Geometric and elastostatic calibration of robotic manipulator using partial pose measurements

The paper deals with the geometric and elastostatic calibration of robotic manipulator using partial pose measurements, which do not provide the end-effector orientation. The main attention is paid to the efficiency improvement of identification procedure. In contrast to previous works, the developed calibration technique is based on the direct measurements only. To improve the identification accuracy, it is proposed to use several reference points for each manipulator configuration. This allows avoiding the problem of non-homogeneity of the least-square objective, which arises in the classical identification technique with the full pose information (position and orientation). Its efficiency is confirmed by the comparison analysis, which deals with the accuracy evaluation of different identification strategies. The obtained theoretical results have been successfully applied to the geometric and elastostatic calibration of a serial industrial robot employed in a machining work cell for aerospace industry.     

Significance of observation strategy on the design of robot calibration experiments

This article examines the factors influencing the identification and observability of kinematic parameters during robot calibration. A generalized calibration experiment has been simulated using two different identification techniques. Details of the identification techniques and considerations for implementing them using standard IMSL routines are presented. The factors considered during the simulations include: initial estimates of parameters, measurement accuracy and noise, encoder resolution and uncertainty, selection of measurement configurations, number of measurements, and range of motion of the joints during observations. Results are tabulated for the various cases and suggestions are made for the design of robot calibration experiments.     

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.     

基于Solis&Wets算法的机器人最优测量构形研究

研究了机器人标定中最优测量构形的选择,采用奇异值分解方法获得了机器人误差传播矩阵的条件数,以该条件数为优化的目标函数,利用Solis&Wets算法来选择机器人的一系列最优测量构形,以最小化参数估计中测量和建模误差的影响。实验结果表明该方法的标定结果优于随机选择的标定构形的标定结果。     

Optimal planning of robot calibration experiments by genetic algorithms

In this article, techniques developed in the science of genetic computing are applied to solve the problem of optimally selecting robot measurement configurations, which is an important element in successfully completing a robot calibration experiment. Genetic algorithms are customized for a type of robot measurement configuration selection problem in which the robot workspace constraints are defined in terms of robot joint limits. Simulation studies are conducted to examine the effectiveness of the genetic algorithms for the application. ©1997 John Wiley & Sons, Inc.     

机器人的位姿标定及其误差补偿

本文用建立机器人目标空间转换矩阵的方法,通过对机器人几点位姿的标定,从而补偿这几点及以这几点为中心的小区域的误差.这种方法简便实用,仅用标定和增加一些软件的方法可使工业机器人位姿精度大大提高.     

An efficient calibration method for serial industrial robots based on kinematics decomposition and equivalent systems

Calibration of the serial industrial robot with large workspace usually requires a time-consuming measurement task due to the exponential growth of measurement configurations with respect to degrees of freedom (DOFs). To improve efficiency, this paper presents a novel calibration method based on kinematics decomposition and equivalent systems. The trick is to use three lower-mobility sub-robot systems to replace the original robot, where these sub-robots possess quite the same base and end effector to avoid detection of any intermediate frame. For calibration, each sub-robot is treated as a kinematically equivalent system that only contains configuration-dependent joint motion errors, and least-squares support vector regression (LS-SVR) is utilized for joint motion error function approximation. Calibration experiments are conducted on a 6-DOF serial robot ABB IRB 2600. Compared with other methods, the proposed method can significantly save the required measurement configurations and the controller's memory space without losing high calibration accuracy. Experimental results show that the maximum position/orientation errors can be reduced to 0.393 mm/0.038 deg. After calibration, the robot can be applied to assemble parts with small clearance successfully, further demonstrating the effectiveness of the proposed method.     

A New Algorithm for Measuring and Optimizing the Manipulability Index

The estimation of the performance characteristics of robot manipulators is crucial in robot application and design. Furthermore, studying the manipulability index for every point within the workspace of any serial manipulator is considered an important problem. Such studies are required for designing trajectories to avoid singular configurations. In this paper, a new method for measuring the manipulability index is proposed, and then some simulations are performed on different industrial manipulators such as the Puma 560 manipulator, a six DOF manipulator and the Mitsubishi Movemaster manipulator.     

Experimental kinematic calibration of parallel manipulators using a relative position error measurement system

Because of errors in the geometric parameters of parallel robots, it is necessary to calibrate them to improve the positioning accuracy for accurate task performance. Traditionally, to perform system calibration, one needs to measure a number of robot poses using an external measuring device. However, this process is often time-consuming, expensive and difficult for robot on-line calibration. In this paper, a methodical way of calibration of parallel robots is introduced. This method is performable only by measuring joint variable vector and positioning differences relative to a constant position in some sets of configurations that the desired positions in each set are fixed, but the moving platform orientations are different. In this method, measurements are relative, so it can be performed by using a simple measurement device. Simulations and experimental studies on a Hexaglide parallel robot built in the Sharif University of Technology reveal the convenience and effectiveness of the proposed robot calibration method for parallel robots.     

Robot calibration using a 3D vision-based measurement system with a single camera

One of the problems that slows the development of off-line programming is the low static and dynamic positioning accuracy of robots. Robot calibration improves the positioning accuracy and can also be used as a diagnostic tool in robot production and maintenance. This work presents techniques for modeling and performing robot calibration processes with off-line programming using a 3D vision-based measurement system. The measurement system is portable, accurate and low cost, consisting of a single CCD camera mounted on the robot tool flange to measure the robot end-effector pose relative to a world coordinate system. Radial lens distortion is included in the photogrammetric model. Scale factors and image centers are obtained with innovative techniques, making use of a multiview approach. Results show that the achieved average accuracy using a common off-the-shelf CCD camera varies from 0.2 to 0.4 mm, at distances from 600 to 1000 mm from the target, respectively, with different camera orientations. Experimentation is performed on two industrial robots to test their position accuracy improvement using the calibration system proposed: an ABB IRB-2400 and a PUMA-500. The robots were calibrated at different regions and volumes within their workspace achieving accuracy from three to six times better when comparing errors before and after calibration, if measured locally. The proposed off-line robot calibration system is fast, accurate and easy to set up.     

Dynamic analysis and determination of the joint characteristics of parallel-drive robot manipulators

This article presents a theoretical and experimental study on structural dynamic response and determination of the joint characteristics of a five degree-of-freedom industrial robot manipulator with a parallel-drive mechanism. The joints were modeled as a linear spring in parallel with a viscous damper while the link members were assumed to be rigid in this study. The dynamic equations of motion of the robot manipulator were derived using the principle of virtual work. Based on these equations, the complex structural characteristics of the manipulator were simplified by carefully arranging the manipulator in proper arm configurations to avoid coupling effects among joints. Hence, the joint stiffness and damping ratio of each joint were determined experimentally. Meanwhile, the dynamic responses of the robot manipulator were also investigated. Good correlation between computer simulations and experimental results was achieved. From the experimental study, an additional troublesome flexural mode of about 10 Hz that tends to dominate the whole dynamic response and influence the positioning accuracy of the manipulator was found due to the weakness of the structural member at the base rotation joint, which was not modeled in the dynamic equations. The results of this study will be useful in providing a basis for improving the design of mechanical components and the articulating members of industrial robot manipulators.     

Kinematic model and calibration of a robot manipulator

In the next generation of industrial robot systems, the absolute positioning accuracy of a robot manipulator is necessary for the manipulation of robot programming systems based on a CAD model database and for integration with multiple robots and hand-eye systems. This paper identifies sources of absolute positioning error, and discusses methods of creating kinematic models and robot calibration including tool-reference-point measurements. High-precision absolute positioning is a key breakthrough required to implement robot systems that can reliably execute control programs generated by offline programming.     

机械臂绝对定位精度标定关键技术综述

目前我国飞机和卫星装配仍主要采用人工装配,装配技术陈旧、机器人绝对定位精度低等问题难以满足飞机和卫星高精度、高性能的要求,阻碍了工业机器人在航空制造行业的发展,因此,在机器人柔性自动化装配过程中,如何提高机械臂绝对定位精度的标定技术已成为学术界和工业界广泛关注的焦点。为了系统地分析和总结现有的研究成果,对绝对定位精度标定方法进行了分类探讨,归纳了国内外机械臂标定技术的研究现状,详细分析了误差不确定性、冗余参数的消除及最优测量结构选择性等关键技术,并对机械臂绝对定位精度标定技术的未来发展趋势进行了构想和展望。     

Robot dynamic calibration: Optimal excitation trajectories and experimental parameter estimation

Advanced robot control schemes require an accurate knowledge of the dynamic parameters of the manipulator. This article examines various issues related to robot dynamic calibration, from generation of optimal excitation trajectories to data acquisition and filtering, and experimental inertial and friction parameter estimation. In particular, a new method is developed for the determination of optimal joint trajectories for the calibration experiment, which is based on evolutionary optimization techniques. A genetic algorithm is used to determine excitation trajectories that minimize either the condition number of the regression matrix or the logarithmic determinant of the Fisher information matrix. All the calibration steps have been carried out on a SCARA two‐link planar manipulator, and the experimental results are discussed. © 2001 John Wiley & Sons, Inc.     

三维立体视觉机械臂智能抓取分类系统的开发

采用工业相机、工业投影机、普通摄像头、计算机和机械臂开发了一套具有三维立体视觉的机械臂智能抓取分类系统。该系统采用自编软件实现了对工业相机、工业投影机的自动控制和同步，通过前期研究提出的双波长条纹投影三维形貌测量法获取了物体的高度信息，结合opencv技术和普通摄像头获取的物体二维平行面信息，实现了物体的自动识别和分类；利用串口通信协议，将上述处理后的数据传送至机械臂，系统进行几何姿态解算，实现了智能抓取，并能根据抓手上压力反馈自动调节抓手张合程度，实现自适应抓取。经实验证明该系统能通过自带的快速三维形貌获取装置实现准确、快速的抓取工作范围内的任意形状的物体并实现智能分类。     

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.     

Laser interferometry-based guidance methodology for high precision positioning of mechanisms and robots

Laser interferometry-based sensing and measurement (LISM) technique was originally investigated to perform dynamic measurements of the end effector of a robot manipulator in motion. This technique can provide dynamic position measurements in real time and has high accuracy, large working space, high sampling rate and automatic target tracking. In this paper, a methodology using LISM technique is proposed to perform laser interferometry-based guidance (LIG) for accurate positioning of a robot manipulator in high precision manufacturing operations. The methodology utilizes the LISM apparatus to guide the robot's end effector to a desired location or along a desired path by directing the robot to follow the trajectory mapped by the laser beam. This is accomplished through the establishment of techniques for path generation, sensing and data acquisition and guidance error determination and compensation in the control algorithm. The algorithms for this methodology, together with the measurement and analysis techniques are described. A number of experiments are carried out to examine and validate the proposed LIG technique. Experimental results show that the established technique can effectively improve the positioning accuracy of the robot manipulator.     

Analysis of Tsai calibration method using two- and three-dimensional calibration objects

Camera calibration is a fundamental process for both photogrammetric and computer vision. Since the arrival of the direct linear transformation method and its later revisions, new methods have been developed by several authors, such as: Tsai, Heikkilä and Zhang. Most of these have been based on the pinhole model, including distortion correction. Some of these methods, such as Tsai method, allow the use of two different techniques for determining calibration parameters: a non-coplanar calibration technique using three-dimensional (3D) calibration objects, and a coplanar technique that uses two-dimensional (2D) calibration objects. The calibration performed by observing a 3D calibration object has good accuracy, and produces very efficient results; however, the calibration object must be accurate enough and requires an elaborate configuration. In contrast, the use of 2D calibration objects yields less accurate results, is much more flexible, and does not require complex calibration objects that are costly to produce. This article compares these two different calibration procedures from the perspective of stereo measurement. Particular attention was focused on the accuracy of the calculated camera parameters, the reconstruction error in the computer image coordinates and in the world coordinate system and advanced image-processing techniques for subpixel detection during the comparison. The purpose of this work is to establish a basis and selection criteria for choosing one of these techniques for camera calibration, according to the accuracy required in each of the many applications using photogrammetric vision: robot calibration methods, trajectory generation algorithms, articulated measuring arm calibration, and photogrammetric systems.     

Prediction of geometric errors of robot manipulators with Particle Swarm Optimisation method

This paper reports on the prediction of the expected positioning errors of robot manipulators due to the errors in their geometric parameters. A Swarm Intelligence (SI) based algorithm, which is known as Particle Swarm Optimization (PSO), has been used to generate error estimation functions. The experimental system used is a Motoman SK120 manipulator. The error estimation functions are based on the robot position data provided by a high precision laser measurement system. The functions have been verified for three test trajectories, which contain various configurations of the manipulator. The experimental results demonstrate that the positioning errors of robot manipulators can be effectively predicted using some constant coefficient polynomials whose coefficients are determined by employing the PSO algorithm. It must be emphasized that once the estimation functions are obtained, there may be no need of any further experimental data in order to determine the expected positioning errors for a subsequent use in the error correction process.     

A new calibration method for joint-dependent geometric errors of industrial robot based on multiple identification spaces

This paper proposes a new calibration method for joint-dependent geometric errors of six-DoF industrial robots. Chebyshev polynomials are adopted to characterize the high-order joint-dependent geometric error model, revealing the impact of strain wave gearing errors and other sources more accurately. This effort also brings higher observability index on condition of an appropriate order. Furthermore, the geometric errors are lumped into different groups according to different sensitivities and the corresponding identification models are also established. In this way, each identification subspace contains much fewer error parameters with similar sensitivity. The simulations prove that better measurement configurations can be acquired using the proposed method according to the evaluation of observability indices. For implementation, sensor systems are designed to be fixed on joint 3 and joint 6 respectively to establish the multiple identification spaces. Alternative strategy for the robot without mechanical interface on joint 3 is also provided. Based on this, a set of real calibrations are performed and the results with joint-dependent models and multiple identification spaces indicate better identification accuracies.