Robot calibration using the CPC error model

The complete and parametrically continuous (CPC) robot kinematic modeling convention has no model singularities and allows the modeling of the robot base and tool in the same manner by which the internal links are modeled. These two properties can be utilized to construct robot kinematic error models employing the minimum number of kinematic error parameters. These error parameters are independent and span the entire geometric error space. The BASE and TOOL error models are derived as special cases of the regular CPC error model. The CPC error model is useful for both kinematic identification and kinematic compensation. This paper focuses on the derivation of the CPC error models and their use in the experimental implementation of robot calibration.     

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.     

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.     

Elasto-geometrical error and gravity model calibration of an industrial robot using the same optimized configuration set

Position error is a significant limitation for industrial robots in high-precision machining and manufacturing. Efficient error measurement and compensation for robots equipped with end-effectors are difficult in industrial environments. This paper proposes a robot calibration method based on an elasto–geometrical error and gravity model. Firstly, a geometric error model was established based on the D-H method, and the gravity and compliance error models were constructed to predict the elastic deformation caused by the self-weight of the robot. Subsequently, the position error model was established by considering the attitude error of the robot flange coordinate system. A two-step robot configuration selection method was developed based on the sequential floating forward selection algorithm to optimize the robot configuration for calibrating the position error and gravity models. Then, the geometric error and compliance coefficient were identified simultaneously based on the hybrid evolution algorithm. The gravity model parameters were identified based on the same algorithm using the joint torque signal provided by the robot controller. Finally, calibration and compensation experiments were conducted on a KR-160 industrial robot equipped with a spindle using a laser tracker and internal robot data. The experimental results show that the robot tool center point error can be significantly improved by using the proposed method.     

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.     

Kinematic calibration of a five-bar planar parallel robot using all working modes

We present a simple low-cost calibration procedure that improves the planar positioning accuracy of a double-arm SCARA robot to levels difficult or impossible to achieve using an equivalent serial robot. Measurements are based on the use of five custom designed magnetic tooling balls fixed to the periphery of a detachable working plate. Three of these tooling balls define the world reference frame of the robot, and the positions of the centers of all balls are measured on a CMM. A special magnetic cup end-effector is used. Measurements are taken by manually positioning the end-effector over each of the tooling balls, with each of the maximum of four possible robot configurations. Each of these measurements is repeatable to within±0.015 mm. The robot calibration model includes all 12 kinematic parameters, and the calibration method used is based on the linearization of the direct kinematics model in each calibration configuration. The optimal number and location of the tooling balls is obtained by studying the observability index. Finally, an experimental validation at 14 additional tooling balls shows that the maximum position error with respect to the world frame is reduced to 0.080 mm within the entire robot's workspace of 600 mm×600 mm.     

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.     

服务机器人智能空间中顶棚投影器建模与外参数标定

研究服务机器人智能空间中顶棚投影器的运动学建模和外参数标定问题.首先,利用D-H方法对投影器进行运动学建模;然后,给出一种全新的求解一类关于旋转矩阵方程组的非线性迭代优化算法,以完成投影器的外参数标定;最后进行了实验验证.实验结果表明,所提出的投影器建模方法和外参数标定算法具有很高的精度,经过标定后的投影器能够在地面上投射出完全按期望路径引导机器人运动的激光斑点,从而实现低成本服务机器人高效和精确地导航.     

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.     

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.     

Simplifying the kinematic calibration of parallel mechanisms using vision-based metrology

In this paper, a vision-based measuring device is proposed and experimentally demonstrated to be an accurate, flexible, and low-cost tool for the kinematic calibration of parallel mechanisms. The accuracy and ease of use of the proposed vision sensor are outlined, with the suppression of the need for an accurate calibration target, and adequacy to the kinematic calibration process is investigated. In particular, identifiability conditions with the use of such an exteroceptive sensor are derived, considering the calibration with inverse or implicit models. Extensive results are given, with the evaluation of the measuring device and the calibration of an H4 robot. Using the full-pose measurement, an experimental analysis of the optimal calibration model is achieved, with study of the kinematic behavior of the mechanism. The efficiency of the provided method is thus evaluated, and the applicability of vision-based measuring devices to the context of kinematic calibration of parallel mechanisms is discussed.     

A novel XY-Theta precision table and a geometric procedure for its kinematic calibration

Spatial precision positioning devices are often based on parallel robots, but when it comes to planar positioning, the well-known serial architecture is virtually the only solution available to industry. Problems with parallel robots are that most are coupled, more difficult to control than serial robots, and have a small workspace. In this paper, new parallel robot is proposed, which can deliver accurate movements, is partially decoupled and has a relatively large workspace. The novelty of this parallel robot lies in its ability to achieve the decoupled state by employing legs of a different kinematic structure. The robot repeatability is evaluated using a CMM and so are the actual lead errors of its actuators. A simple geometric method is proposed for directly identifying the actual base and mobile reference frames, two actuator's offsets and one distance parameter, using a measurement arm from FARO Technologies. While this method is certainly not the most efficient one, it yields a satisfactory improvement of the robot accuracy without the need for any background in robot calibration. An experimental validation shows that the position accuracy achieved after calibration is better than 0.339 mm within a workspace of approximately 150 mm×200 mm.     

Autonomous robot calibration using a trigger probe

This paper presents a new robot autonomous calibration method using a trigger probe. The robot grips a simple probe (which was manufactured as a standard end-effector tool) automatically to touch constraint planes in a workspace (the locations of the constraint planes are not necessarily known exactly). The robot internal sensor measurements are recorded for kinematic calibration while the tip-point of the probe is in contact with the constraint plane. The kinematic constraint conditions are obtained from the known shape of the constraint surface, rather than from the measured reference locations in a workspace. The new method eliminates any use of external measuring devices for robot end-effector location measurements for robot calibration; thus it is suitable for a periodic robot re-calibration in a shop-floor environment. Both simulation and experimental results for a six degree-of-freedom (DOF) PUMA robot are given in this paper. The evaluation results using an external precision measuring device — Coordinate Measuring Machine(CMM) — are also presented.     

机器人几何连杆参数辨识

本文给出了一种通用的机器人几何连杆参数估计方法.基于机器人运动学模型和运动学 误差模型,可以推导出包含未知参数的线性输入输出方程;然后采用最小二乘法得到参数估计 值.该方法已应用于PUMA机器人参数辨识.     

Kinematic calibration of modular reconfigurable robots using product-of-exponentials formula

A modular reconfigurable robot system is a collection of individual link and joint components that can be assembled into different robot geometries for specific task requirements. However, the machining tolerance and assembly errors at the module interconnections affect the positioning accuracy of the end-effector. This article describes a novel kinematic calibration algorithm for modular robots based on recursive forward dyad kinematics. The forward kinematic model derived from the Product-of-Exponentials formula is configuration independent. The error correction parameters are assumed to be in the relative initial positions of the dyads. Two calibration models, namely the six- and seven-parameter methods, are derived on the grounds of the linear superposition principle and differential transformation. An iterative least square algorithm is employed for the calibration solution. Two simulation examples of calibrating a three-module manipulator and a 4-DOF SCARA type manipulator are demonstrated. The result has shown that the average positioning accuracy of the end-effector increases two orders of magnitude after the calibration. © 1997 John Wiley & Sons, Inc.     

一种新型机器人自标定装置及其算法

针对传统基于几何约束的机器人自标定装置仅能对局部工作空间内的机器人位型进行标定测量的问题,提出了一种由安装于机器人末端的球心位置测量装置和可移动球杆组成的新型便携式机器人自标定装置,通过利用球面约束和距离约束,可在较大工作空间内对机器人进行标定测量,从而提高标定结果的可靠性．根据可移动球杆的单、双球布置方式,分别建立了基于向量差和距离差的2种机器人自标定模型及其算法．通过采用局部指数积公式并引入位置伴随变换矩阵,简化了2种自标定模型,从而降低了对运动学方程线性化的计算量．最后,对一种6自由度串联机器人进行了仿真实验,实验结果表明2种自标定算法均能够快速收敛,验证了2种算法的有效性和鲁棒性．     

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。     

Uncalibrated Eye-to-Hand Visual Servoing Using Inverse Fuzzy Models

A new uncalibrated eye-to-hand visual servoing based on inverse fuzzy modeling is proposed in this paper. In classical visual servoing, the Jacobian plays a decisive role in the convergence of the controller, as its analytical model depends on the selected image features. This Jacobian must also be inverted online. Fuzzy modeling is applied to obtain an inverse model of the mapping between image feature variations and joint velocities. This approach is independent from the robot's kinematic model or camera calibration and also avoids the necessity of inverting the Jacobian online. An inverse model is identified for the robot workspace, using measurement data of a robotic manipulator. This inverse model is directly used as a controller. The inverse fuzzy control scheme is applied to a robotic manipulator performing visual servoing for random positioning in the robot workspace. The obtained experimental results show the effectiveness of the proposed control scheme. The fuzzy controller can position the robotic manipulator at any point in the workspace with better accuracy than the classic visual servoing approach.     

Kinematic Calibration of a Parallel Manipulator for a Semi-physical Simulation System

In the application of a semi-physical simulation system of a space docking mechanism, the simulation precision is determined by pose accuracy of the parallel manipulator. In order to improve pose accuracy, an effective kinematic calibration method is presented to enable the full set of kinematic parameter errors to be estimated by measuring the docking mechanism’s poses. A new calibration model that takes into account geometrical parameter errors and coordinates transformation errors is derived by using a differential geometry method. Based on the calibration model, an iterative least square algorithm is utilized to calculate the above errors. Simulation and experimental results show the calibration method can obviously improve pose accuracy.     

A new approach to improve absolute positioning accuracy of robot manipulators

This article describes a new calibration system for robot manipulators which improves their absolute positioning accuracy by using parameter-estimation algorithms based on the Newton method. When 3D position data of the specified points on a manipulator and the joint encoder values are input to the calibration system, the system estimates the offset values of joint encoders, link lengths, and position and orientation of the manipulator base coordinate system with respect to the world coordinate system which is difficult to obtain by conventional calibration methods. This calibration system can be applied to various manipulator types by just changing the basic kinematic equations. The system employs an algebraic programming system called REDUCE to automatically reduce the manipulator kinematic equation and partial differential calculus in the Newton method. For efficiency, first only the arm part with three degrees of freedom and then the hand part are calibrated. The experimental results demonstrate the effectiveness of this system by reducing the robot's absolute positioning errors to the order of repeatability errors.