A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal,Inverse-Kinematic and Geometric-Constraint Error Models

Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.

Relationships between Terrain Features and Forecasting Errors of Surface Wind Speeds in a Mesoscale Numerical Weather Prediction Model

Numerical weather prediction(NWP)models have always presented large forecasting errors of surface wind speeds over regions with complex terrain.In this study,surface wind forecasts from an operational NWP model,the SMS-WARR(Shanghai Meteorological Service-WRF ADAS Rapid Refresh System),are analyzed to quantitatively reveal the relationships between the forecasted surface wind speed errors and terrain features,with the intent of providing clues to better apply the NWP model to complex terrain regions.The terrain features are described by three parameters:the standard deviation of the model grid-scale orography,terrain height error of the model,and slope angle.The results show that the forecast bias has a unimodal distribution with a change in the standard deviation of orography.The minimum ME(the mean value of bias)is 1.2 m s^(-1) when the standard deviation is between 60 and 70 m.A positive correlation exists between bias and terrain height error,with the ME increasing by 10%−30%for every 200 m increase in terrain height error.The ME decreases by 65.6%when slope angle increases from(0.5°−1.5°)to larger than 3.5°for uphill winds but increases by 35.4%when the absolute value of slope angle increases from(0.5°−1.5°)to(2.5°−3.5°)for downhill winds.Several sensitivity experiments are carried out with a model output statistical(MOS)calibration model for surface wind speeds and ME(RMSE)has been reduced by 90%(30%)by introducing terrain parameters,demonstrating the value of this study.

Kinematic Calibration and Forecast Error Compensation of a 2-DOF Planar Parallel Manipulator

Due to large workspace,heavy-duty and over-constrained mechanism,a small deformation is caused and the precision of the 2-DOF planar parallel manipulator is affected.The kinematic calibration cannot compensate the end-effector errors caused by the small deformation.This paper presents a method combined step kinematic calibration and linear forecast real-time error compensation in order to enhance the precision of a two degree-of-freedom(DOF) planar parallel manipulator of a hybrid machine tool.In the step kinematic calibration phase of the method,the end-effector errors caused by the errors of major constant geometrical parameters is compensated.The step kinematic calibration is based on the minimal linear combinations(MLCs) of the error parameters.All simple and feasible measurements in practice are given,and identification analysis of the set of the MLCs for each measurement is carried out.According to identification analysis results,both measurement costs and observability are considered,and a step calibration including step measurement,step identification and step error compensation is determined.The linear forecast real-time error compensation is used to compensate the end-effector errors caused by other parameters after the step kinematic calibration.Taking the advantages of the step kinematic calibration and the linear forecast real-time error compensation,a method for improving the precision of the 2-DOF planar parallel manipulator is developed.Experiment results show that the proposed method is robust and effective,so that the position errors are kept to the same order of the measurement noise.The presented method is attractive for the 2-DOF planar parallel manipulator and can be also applied to other parallel manipulators with fewer than six DOFs.

Multi-camera calibration method based on minimizing the difference of reprojection error vectors

In order to achieve a high precision in three-dimensional（3D） multi-camera measurement system, an efficient multi-cameracalibration method is proposed. A stitching method of large scalecalibration targets is deduced, and a fundamental of multi-cameracalibration based on the large scale calibration target is provided.To avoid the shortcomings of the method, the vector differencesof reprojection error with the presence of the constraint conditionof the constant rigid body transformation is modelled, and mini-mized by the Levenberg-Marquardt （LM） method. Results of thesimulation and observation data calibration experiment show thatthe accuracy of the system calibrated by the proposed methodreaches 2 mm when measuring distance section of 20 000 mmand scale section of 7 000 mm × 7 000 mm. Consequently, theproposed method of multi-camera calibration performs better thanthe fundamental in stability. This technique offers a more uniformerror distribution for measuring large scale space.

Self-calibration and Compensation of Setting Errors for Surface Profile Measurement of a Microstructured Roll Workpiece

Microstructured roll workpieces have been widely used as functional components in the precision industries. Current researches on quality control have focused on surface profile measurement of microstructured roll workpieces, and types of measurement systems and measurement methods have been developed. However, low measurement efficiency and low measurement accuracy caused by setting errors are the common disadvantages for surface profile measurement of microstructured roll workpieces. In order to shorten the measurement time and enhance the measurement accuracy, a method for self-calibration and compensation of setting errors is proposed for surface profile measurement of microstructured roll workpieces. A measurement system is constructed for the measurement, in which a precision spindle is employed to rotate the roll workpiece and an air-bearing displacement sensor with a micro-stylus probe is employed to scan the microstructured surface of the roll workpiece. The resolution of the displacement sensor is 0.14 nm and that of the rotary encoder of the spindle was 0.15r~. Geometrical and mathematical models are established for analyzing the influences of the setting errors of the roll workpiece and the displacement sensor with respect to the axis of the spindle, including the eccentric error of the roll workpiece, the offset error of the sensor axis and the zero point error of the sensor output. Measurement experiments are carded out on a roll workpiece on which periodic microstructures are a period of 133 i^m along the circumferential direction. Experimental results demonstrate the feasibility of the self-compensation method. The proposed method can be used to detect and compensate the setting errors without using any additional accurate artifact.

On-Line Measurement of the Chemical Oxygen Demand in Wastewater in a Pulp and Paper Mill Using Near Infrared Spectroscopy

Although near infrared (NIR) spectroscopy has been evaluated for numerous applications, the number of actual on-line or even on-site industrial applications seems to be very limited. In the present paper, the attempts to produce online predictions of the chemical oxygen demand (COD) in wastewater from a pulp and paper mill using NIR spectroscopy are described. The task was perceived as very challenging, but with a root mean square error of prediction of 149 mg/l, roughly corresponding to 1/10 of the studied concentration interval, this attempt was deemed as successful. This result was obtained by using partial least squares model regression, interpolated reference values for calibration purposes, and by evenly distributing the calibration data in the concentration space. This work may also represent the first industrial application of online COD measurements in wastewater using NIR spectroscopy.

Dynamic Calibrating Technique for Super－Precision Gyrorotor Measuring Instrument

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A Survey of Error Analysis and Calibration Methods for MEMS Triaxial Accelerometers

MEMS accelerometers are widely used in various fields due to their small size and low cost,and have good application prospects.However,the low accuracy limits its range of applications.To ensure data accuracy and safety we need to calibrate MEMS accelerometers.Many authors have improved accelerometer accuracy by calculating calibration parameters,and a large number of published calibration methods have been confusing.In this context,this paper introduces these techniques and methods,analyzes and summarizes the main error models and calibration procedures,and provides useful suggestions.Finally,the content of the accelerometer calibration method needs to be overcome.

NOVEL METHOD FOR ERROR ANALYSIS AND SELF-CALIBRATION OF LASER TRACKING MIRROR MECHANISM

Laser tracking system （LTS） is an advanced device for large size 3D coordinates measuring with the advantages of broad range, high speed and high accuracy. However, its measuring accuracy is highly dominated by the geometric errors of the tracking mirror mechanism. Proper calibration of LTS is essential prior to the use of it for metrology. A kinematics model that describes not only the motion but also the geometric variations of LTS is developed. Through error analysis of the proposed model, it is claimed that gimbals axis misalignments and tracking mirror center off-set are the key contributors to measuring errors of LTS. A self-calibration method is presented of calibrating LTS with planar constraints. Various calibration strategies utilizing single-plane and multiple-plane constraints are proposed for different situations. For each calibration strategy, issues about the error parameter estimation of LTS are exploded to find out in which conditions these parameters can be uniquely estimated. Moreover, these conditions reveal the applicability of the planar constraints to LTS self-calibration. Intensive studies have been made to check validity of the theoretical results. The results show that the measuring accuracy of LTS has increased by 5 times since this technique for calibration is used.

Calibration and compensation methods of installation error of electronic compass

Installation error angle is one of the factors that affect the accuracy of electronic compass used for geomagnetic navigation.To solve this problem,the calibration and compensation methods for installation error angle are studied.By analyzing the generation mechanism of installation error angle of electronic compass,an installation error model is established,compensation formulae are derived,and calibration scheme is proposed.To verify the correctness of the calibration and compensation methods,the verification experiment is conducted by computer simulation.The simulation results show that the proposed calibration and compensation methods are effective and practical.

Automatic calibration for wobble errors in shallow water multibeam bathymetries

The wobble errors caused by the imperfect integration of motion sensors and transducers in multibeam echo-sounder systems(MBES)manifest as high-frequency wobbles in swaths and hinder the accurate expression of high-resolution seabed micro-topography under a dynamic marine environment.There are many types of wobble errors with certain coupling among them.However,those current calibration methods ignore the coupling and are mainly manual adjustments.Therefore,we proposed an automatic calibration method with the coupling.First,given the independence of the transmitter and the receiver,the traditional georeferenced model is modified to improve the accuracy of footprint reduction.Secondly,based on the improved georeferenced model,the calibration model associated with motion scale,time delay,yaw misalignment,lever arm errors,and soundings is constructed.Finally,the genetic algorithm(GA)is used to search dynamically for the optimal estimation of the corresponding error parameters to realize the automatic calibration of wobble errors.The simulated data show that the accuracy of the calibrated data can be controlled within 0.2%of the water depth.The measured data show that after calibration,the maximum standard deviation of the depth is reduced by about 5.9%,and the mean standard deviation of the depth is reduced by about 11.2%.The proposed method has significance in the precise calibration of dynamic errors in shallow water multibeam bathymetrie s.

Error Coefficient Estimation of Inertial Platform in Its Calibration

The error coefficient estimation of inertial platform in the course of its consecutive ground calibration is studied.A separate-bias algorithm is adopted to estimate the error parameters effectively. The ill-conditioning problem of the equation solution caused by the huge state dimension is also resolved. And the simulation result shows its validity.

10-Bit Single-Slope ADC with Error Calibration for TDI CMOS Image Sensor

A 10-bit single-slope analog-to-digital converter (ADC) for time-delay-integration CMOS image sensor was proposed. A programmable ramp generator was applied to accomplish the error calibration and improve the linearity. The ADC was fabricated in a 180 nm 1P4M CMOS process. Experimental results indicate that the differential nonlinearity and integral nonlinearity were 0.51/-0.53 LSB and 0.63/-0.71 LSB, respectively. The sampling rate of the ADC was 32 kHz.

Research on Consistency Judgement of Indication Error for Calibration Result of Humidity Sensor in Meteorology

In order to solve the lack of relevant evaluation research on the accuracy of HMP155A humidity sensor calibration results in the past, this paper designs the corresponding experimental scheme, and obtains the corresponding calibration results according to the experimental scheme;Then the measurement uncertainty of the indication error in the calibration results is evaluated by GUM, and the corresponding extended uncertainty U95 is obtained. Finally, according to the requirements of JJF1094-2016 characteristic evaluation of measuring instruments, combined with the calibration results and the actual situation of U95, the conformity of the indication error of calibration is determined. The result is that each calibration point of the sensor meets the requirements of conformity determination and is within the qualified range. This research effectively makes up for the blank of the previous research on the conformity determination of the indication error of the calibration results and has strong theoretical and practical significance.

Novel camera calibration method based on invariance of collinear points and pole-polar constraint

To address the eccentric error of circular marks in camera calibration,a circle location method based on the invariance of collinear points and pole–polar constraint is proposed in this paper.Firstly,the centers of the ellipses are extracted,and the real concentric circle center projection equation is established by exploiting the cross ratio invariance of the collinear points.Subsequently,since the infinite lines passing through the centers of the marks are parallel,the other center projection coordinates are expressed as the solution problem of linear equations.The problem of projection deviation caused by using the center of the ellipse as the real circle center projection is addressed,and the results are utilized as the true image points to achieve the high precision camera calibration.As demonstrated by the simulations and practical experiments,the proposed method performs a better location and calibration performance by achieving the actual center projection of circular marks.The relevant results confirm the precision and robustness of the proposed approach.

Sensor array calibration for uniform rectangular array in presence of mutual coupling and sensor gain-and-phase errors

The sensor array calibration methods tailored to uniform rectangular array(URA)in the presence of mutual coupling and sensor gain-and-phase errors were addressed.First,the mutual coupling model of the URA was studied,and then a set of steering vectors corresponding to distinct locations were numerically computed with the help of several time-disjoint auxiliary sources with known directions.Then,the optimization modeling with respect to the array error matrix(defined by the product of mutual coupling matrix and sensor gain-and-phase errors matrix)was constructed.Two preferable algorithms(called algorithm I and algorithm II)were developed to minimize the cost function.In algorithm I,the array error matrix was regarded as a whole parameter to be estimated,and the exact solution was available.Compared to some existing algorithms with the similar computation framework,algorithm I can make full use of the potentially linear characteristics of URA's error matrix,thus,the calibration precision was obviously enhanced.In algorithm II,the array error matrix was decomposed into two matrix parameters to be optimized.Compared to algorithm I,it can further decrease the number of unknowns and,thereby,yield better estimation accuracy.However,algorithm II was incapable of producing the closed-form solution and the iteration operation was unavoidable.Simulation results validate the excellent performances of the two novel algorithms compared to some existing calibration algorithms.

Towards cognitive navigation:A biologically inspired calibration mechanism for the head direction cell network

To derive meaningful navigation strategies,animals have to estimate their directional headings in the environment.Accordingly,this function is achieved by the head direction cells that were found in mammalian brains,whose neural activities encode one’s heading direction.It is believed that such head direction information is generated by integrating self-motion cues,which also introduces accumulative errors in the long term.To eliminate such errors,this paper presents an efficient calibration model that mimics the animals’behavior by exploiting visual cues in a biologically plausible way,and then implements it in robotic navigation tasks.The proposed calibration model allows the agent to associate its head direction and the perceived egocentric direction of a visual cue with its position and orientation,and therefore to calibrate the head direction when the same cue is viewed again.We examine the proposed head direction calibration model in extensive simulations and real-world experiments and demonstrate its excellent performance in terms of quick association of information to proximal or distal cues as well as accuracy of calibrating the integration errors of the head direction.Videos can be viewed at https://videoviewsite.wixsite.com/hdc-calibration.

工业机器人手眼标定综合实验设计

为了提高工业机器人技术课程的多学科交叉应用与集成创新能力培养的教学效果,设计了一种针对眼在手外模式的机械臂手眼标定综合实验。采用机械臂、相机、标定板和Visual Studio软件完成手眼标定工程化实验平台的搭建,利用软件编程将采集到的机械臂末端位姿信息转化为位姿矩阵,获得了标定板图片中圆心位置并求解了手眼矩阵,最后进行标定结果误差分析。通过熟悉设备、编写代码、调试程序、测试验证等步骤,帮助学生理解手眼标定理论知识,增强应用实践和创新能力。

一种基于光电自准直法的装甲战车原位校炮系统

为了解决当前装甲战车校炮时空受限、精度低、过程复杂、无法现场原位校炮等问题,提出了一种基于光电自准直法的装甲战车原位校炮系统。基于镜炮一致性原理,设计校炮装置的机械结构;构建平行光管及其内部光路结构,利用光学自准直原理实现模拟无穷远处虚拟靶标;建立校炮装置的误差模型,通过对误差模型进行分析与合成以评定校炮装置参数的精确性,确定装置允许的最大误差值;通过实验对系统性能进行了实际测试与验证。结果表明:利用所设计的误差模型,其校准误差最大不超过传统校炮方式的60%,且时间缩短了一半以上,符合设计要求,具有较强的稳定性。装甲战车原位校炮系统可应用于装甲战车校炮工作,提高校炮的效率及精度、实现现场原位校准,为装甲战车校炮提供了一种新方法、新思路。

随机噪声平板下光学复眼内外参联合标定

光学复眼在无人系统的精确定位制导、避障导航等任务中得到了越来越广泛的应用,其中光学复眼的高精度标定是保障上述任务质量的前提。通常经典的张氏棋盘格标定法要求光学复眼的每个子眼都必须观测到完整的棋盘格,然而,由于光学复眼结构的复杂性,在实际标定过程中难以满足这一要求。为解决张氏标定法的局限性,该文提出一种基于随机噪声平板的光学复眼内外参联合标定算法,该算法通过子眼拍摄随机噪声平板的局部信息,可简单快速地实现任意构型和子眼数量的光学复眼内外参联合标定。为了提高光学复眼标定的稳定性,设置多阈值匹配机制解决子眼视场特征点数量稀疏导致图像匹配失效的问题。同时,给出了光学复眼内外参联合标定的误差模型,用来衡量所提出算法的精确度。在与张氏棋盘格标定法进行实验对比中,验证所提算法的稳定性和鲁棒性,并在光学复眼实物系统中,验证了所提联合标定算法具有较高的精度。