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.     

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 Currently both types of methods are mainly offline and will be no longer applicable when the pose of the end-effector in the workspace changes dramatically or the working performance of the robot degrades.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.     

工业机器人定位误差规律分析及基于ELM算法的精度补偿研究

针对工业机器人应用于飞机零部件自动化钻孔时绝对定位精度较差的问题,提出利用极限学习机（ELM）算法建立机器人法兰中心点理论位置与实际位置之间的误差模型,并优化补偿机器人定位精度的方法．首先基于空间网格采样方法,获得了机器人绝对定位误差沿机器人基坐标系不同方向的误差变化规律,分析了建模补偿的可行性;其次建立基于ELM算法的误差补偿模型,并针对误差模型训练中隐含层神经元个数取值问题进行了分析优化．实验结果表明,机器人绝对定位误差值沿其坐标系不同方向存在不同的变化规律,补偿前绝对定位误差分布范围为0.29 mm~0.58 mm,平均误差为0.41 mm;补偿后定位误差分布范围降低到0.04 mm~0.32 mm,平均误差为0.18 mm;采用ELM算法建模的补偿速度快,泛化性能好．     

Accuracy improvement of a 3D passive laser tracker for the calibration of industrial robots

The laser tracker has been used as the mainstream instrument for the position accuracy calibration of industrial robots for quite a long time. However, due to the complexity of the built-in dual-axis active servo tracking system, its cost is high and the target reflector has to adjust its pose frequently, so it cannot be popularized in the production and application sites of industrial robots. Based on this drawback, a 3D passive laser tracker (3DPLT) with high precision, simple structure, easy operation and low cost is proposed in this paper. Firstly, the overall structure of the system is designed, and its position error model based on the principle of spherical coordinate measurement and vector transfer method is established. Then, the error parameters are identified by experiments to formulate the error compensation model. Finally, the multi-pose and large-range spatial error compensation verification experiments of the system are carried out on a commercial coordinate measuring machine. The results show that the spatial volumetric errors of the 3DPLT can achieve within 40 μm after compensation with a good repeatability of ±4 μm. A comparison contouring test with a commercial ballbar is also carried out to validate its applicability of robot calibration.     

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.     

Static calibration of industrial manipulators: Design of an optical instrumentation and application to SCARA robots

This article presents a method for the static calibration of industrial robots based on optical measurements using a laser. Measured pose errors are used to estimate the geometric errors in the links. This allows the prediction of the pose error for every robot configuration, permitting the improvement of accuracy by means of slight variations of the joint motions. After a theoretical introduction on the methodology, it is applied to a SCARA robot analyzing the design of the set-up and the final precision that could be achieved. Preliminary experimental results are also presented. © 1996 John Wiley & Sons, Inc.     

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.     

Improve the robot calibration accuracy using a dynamic online fuzzy error mapping system.

Traditional robot calibration implements model and modeless methods. The compensation of position error in modeless method is to move the end-effector of robot to the target position in the workspace, and to find the position error of that target position by using a bilinear interpolation method based on the neighboring 4-point's errors around the target position. A camera or other measurement devices can be utilized to find or measure this position error, and compensate this error with the interpolation result. This paper provides a novel fuzzy interpolation method to improve the compensation accuracy obtained by using a bilinear interpolation method. A dynamic online fuzzy inference system is implemented to meet the needs of fast real-time control system and calibration environment. The simulated results show that the compensation accuracy can be greatly improved by using this fuzzy interpolation method compared with the bilinear interpolation method.     

基于位置反解算法的并联机器人坐标变换方法

目的为提高工作效率,提升工业机器人的可靠性、稳定性和运动精度,避免机器人出现速度以及加速度的突变,对机器人的位置进行准确的控制。方法 以RBT-6T03P并联机器人为例,应用坐标变化法和位置反解算法对并联机器人机构的位置坐标进行分析并利用MATLAB进行仿真。结果 结果表明：通过位置反解对并联机器人的坐标进行变换求解是方便可行。结论 所述控制方法相对于并联机器人求正解算法更加简单、方便、快捷。     

Three methodologies for the calibration of industrial manipulators: Experimental results on a SCARA robot

This article presents and compares three algorithms for the geometric parameter identification of industrial robots to increase its accuracy (static calibration). The estimation is based on the measure of the gripper pose errors when the robot follows suitable trajectories. The algorithms are general and can be applied to any robot providing that its kinematics is known. After a theoretical introduction to the general methodologies, these are applied to a selective compliance assembly robot arm (SCARA) robot analyzing its performance (precision, efficiency). Experimental results obtained with three methodologies are presented and discussed. The measure of the gripper pose error is based on a laser triangulation technique whose working principles are also recalled. © 2000 John Wiley & Sons, Inc.     

基于粒子群优化算法的工业机器人定位抓取控制系统设计

为消除工业机器人实际抓取位置与定位位置之间的误差,实现对机器人抓取行为的有效控制,设计基于粒子群优化算法的工业机器人定位抓取控制系统。根据主要机器部件选型情况建立电气网络结构,再联合视觉传感器与定位控制平台,控制抓取夹爪的行动范围,完成工业机器人定位抓取控制系统硬件的总体设计。遵循粒子群优化算法应用需求,实施Gbest选取与Pbest更新,并联合所得计算结果,定义三维坐标系表达式,建立基于粒子群优化算法的定位坐标系。根据跟踪点坐标求解结果,确定控制系数优化处理条件,完善抓取控制原则,再联合相关应用结构,实现基于粒子群优化算法的工业机器人定位抓取控制系统的设计。实验结果表明,粒子群优化算法作用下,工业机器人实际抓取位置坐标在X轴、Y轴方向上均准确符合定位位置坐标,有效消除了抓取误差,能够实现对机器人抓取行为的有效控制。     

矢量场逐次逼近的康复机器人柔顺交互控制

为了实现康复机器人的主动柔顺交互,提出了一种基于矢量场逐次逼近的控制模型;设计了矢量场逐次逼近系统,可输出机器人关节期望位移,该输出能与输入的扭矩、表面肌电及脑电等信号在振幅、频率和相位上保持同步,且通过调节遗忘因子参数值,可改变主动柔顺交互的积极性;利用自行设计的穿着型下肢康复机器人样机进行柔顺辅助实验,以验证所提出控制模型的有效性;通过FFT（Fast Fourier transformation）频谱对机器人关节扭矩的组成成分进行了分析,并采用基于最小二乘法的参数辨识方法实施了重力补偿,以便康复机器人实时控制.实验结果表明,该控制模型对于实现康复机器人与人之间的柔顺交互是有效的.     

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.     

五轴磨抛机器人补偿算法研究与实现

通过分析基于模型的补偿方法和非模型补偿方法的优缺点,结合一个五轴磨抛机器人的结构特点,提出了两种补偿方法相结合的混合补偿算法．针对平移关节误差的主要来源难于建模的特点,采用非模型的方法进行补偿;针对转动关节误差主要来源为几何参数误差,能够建模,但有些参数随机器人末端位置不同而变化的特点,采用二者相结合的混合方法进行补偿．通过对该机器人系统的实验,验证了方法的有效性和可行性．     

Estimation and Compensation of Gravity and Friction Forces for Robot Arms: Theory and Experiments

This paper considers the estimation and compensation of the unknown gravity force and static friction for robot motion control. Utilizing the stability feature of PD set-point control, the estimates of gravity-related parameters and static friction can be solved from two steady state equations obtained by stopping robots at two nonsingular positions. The estimates obtained can then be used to eliminate the position error. Under a mild assumption that the mass center of each robot link is distributed on a straight line connecting two adjacent joints, the gravity force regression matrix becomes upper-triangle which can significantly simplify the algorithm. The positive experimental result obtained for practical verification is also presented.     

一种新的机器人机构距离误差模型及补偿算法

在标定机器人绝对位置精度和实施误差综合补偿过程中,必然涉及到测量系统坐标系与机器人基础坐标系间的变换.由于这一变换很难精确测定.从而给机器人绝对位置精度标定与误差补偿带来了难以克服的困难.本文首次提出了一种新的机器人机构距离误差计算模型及补偿算法,论证了距离误差同样可以作为机器人绝对位置精度的一种度量.利用该模型和算法对机器人进行误差分析和实施误差综合补偿,可避开上述测量系统与机器人系统间的坐标变换,从而简化了机器人绝对位置精度的标定过程,为提高机器人的绝对位置精度开辟了一个新的简便的途径.     

Mobile Robot Self-Localization without Explicit Landmarks

Localization is the process of determining the robot's location within its environment. More precisely, it is a procedure which takes as input a geometric map, a current estimate of the robot's pose, and sensor readings, and produces as output an improved estimate of the robot's current pose (position and orientation). We describe a combinatorially precise algorithm which performs mobile robot localization using a geometric model of the world and a point-and-shoot ranging device. We also describe a rasterized version of this algorithm which we have implemented on a real mobile robot equipped with a laser rangefinder we designed. Both versions of the algorithm allow for uncertainty in the data returned by the range sensor. We also present experimental results for the rasterized algorithm, obtained using our mobile robots at Cornell. Received November 15, 1996; revised January 13, 1998.     

一般7R串联机器人标定的仿真与实验

为了标定一般7R冗余度串联机器人的所有几何参数,提出了一种实效的算法．首先,使用D-H矩阵对机器人建立了运动学模型和几何参数识别模型,对雅可比矩阵进行奇异值分解并对分解后的正交阵的最后5行进行初等行变换,以确定需要补偿的几何参数．通过机器人关节角和末端手爪位置的测量数据,计算雅可比矩阵以及手爪位置理论值和实测值的误差,采用最小二乘法对机器人的尺寸参数进行补偿量的计算．仿真过程表明,在有测量扰动的情况下,算法是稳定的和可靠的．最后,对机器人进行了实际的测量和标定,取得了满意的结果．     

面向工业零件的机器人单目立体匹配与抓取

为实现通用性强、快速、准确的工业机器人6自由度零件抓取,提出了一种基于单目视觉引导的零件3维抓取方法．首先,采用按倾角分层的Chamfer距离匹配算法建立图像与待匹配模板的相似度函数,并运用爬山法局部优化的遗传算法搜索最优匹配结果;然后,通过CAD（计算机辅助设计）模型建立离线3D模板库,将匹配算法拓展到适用于复杂结构零件的空间6自由度位姿检测;最后,由各坐标系间的矩阵转换和系统标定得到机器人的抓取信息,从而实现零件的3维抓取．实验结果表明,优化后的位姿检测算法在匹配速度和准确性上均有所提升,且基于该检测算法的机器人3维抓取实验的位置误差在2 mm以内、转角误差在2°以内,可用于工业智能机器人的零件抓取．     

Error-model-based robot calibration using a modified CPC model

Selection of a proper robot kinematic model is a critical step in error-model-based robot calibration. The Denavit-Hartenberg (DH) model exhibits singularities in calibration of robots having consecutive parallel joint axes. The complete and parametrically continuous (CPC) modeling technique is one of the more versatile alternative modeling conventions designated to fit the needs of manipulator calibration. No modeling convention is, however, perfect. One “user-unfriendly” aspect of the CPC model is a condition handling technique needed, when constructing the error model, to avoid model singularities due to the adoption of the direction vectors of the joint axes as link parameters.This paper presents a modification to the CPC model which brings the model closer to the DH model. Rather than using the direction vectors of joint axes, the modified CPC (MCPC) model employs angular parameters to acommodate the required rotations for each link transformation. This modification results in a much simplified error model. The model, like the CPC model, is capable of completely describing the geometry and motion of the manipulator in a reference coordinate frame. Its error model possesses a minimum number of parameters to span the entire geometric error space and it can be made singularity-free by proper selection of the tool axis. This paper presents a calibration study of the PUMA robot using the MCPC model. A moving stereo camera system was employed for end-effector pose measurements. The MCPC error model was then used for kinematic identification. Results on the PUMA arm show that the MCPC performs well for robot calibration. The well-defined structure and user friendliness of the MCPC model may facilitate the implementation of robot calibration techniques on the factory floor.