一种新的摄像机线性标定方法

计算机视觉中,在对景物进行定量分析或对物体进行精确定位时,都需要进行摄像机标定,即准确确定摄影机的内部参数和外部参数,因此寻找新的快速有效的摄像机标定计算方法是计算机视觉应用中的一个重要问题。为也快速有效地进行摄像机的标定,并针对常用的带有一阶径向畸变的摄像机模型,提出了一种线性求解摄像机参数的标定方法,它可分步标定各参数,且全部采用线性方法求解,从而避免了非线性优化中的不稳定性,使得算法更为实用,简单快捷。实验结果表明,该方法具有较高的标定精度,是一种实用的标定方法。     

3D靶标的摄像机三步标定算法与实现

摄像机标定是计算机视觉中的一个必不可少的重要环节,其标定精度影响着三维重建结果的精度。利用摄像机对一个三维正交的棋盘格拍摄一幅有效靶标图像,提取角点,第一步通过透视变换矩阵算法线性求解各内外参数;第二步引入径向和切向畸变,将第一步求得的内外参数作为初始值,求得畸变系数的解;第三步对内参数进行线性优化,得到更为精确的内参数值;最后求解反投影后图像坐标的绝对误差。实验结果表明,该方法具有较高的精度,且简单有效。     

3D靶标的摄像机三步标定算法与实现

摄像机标定是计算机视觉中的一个必不可少的重要环节,其标定精度影响着三维重建结果的精度。利用摄像机对一个三维正交的棋盘格拍摄一幅有效靶标图像,提取角点,第一步通过透视变换矩阵算法线性求解各内外参数;第二步引入径向和切向畸变,将第一步求得的内外参数作为初始值,求得畸变系数的解;第三步对内参数进行线性优化,得到更为精确的内参数值;最后求解反投影后图像坐标的绝对误差。实验结果表明,该方法具有较高的精度,且简单有效。     

简便高精度的机器人手眼视觉标定方法

对摄像机成像模型进行了分析,论述了机器人手眼系统标定原理。在此基础上,不改变机器人的外臂与基坐标系的旋转关系,设计了一种机器人手眼视觉的标定方法,与传统的方法比较,它不需要预先标定摄像机的内外参数。实验证明:该方法具有算法方便快捷、实验过程简单易行,且精度高等优点,可用于机器人进行运动目标定位与跟踪。     

双目视觉的立体标定方法

为实现双目视觉系统的立体标定,分析了摄像机成像模型,并充分考虑了透镜的径向畸变和切向畸变,提出了一种新的立体标定算法。该算法利用张正友的灵活标定算法,初步求取摄像机的内参数,结合Brown算法并提取图像中角点的子像素级坐标,精确求取摄像机内参数和畸变向量。为方便后续的图像校正,基于前面的单个摄像机标定,通过计算空间中的景物点在左右摄像机成像平面上的位置关系,计算出双目视觉系统中两个摄像机之间的旋转矩阵R和平移向量T,从而实现了立体标定。实验结果表明,该算法能取得较高的精度,可以应用于双目视觉系统。     

基于Matlab工具箱的摄像机标定

研究了摄像机成像的基本原理,论述了摄像机内部参数和外部参数的推导过程,借助Matlab标定工具箱,采用平面靶标的标定方法,快速准确地完成了标定实验,得出内部参数和外部参数,并对所得外部参数进行数据处理,得出摄像机运动前后两坐标系之间的相互位置关系.     

快速有效的摄像机标定方法

提出了一种快速有效的基于径向约束的两步算法.该算法综合了线性模型和非线性模型的优点,在求解摄像机参数的过程中,采用线性模型标定摄像机中的一部分参数,进一步考虑非线性畸变,通过条件化简将非线性方程转化成线性方程求解其余摄像机参数,有效避免了直接求解非线性方程带来的计算繁琐和结果不稳定的缺陷.最后对标定结果采取最优化算法求精.实验结果表明,优化后的两步算法提高了摄像机标定的效率和准确性.     

直线运动摄像机在线动态标定

为实现AS-R智能机器人在运动情况下摄像机在线动态标定,提出一种新的基于粒子滤波的直线运动摄像机标定方法。用状态空间方法描述直线运动摄像机模型,把摄像机内参数和位置运动参数作为状态量,特征点图像坐标作为观测量,根据粒子滤波算法求得摄像机内参数和位置运动参数的最优估计,并用双线程实现整个标定过程。AS-R机器人在直线运动情况下的摄像机在线动态标定实验结果表明：该算法是合理可行的,并且具有很高的标定精度和良好的鲁棒性。该方法适用于各种类型的系统噪声。     

一种基于混沌天牛须搜索算法的摄像机标定方法

为了较好地解决传统智能优化方法在摄像机标定中存在标定精度低、效率和鲁棒性差的问题，提出一种基于混沌天牛须搜索算法的摄像机标定方法。该方法使用MATLAB标定工具箱对摄像机非线性成像模型进行预标定，预标定结果作为混沌天牛须搜索算法的初始值；构造平均重投影误差适应度函数，建立混沌天牛须搜索算法优化模型对标定参数进行优化；与基于传统智能优化方法的摄像机标定方法进行实验对比。实验结果表明，该方法得到的平均重投影误差为0.005 72像素，算法总的运行时间为46.15 s,可以有效提高摄像机标定的精度、鲁棒性与效率。     

线结构光传感器参数现场标定方法

为了精确、快速、高效地标定线结构光传感器参数,提出了一种线结构光传感器参数现场标定方法。根据摄像机标定方法,并结合L-M非线性优化算法对摄像机内外参数及镜头畸变系数进行标定。拍摄不同姿态下的平面靶标图像,利用靶标图像计算摄像机外参计算靶标上的圆点在摄像机坐标系下的三维坐标,并构建靶标平面方程。将激光线投射到不同姿态的靶标平面上,通过靶标平面方程计算出激光线上点在摄像机坐标系下的3D坐标,由不同位置重构出激光点在摄像机坐标系下的3D坐标来完成光平面参数标定。通过对摄像机参数、畸变系数和光平面参数的标定,重构目标物体进行测试。测量结果表明:该算法能够快速、准确地获取小车车体的三维坐标,并构造出车体的三维模型。该方法适用于大视场的工业现场标定。     

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.     

Modelling an arm's spatially correlated biases: an application to camera calibration for teleoperation

Calibration of the extrinsic and intrinsic parameters of cameras viewing the workspace of a teleoperated robot arm is a necessary step in the recovery of metric information for transmission to the operator. In this paper, we develop an algorithm that uses the robot slave manipulator to generate the calibration pattern of points in three dimensions which define the world frame. These points are used, along with their associated image positions, as measurements in a maximum likelihood estimation of the calibration parameters. However, the algorithm does not assume that the robot generates perfect world positions. Instead they are optimised using a model for covariance which respects the physical attributes of the robot arm and its linkages. Errors in world positions are actually correlated biases rather than stochastic noise, and so they are assigned a covariance that is a function of position and that encodes a coherence length over which relative position measurements are accurate. Experiments are presented which compare the calibration results with the camera parameters obtained using a conventional calibration grid, and which validate the proposed covariance model.     

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.     

移动机器人立体视觉高精度标定技术

摄像机标定是移动机器人立体视觉的一个关键步骤,标定精度直接影响到障碍检测和路径规划的精度。在前人研究的基础上,提出了一种迭代方式的摄像机标定算法。算法将摄像机参数分为畸变参数和非畸变参数两类,每次迭代中固定一类参数来求解另一类参数,最终得到优化解。通过合理组织参数求解次序,迭代的每一步都可以通过最小二乘法得到闭式解,从而简化了计算。算法可以方便地进行扩展以包含不同类型的畸变参数,而不会增加算法的复杂度。实验结果表明此算法可以有效提高标定精度,可用于移动机器人的视觉系统。     

基于标准圆柱的线激光轮廓扫描机器人手眼标定方法

在搭载线激光轮廓传感器的机器人平台手眼标定问题中,依靠线激光轮廓传感器输出的2维点云信息进行标定,存在标定过程复杂、标定精度低的缺点。本文针对这些问题,提出一种基于圆柱侧面约束的手眼标定方法。通过改变扫描机器人末端位姿,获得不同位姿下圆柱侧面扫描数据。对于激光平面与圆柱侧面相交得到的椭圆轮廓,利用随机抽样一致性（RANSAC）算法得到椭圆轮廓中心点坐标。利用椭圆轮廓的估计中心点到圆柱中轴线的距离建立约束优化方程,将手眼标定问题转化为约束优化问题。利用粒子群优化（PSO）算法和广义拉格朗日乘子法的融合算法求解约束优化问题,得到手眼标定的变换矩阵。最后基于所提方法进行模拟仿真和扫描重建试验。分别讨论了标定数据误差、标定参照物位置和标定参数初始值对标定结果的影响,并验证了手眼标定精度。结果表明,该方法不受标定参照物位置和标定参数初始值的影响,具有操作简单、通用性强、标定精度高等特点,标定精度在0.15mm以内,适合现场标定。     

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.     

Estimating parameters of noncentral catadioptric systems using bundle adjustment

This paper describes a new method to calibrate the intrinsic and extrinsic parameters of a generalized catadioptric camera (central or noncentral). The algorithm has two steps. The first one is the estimation of correspondences between incident lines in space and pixels (black box model calibration) in an arbitrary world reference frame. The second step is the calibration of the intrinsic parameters of the pinhole camera, the coefficients of the mirror expressed by a quadric (quadric mirror shape and the pose of the camera in relation to it), the position of the optical center of the camera in the world reference frame and its relative orientation (pose of the camera in world reference frame). A projection model relaxing Snell’s Law is derived. The deviations from Snell’s Law and the image reprojection errors are minimized by means of bundle adjustment. Information about the apparent contour of the mirror can be used to reduce the uncertainty in the estimation by introducing a new term in the cost function of the second step minimization process. Simulations and real experiments show good accuracy and robustness for this framework. However, the convergence is dependent on the initial guess as expected. A well-behaved algorithm to automatically generate the initial estimate to be used in the bundle adjustment is also presented.     

Sensitivity Analysis and Model Validation of a 2-DoF Mini Spherical Robot

This paper is focused on the development and validation of an error kinematic model of a mini spherical robot, aimed at its kinematic calibration. The robot is actually a spatial five-bar linkage, provided with two rotational degrees of freedom. A non-overconstrained kinematics is assumed for the robot in order to provide a simple mathematical model and allow a sensitivity analysis of all the involved geometric parameters. A simplified version of the model is proposed. It differs only for the degree of approximation. A comparison between full and reduced models is presented by means of numerical simulations, analyzing their behavior in a significant region of the robot workspace. In order to validate both of them a robot calibration is carried out on a physical prototype of the robot using a vision system, namely a fixed camera in a eye-to-hand configuration. An iterative algorithm aimed at the experimental identification of the geometric data of the robot is used. Some experimental results show the effectiveness of the study.