ability to realize processing in situ, have considerable application potential in the field of processing and manufacturing. In this paper, a hybrid mobile robot used for wind turbine blade polishing is presented. The robot combines an automated guided vehicle, a 2-DoF robotic arm, and a 3-RCU parallel module. To improve the accuracy, investigating the elasto-geometrical calibration of the robot is necessary. Considering that the 3-RCU parallel module has weak stiffness along the gravitational direction, the stiffness model was established to estimate the deformation caused by the gravity of the mobile platform, ball screws, and motors. Subsequently, a rigid-flexible coupling error model considering structural and stiffness parameter errors is established. Based on these, a parameter identification method for the simultaneous identification of structural and stiffness parameter errors is proposed herein. For the 2-DoF robotic arm with parallelogram mechanisms, an intuitive error model considering the posture error caused by the parallelogram mechanism errors is established. The regularized nonlinear least squares method was adopted for parameter identification. Thereafter, a compensation strategy for the hybrid mobile robot that comprehensively considers the pose errors of the 3-RCU parallel module and 2-DoF robotic arm is proposed. Finally, a verification experiment was performed on the prototype, and the results indicated that after elasto-geometrical calibration, the maximum/mean of the position and posture errors of the hybrid mobile robot decreased from 3.738 mm/2.573 mm to 0.109 mm/0.063 mm and 0.236°/0.179° to 0.030°/0.013°, respectively. Owing to the decrease in the robot pose errors, the quality of the polished surface was more uniform. The range and standard deviation of roughness distribution of the polished surface were reduced from 0.595 μm and 0.248 μm to 0.397 μm and 0.127 μm. The methods proposed herein have reference significance for elasto-geometrical calibration of other parallel or hybrid robots.     

A novel kinematic parameters calibration method for industrial robot based on Levenberg-Marquardt and Differential Evolution hybrid algorithm

The poor absolute positioning accuracy of industrial robots is the main obstacle for its further application in precision grinding of complex surfaces, such as blisk, blade, etc. Based on the established kinematic error model of a typical industrial robot FANUC M710ic/50, a novel kinematic parameters calibration method is proposed in this paper to improve the absolute positioning accuracy of robot. The pre-identification of the kinematic parameter deviations of robot was achieved by using the Levenberg-Marquardt algorithm. Subsequently, these identified suboptimal values of parameter deviations were defined as central values of the components of initial individuals to complete accurate identification by using Differential Evolution algorithm. The above two steps, which were regarded as the core of this Levenberg-Marquardt and Differential Evolution hybrid algorithm, were used to obtain the preferable values for kinematic parameters of the robot. On this basis, the experimental investigations of kinematic parameters calibration were conducted by using a laser tracker and numerical simulation method. The results revealed that the robot positioning error decreased from 0.994 mm, initial positioning error measured by laser tracker, to 0.262 mm after calibration with this proposed hybrid algorithm. The absolute positioning accuracy has increased by 40.86% than that of the Levenberg-Marquardt algorithm, increased by 40.31% than that of the Differential Evolution algorithm, and increased by 25.14% than that of the Simulated Annealing algorithm. This work shows that the proposed kinematic parameters calibration method has a significant improvement on the absolute positioning accuracy of industrial robot.     

Calibration of stewart platforms and other parallel manipulators by minimizing inverse kinematic residuals

This paper focuses on the accuracy enhancement of Stewart platforms through kinematic calibration. The calibration problem is formulated in terms of a measurement residual, which is the discrepancy between the measured leg length and the computed leg length. With this formulation, one is able to identify kinematic error parameters of the Stewart platform without the necessity of solving the forward kinematic problem; thus avoiding the numerical problems associated with any forward kinematic solution. By this formulation, a concise differential error model with a well-structured identification Jacobian, which relates the pose measurement residual to the errors in the parameters of the platform, is derived. Experimental studies confirmed the effectiveness of the method. It is also shown in this paper that the proposed approach can be applied to other types of parallel manipulators, assuming that their inverse kinematic solution is simpler than its forward kinematic solution. Because this condition is satisfied by almost all parallel manipulators, the method is very useful for kinematic calibration of such machines. © 1998 John Wiley & Sons, Inc.     

基于M型标准块的视觉引导机器人系统手眼标定方法研究

针对线结构光传感器引导的机器人系统的手眼标定问题,提出了一种以M型标准块为标定物的方法。该M型标定物的两条平行的脊线作为约束,基于两条平行脊线的约束建立包含手眼关系、机器人运动学以及两条直线位姿参数误差的模型。首先基于定点约束求解手眼关系初值并以此为基础解算出直线位姿参数的初值,然后通过最小二乘法解算误差参数并补偿到模型中,不断迭代直至计算的误差参数小于阈值,最终得到最终的机器人手眼关系及运动学误差参数。为了验证标定方法的有效性,以某精加工平面为被测物,利用线结构光机器人系统对平面进行测量,得到平面点云;拟合最小二乘平面,计算点到平面距离的均方根值作为评价依据。分别对所述M型标准块和标准球两种方法进行了实验对比,结果表明,相较于标准球方法,所述M型标准块方法得到的均方根误差由0.152 mm减少到0.080 mm,均方根误差的标准差由0.043 mm减少到0.005 mm,其标定结果的精度及稳定性得到显著提高。     

Kinematic analysis and error modeling of TAU parallel robot

The TAU robot presents a new configuration of parallel robots with three degrees of freedom. This robotic configuration is well adapted to perform with a high precision and high stiffness within a large working range compared with a serial robot. It has the advantages of both parallel robots and serial robots. In this paper, the kinematic modeling and error modeling are established with all errors considered using Jacobian matrix method for the robot. Meanwhile, a very effective Jacobian approximation method is introduced to calculate the forward kinematic problem instead of Newton–Raphson method. It denotes that a closed form solution can be obtained instead of a numerical solution. A full size Jacobian matrix is used in carrying out error analysis, error budget, and model parameter estimation and identification. Simulation results indicate that both Jacobian matrix and Jacobian approximation method are correct and with a level of accuracy of micron meters. ADAMS's simulation results are used in verifying the established models.     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.     

Adaptive hierarchical positioning error compensation for long-term service of industrial robots based on incremental learning with fixed-length memory window and incremental model reconstruction

Industrial robots have been extensively used in industry, however, geometric errors mainly caused by connecting rod parameter error and non-geometric errors caused by deflection and friction, etc., limit its application in high-accuracy machining. Aiming at addressing these two types of errors, parametric methods for error compensation based on the kinematic model and non-parametric methods of directly establishing the mapping relationship between the actual and target poses of the robot end-effector are investigated and proposed. Currently both types of methods are mainly offline and will be no longer applicable when the pose of the end-effector in the workspace changes dramatically or the working performance of the robot degrades. Thus, to compensate the positioning error of an industrial robot during long-term operation, this research proposes an adaptive hierarchical compensation method based on fixed-length memory window incremental learning and incremental model reconstruction. Firstly, the correlation between positioning errors and robot poses is studied, a calibration sample library is created, and thus the actively evaluating mechanism of the pose mapping model is established to overcome the problem of the robot’ workspace having a differential distribution of error levels. Then, an incremental learning algorithm with fixed-length memory window and an incremental model reconstruction algorithm are designed to optimize the pose mapping model in terms of its parameters and architecture and overcome the problem that the performance degradation of the robot exacerbates the positioning error and affects the applicability of the pose mapping model, ensuring that the pose mapping model runs stably above the target accuracy level. Finally, the proposed method is applied to the long-term compensation case of a Stäubli industrial robot and a UR robot, and compared to state-of-art methods. Verification results show the proposed method reduces the position error of the Stäubli robot from 0.85mm to 0.13mm and orientation error from 0.68° to 0.07°, as well as reduces the position error of the UR robot from 2.11mm to 0.17mm, demonstrating that the proposed method works in real world scenarios and outperforms similar methods.     

New closed-form solution for kinematic parameter identification ofa binocular head using point measurements

This paper proposes a new closed-form solution for identifying the kinematic parameters of an active binocular head having four revolute joints and two prismatic joints by using three-dimensional (3-D) point (position) measurements of a calibration point. Since this binocular head is composed of off-the-shelf components, its kinematic parameters are unknown. Therefore, we can not directly apply those existing nonlinear optimization methods. Even if we want to use the nonlinear optimization methods, a closed-form solution can be first applied to obtain accurate enough initial values. Hence, this paper considers only methods that provide closed-form solutions, i.e., those requiring no initial estimates. Notice that most existing closed-form solutions require pose (i.e., both position and orientation) measurements. However, as far as we know, there is no inexpensive technique which can provide accurate pose measurements. Therefore, existing closed-form solutions based on pose measurements can not give us the required accuracy. As a result, we have developed a new method that does not require orientation measurements and can use only the position measurements of a calibration point to obtain highly accurate estimates of kinematic parameters using closed-form solutions. The proposed method is based on the complete and parametrically continuous (CPC) kinematic model, and can be applied to any kind of kinematic parameter identification problems with or without multiple end-effecters, providing that the links are rigid, the joints are either revolute or prismatic and no closed-loop kinematic chain is included.     

一种基于指数积的移动机械臂联合标定方法

提出一种基于指数积的移动机械臂联合标定方法,以实现移动平台和机械臂两者间位姿标定与机械臂运动学参数标定模型的统一.机械臂运动学参数标定使用最多的是基于D-H参数法,但D-H参数法无法克服相邻关节平行或接近平行时的奇异性问题,以及建模过程复杂、建模后的模型通用性差等问题.基于指数积的移动机械臂联合标定方法建模时不会因为关节轴平行而出现奇异性问题,建模过程简单.通过对整个系统的运动学方程进行微分运算,获得末端位姿误差和移动机械臂零位状态旋量误差及关节旋量误差的线性化模型.利用伴随矩阵方式建立关节旋量理论值与关节旋量实际值的关系,并通过改变伴随矩阵实现基于最小二乘法的参数辨识计算过程中参数更新.使用高精度激光跟踪仪作为测量工具,通过实验验证所提出方法的有效性.     

基于双目视觉导航的仿生机器人鲁棒控制算法

仿生机器人在定姿过程中受到空间扰动因素的影响容易产生控制误差,需要对机器人进行精确标定,提高仿生机器人的定位控制精度,因此提出一种基于双目视觉导航的仿生机器人鲁棒控制算法。利用光学CCD双目视觉动态跟踪系统进行仿生机器人的末端位姿参量测量,建立被控对象的运动学模型;以机器人的转动关节的6自由度参量为控制约束参量,建立机器人的分层子维空间运动规划模型;采用双目视觉跟踪方法实现仿生机器人的位姿自适应修正,实现鲁棒性控制。仿真结果表明,采用该方法进行仿生机器人控制的姿态定位时对机器人末端位姿参量的拟合误差较低,动态跟踪性能较好。     

Geometric calibration of industrial robots using enhanced partial pose measurements and design of experiments

The paper deals with geometric calibration of industrial robots and focuses on reduction of the measurement noise impact by means of proper selection of the manipulator configurations in calibration experiments. Particular attention is paid to the enhancement of measurement and optimization techniques employed in geometric parameter identification. The developed method implements a complete and irreducible geometric model for serial manipulator, which takes into account different sources of errors (link lengths, joint offsets, etc). In contrast to other works, a new industry-oriented performance measure is proposed for optimal measurement configuration selection that improves the existing techniques via using the direct measurement data only. This new approach is aimed at finding the calibration configurations that ensure the best robot positioning accuracy after geometric error compensation. Experimental study of heavy industrial robot KUKA KR-270 illustrates the benefits of the developed pose strategy technique and the corresponding accuracy improvement.     

机器人逆标定方法研究

在分析传统机器人位姿标定方法的基础上，提出了一种新的机器人标定方法：基于神经网络的逆标定方法。这种标定方法把机器人实际位姿和相应的关节角误差分别作为前馈神经网络的输入和输出来训练网络，从而获得机器人任意位姿时的关节角误差值，通过修改关节值来提高机器人的位姿精度。这种标定方法把所有因素引起的误差均归结为关节角误差，无须求解机器人逆运动学方程，实现了误差的在线补偿。把标定结果与基于运动学模型的参数法的标定结果进行了比较分析。仿真和试验结果均证明了这种方法比传统方法标定效果更好，且更方便简单，避免了其他传统标定方法繁琐的建模及参数辨识过程。