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.     

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。     

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.     

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。     

Method for kinematic calibration of stewart platforms

A Stewart platform is a six degrees of freedom parallel manipulator composed of six variable-length legs connecting a fixed base to a movable plate. Like all parallel manipulators, Stewart platforms offer high force/torque capability and high structural rigidity in exchange for small workspace and reduced dexterity. Because the solution for parallel manipulators' forward kinematics is in general much harder than their inverse kinematics, a typical control strategy for such manipulators is to specify the plate's pose in world coordinates and then solve the individual leg lengths. The accuracy of the robot critically depends on accurate knowledge of the device's kinematic parameters. This article focuses on the accuracy improvement of Stewart platforms by means of calibration. Calibration of Stewart platforms consists of construction of a kinematic model, measurement of the position and orientation of the platform in a reference coordinate frame, identification of the kinematic parameters, and accuracy compensation. A measurement procedure proposed in this article allows a great simplification of the kinematic identification. The idea is to keep the length of the particular leg, whose parameters are to be identified, fixed while the other legs change their lengths during the measurement phase. By that, redundant parameters can be eliminated systematically in the identification phase. The method also shows the estimation of each leg's parameters separately because the measurement equations are fully decoupled, which results in a drastical reduction of the computational effort in the parameter identification. Simulation results assess the performance of the proposed approach. © 1993 John Wiley & Sons, Inc.     

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.     

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.     

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.     

一种3 自由度并联柔索驱动机器人的精度研究

研究了一种3 自由度并联柔索驱动机器人精度分析和精度综合的问题．分析了影响机器人位姿精度 的主要因素,推导建立了关节误差及柔索误差模型．提出了一种精度综合算法,并基于给定的机器人关节允差, 综合分析出装配误差及柔索误差的最大取值．通过仿真验证了误差模型的正确性．样机试验表明,利用柔索误差 模型可以提高机器人的运动精度．     

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.     

Unifying Kinematic Modeling, Identification, and Control of a Gough–Stewart Parallel Robot Into a Vision-Based Framework

In this paper, it is shown that computer vision, used as an exteroceptive redundant metrology mean, simplifies the control of a Gough-Stewart parallel robot. Indeed, contrary to the usual methodology, where the robot is modeled independently from the control law which will be implemented, we take into account that vision will be used for control, from the early modeling stage. Hence, kinematic modeling and projective geometry are fused into a control-devoted projective kinematic model. Thus, a novel vision-based kinematic modeling of such a robot is proposed through the observation of its legs. Inspired by the geometry of lines, this model unifies and simplifies both identification and control. Indeed, it has a reduced parameter set, and allows us to propose a linear solution to its calibration. Using the same model, a visual servoing scheme is presented, where the attitudes of the nonrigidly linked legs are servoed, rather than the end-effector pose. Finally, theoretical results concerning the stability of this control law are provided     

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.     

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.     

基于末端转角误差的并联机器人零点标定方法

针对一种4自由度高速并联机器人（Cross-IV机器人）的零点标定问题,提出了一种基于末端转角误差信息的快速零点标定方法．基于机器人的单支链闭环矢量方程,建立了零点误差全集与末端误差之间的映射模型．通过对误差传递矩阵的分解,在仅利用旋转编码器对末端转角误差进行测量的基础上,构建了该机器人的快速零点误差辨识模型．为进一步最大化测量效率及提高辨识矩阵的鲁棒性,提出了一种优化的测量点选择方案．通过仿真详细验证了该零点标定方法的鲁棒性与准确性．基于激光跟踪仪的验证实验表明,经标定后机器人末端位置误差降低至1.312 mm,转角误差降低至0.202°,标定结果表明该零点标定方法简单、有效．     

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.     

Robotic Hand Pose Estimation Based on Stereo Vision and GPU-enabled Internal Graphical Simulation

Humanoid robots have complex kinematic chains whose modeling is error prone. If the robot model is not well calibrated, its hand pose cannot be determined precisely from the encoder readings, and this affects reaching and grasping accuracy. In our work, we propose a novel method to simultaneously i) estimate the pose of the robot hand, and ii) calibrate the robot kinematic model. This is achieved by combining stereo vision, proprioception, and a 3D computer graphics model of the robot. Notably, the use of GPU programming allows to perform the estimation and calibration in real time during the execution of arm reaching movements. Proprioceptive information is exploited to generate hypotheses about the visual appearance of the hand in the camera images, using the 3D computer graphics model of the robot that includes both kinematic and texture information. These hypotheses are compared with the actual visual input using particle filtering, to obtain both i) the best estimate of the hand pose and ii) a set of joint offsets to calibrate the kinematics of the robot model. We evaluate two different approaches to estimate the 6D pose of the hand from vision (silhouette segmentation and edges extraction) and show experimentally that the pose estimation error is considerably reduced with respect to the nominal robot model. Moreover, the GPU implementation ensures a performance about 3 times faster than the CPU one, allowing real-time operation.     

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.     

基于对偶四元数的机器人方位与手眼关系同时标定方法

针对相机姿态估计及机器人运动学正解存在测算偏差时,手眼标定及机器人坐标系-世界坐标系标定结果不能准确收敛到全局最优解的问题,提出了一种基于对偶四元数理论的机器人方位与手眼关系同时标定方法.该方法首先将标定方程中坐标系刚体变换关系用螺旋轴、旋转角度和平移量参数化表示,再结合全局优化算法对平移量进行优化.搭建了PUMA560机器人数值仿真系统和工业机器人实测实验平台,将该方法与经典的四元数和对偶四元数标定方法进行了比较分析.仿真和实测结果表明,在相机姿态估计及机器人运动学正解存在测量误差的情况下,该方法无需初值估计和数据筛选依然可以保证求解结果的最优性.     

激光线扫式形貌测量机器人的标定研究

为能够高效、高精度的获取大型自由曲面物体的形貌,研究了基于通用工业机器人和激光线扫描传感器的测量方法。论述了激光线扫式形貌测量系统的原理与结构,利用标准球及优化算法实现了机器人和激光扫描传感器位姿关系的精确解算,并针对机器人运动学误差对系统测量影响较大,通过对机器人运动学参数的修正有效减小了机器人的绝对定位误差。实验和分析结果表明,经标定和运动学参数校正后的测量系统对标准球的测量能达到较高精度,为采集高精度三维点云提供了保证。