Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM

Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.

Research on Hand-eye Calibration Technology of Visual Service Robot Grasping Based on ROS

For the hand-eye calibration of the vision service robot,the traditional hand-eye calibration tech-nology can’t be realized which because the service robot is independently developed and there is no teaching device to feed back the pose information of the service robot in real time.In this paper,a hand-eye calibration method based on ROS(Robot Operating System)is proposed.In this method,ROS system is used to accurately control the arm of the service robot to rotate in different positions for many times.Meanwhile,the head camera of the service robot takes images of a fixed point in the scene.Then,the nonlinear equations were established ac-cording to the homography matrix of the two images and the position and pose information of the ROS system,and the accurate hand-eye relationship was optimized by the least square method.Finally,an experimental platform is built and the proposed hand-eye calibration method is verified.The experiment results show that the method is easy to operate,simple algorithm and correct result,which verifies the effectiveness of the algorithm and provides conditions for the realization of humanoid grasping of visual service robot.

IABC: An iteratively automatic machine learning boosted hand-eye calibration method for laser displacement sensor

An on-machine measuring(OMM)system with a laser displacement sensor(LDS)is designed for measuring free-form surfaces of hypersonic aircraft’s radomes.To improve the measurement accuracy of the OMM system,a novel Iteratively Automatic machine learning Boosted hand-eye Calibration(IABC)method is proposed.Both the hand-eye relationship and LDS measurement errors can be calibrated in one calibration process without any hardware changes via IABC.Firstly,a new objective function is derived,containing analytical parameters of the handeye relationship and LDS errors.Then,a hybrid calibration model composed of two kernels is proposed to solve the objective function.One kernel is the analytical kernel designed for solving analytical parameters.Another kernel is the automatic machine learning(AutoML)kernel designed to model LDS errors.The two kernels are connected with stepwise iterations to find the best calibration results.Compared with traditional methods,hand-eye experiments show that IABC reduces the calibration RMSE by about 50%.Verification experiments show that IABC reduces the measurement deviations by about 25%-50%and RMSEs within 40%.Even when the training data are obviously less than the test data,IABC performs well.Experiments demonstrate that IABC is more accurate than traditional hand-eye methods.

Effective Self-calibration for Camera Parameters and Hand-eye Geometry Based on Two Feature Points Motions

A novel and effective self-calibration approach for robot vision is presented, which can effectively estimate both the camera intrinsic parameters and the hand-eye transformation at the same time. The proposed calibration procedure is based on two arbitrary feature points of the environment, and three pure translational motions and two rotational motions of robot endeffector are needed. New linear solution equations are deduced,and the calibration parameters are finally solved accurately and effectively. The proposed algorithm has been verified by simulated data with different noise and disturbance. Because of the need of fewer feature points and robot motions, the proposed method greatly improves the efficiency and practicality of the calibration procedure.

Development of a novel hand-eye calibration for intuitive control of minimally invasive surgical robot

Robotic-assisted surgical system has introduced a powerful platform through dexterous instrument and hand-eye coordination intuitive control.The knowledge of laparoscopic vision is a crucial piece of information for robot-assisted minimally invasive surgery focusing on improved surgical outcomes.Obtaining the transformation with respect to the laparoscope and robot slave arm frames using hand-eye calibration is essential,which is a key component for developing intuitive control algorithm.We proposed a novel two-step modified dual quaternion for hand-eye calibration in this study.The dual quaternion was exploited to solve the hand-eye calibration simultaneously and powered by an iteratively separate solution.The obtained hand-eye calibration result was applied to the intuitive control by using the hand-eye coordination criterion.Promising simulations and experimental studies were conducted to evaluate the proposed method on our surgical robot system.We extensively compared the proposed method with state-of-the-art methods.Results demonstrate this method can improve the calibration accuracy.The effectiveness of the intuitive control algorithm was quantitatively evaluated,and an improved hand-eye calibration method was developed.The relationship between laparoscope and robot kinematics can be established for intuitive control.

Wavelength calibration and spectral analysis of vacuum ultraviolet spectroscopy in EAST

A vacuum ultraviolet(VUV)spectroscopy with a focal length of 1 m has been engineered specifically for observing edge impurity emissions in Experimental Advanced Superconducting Tokamak(EAST).In this study,wavelength calibration for the VUV spectroscopy is achieved utilizing a zinc lamp.The grating angle and charge-coupled device(CCD)position are carefully calibrated for different wavelength positions.The wavelength calibration of the VUV spectroscopy is crucial for improving the accuracy of impurity spectral data,and is required to identify more impurity spectral lines for impurity transport research.Impurity spectra of EAST plasmas have also been obtained in the wavelength range of 50–300 nm with relatively high spectral resolution.It is found that the impurity emissions in the edge region are still dominated by low-Z impurities,such as carbon,oxygen,and nitrogen,albeit with the application of fulltungsten divertors on the EAST tokamak.

A Weakly-Supervised Crowd Density Estimation Method Based on Two-Stage Linear Feature Calibration

In a crowd density estimation dataset,the annotation of crowd locations is an extremely laborious task,and they are not taken into the evaluation metrics.In this paper,we aim to reduce the annotation cost of crowd datasets,and propose a crowd density estimation method based on weakly-supervised learning,in the absence of crowd position supervision information,which directly reduces the number of crowds by using the number of pedestrians in the image as the supervised information.For this purpose,we design a new training method,which exploits the correlation between global and local image features by incremental learning to train the network.Specifically,we design a parent-child network(PC-Net)focusing on the global and local image respectively,and propose a linear feature calibration structure to train the PC-Net simultaneously,and the child network learns feature transfer factors and feature bias weights,and uses the transfer factors and bias weights to linearly feature calibrate the features extracted from the Parent network,to improve the convergence of the network by using local features hidden in the crowd images.In addition,we use the pyramid vision transformer as the backbone of the PC-Net to extract crowd features at different levels,and design a global-local feature loss function(L2).We combine it with a crowd counting loss(LC)to enhance the sensitivity of the network to crowd features during the training process,which effectively improves the accuracy of crowd density estimation.The experimental results show that the PC-Net significantly reduces the gap between fullysupervised and weakly-supervised crowd density estimation,and outperforms the comparison methods on five datasets of Shanghai Tech Part A,ShanghaiTech Part B,UCF_CC_50,UCF_QNRF and JHU-CROWD++.

Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift.In this method, the geometric parameters are calibrated by the traditional calibration method at first. Then, in order to calibrate the parameters affected by the random colored noise, the expectation maximization (EM) algorithm is introduced. Through the use of geometric parameters calibrated by the traditional calibration method, the iterations under the EM framework are decreased and the efficiency of the proposed method on embedded system is improved. The performance of the proposed kinematic calibration method is compared to the traditional calibration method. Furthermore, the feasibility of the proposed method is verified on the EI-MoCap system. The simulation and experiment demonstrate that the motion capture precision is significantly improved by 16.79%and 7.16%respectively in comparison to the traditional calibration method.

Non-crossing Quantile Regression Neural Network as a Calibration Tool for Ensemble Weather Forecasts

Despite the maturity of ensemble numerical weather prediction(NWP),the resulting forecasts are still,more often than not,under-dispersed.As such,forecast calibration tools have become popular.Among those tools,quantile regression(QR)is highly competitive in terms of both flexibility and predictive performance.Nevertheless,a long-standing problem of QR is quantile crossing,which greatly limits the interpretability of QR-calibrated forecasts.On this point,this study proposes a non-crossing quantile regression neural network(NCQRNN),for calibrating ensemble NWP forecasts into a set of reliable quantile forecasts without crossing.The overarching design principle of NCQRNN is to add on top of the conventional QRNN structure another hidden layer,which imposes a non-decreasing mapping between the combined output from nodes of the last hidden layer to the nodes of the output layer,through a triangular weight matrix with positive entries.The empirical part of the work considers a solar irradiance case study,in which four years of ensemble irradiance forecasts at seven locations,issued by the European Centre for Medium-Range Weather Forecasts,are calibrated via NCQRNN,as well as via an eclectic mix of benchmarking models,ranging from the naïve climatology to the state-of-the-art deep-learning and other non-crossing models.Formal and stringent forecast verification suggests that the forecasts post-processed via NCQRNN attain the maximum sharpness subject to calibration,amongst all competitors.Furthermore,the proposed conception to resolve quantile crossing is remarkably simple yet general,and thus has broad applicability as it can be integrated with many shallow-and deep-learning-based neural networks.

Calibration of CO and CO2 Monitors Used in Periodic Inspection of Vehicles at Fixed Stations for Environmental Control

Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuring the quantitative assessment of emissions for informed decisions on environmental treatments. This paper describes a method for the calibration of CO/CO2 monitors used for periodic inspections of vehicles in cites. The calibration was performed in the selected ranges: 900 - 12,000 µmol/mol for CO and 2000 - 20,000 µmol/mol for CO2. The traceability of the measurement results to the SI units was ensured by using certified reference materials from CO/N2 and CO2/N2 primary gas mixtures. The method performance was evaluated by assessing its linearity, accuracy, precision, bias, and uncertainty of the calibration results. The calibration data exhibited a strong linear trend with R² values close to 1, indicating an excellent fit between the measured values and the calibration lines. Precision, expressed as relative standard deviation (%RSD), ranged from 0.48 to 4.56% for CO and from 0.97 to 3.53% for CO2, staying well below the 5% threshold for reporting results at a 95% confidence level. Accuracy measured as percent recovery, was consistently high (≥ 99.1%) for CO and ranged from 84.90% to 101.54% across the calibration range for CO2. In addition, the method exhibited minimal bias for both CO and CO2 calibrations and thus provided a reliable and accurate approach for calibrating CO/CO2 monitors used in vehicle inspections. Thus, it ensures the effectiveness of exhaust emission control for better environment.

Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage(TSID)model is a novel and powerful constitutive model for rock-like materials.This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone.The basic parameters of sandstone are determined through a series of static and dynamic tests,including uniaxial compression,Brazilian disc,triaxial compression under varying confining pressures,hydrostatic compression,and dynamic compression and tensile tests with a split Hopkinson pressure bar.Based on the sandstone test results from this study and previous research,a step-by-step procedure for parameter calibration is outlined,which accounts for the categories of the strength surface,equation of state(EOS),strain rate effect,and damage.The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions.Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters.The methodology presented in this study is scientifically sound,straightforward,and essential for improving the TSID model.Furthermore,it has the potential to contribute to other rock constitutive models,particularly new user-defined models.

Global Calibration Method for Monocular Multi-View System Using Rotational Dual-Target

To make the problems of existing high requirements of calibration tools, complex global calibration process addressed for monocular multi-view visual measurement system during measurement, in the paper, a global calibration method is proposed for the geometric properties of rotational correlation motion and the absolute orientation of the field of view without over lap. Firstly, a dual-camera system is constructed for photographing and collecting the rotating image sequence of two flat targets rigidly connected by a long rod at different positions, and based on the known parameters, such as, target feature image, world coordinates, camera internal parameters and so on, then the global PnP optimization method is used to solve the rotation axis and the reference point at different positions;Then, the absolute orientation matrix is constructed based on the parameters of rotation axis, reference point and connecting rod length obtained by this method. In the end, the singular value decomposition method is used to find the optimal rotation matrix, and then get the translation matrix. It’s shown based on simulation and actual tests that in comparison with the existing methods, the maximum attitude and pose errors is 0.0083˚ and 0.3657 mm, respectively, which improves the accuracy by 27.8% and 24.4%, respectively. The calibration device in this paper is simple, and there are no parallel, vertical and coplanar requirements between multiple rotating positions. At the same time, in view of the calibration accuracy, the accuracy requirements of most application scenarios can be met.

New self-calibration approach to space robots based on hand-eye vision

To overcome the influence of on-orbit extreme temperature environment on the tool pose(position and orientation) accuracy of a space robot,a new self-calibration method based on a measurement camera(hand-eye vision) attached to its end-effector was presented.Using the relative pose errors between the two adjacent calibration positions of the space robot,the cost function of the calibration was built,which was different from the conventional calibration method.The particle swarm optimization algorithm(PSO) was used to optimize the function to realize the geometrical parameter identification of the space robot.The above calibration method was carried out through self-calibration simulation of a six-DOF space robot whose end-effector was equipped with hand-eye vision.The results showed that after calibration there was a significant improvement of tool pose accuracy in a set of independent reference positions,which verified the feasibility of the method.At the same time,because it was unnecessary for this method to know the transformation matrix from the robot base to the calibration plate,it reduced the complexity of calibration model and shortened the error propagation chain,which benefited to improve the calibration accuracy.

On the calibration and verification of Voronoi-based discontinuous deformation analysis for modeling rock fracture

Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

Design and development of the deep-rock in-situ condition-preserved coring calibration platform

To systematically validate and calibrate the theory and technology of the deep in-situ conditionpreserved coring, the in-situ conditions at different depths should be simulated, and the full-size coring tests should be carried out in this simulated environment. Therefore, a deep-rock in-situ conditionpreserved coring calibration platform was designed and developed. The self-tightening sealing structure and the quick-disassembly structure were designed on the basis of an innovative segmented nonuniformdiameter structure, which was a breakthrough from the traditional high-pressure vessel frame and was verified by finite element simulation and actual testing under extreme working conditions, respectively.To simulate the actual deep in-situ environment with a temperature of 150℃ and pressure of 140 MPa for a large Φ450 mm×H1400 mm core, temperature and pressure control systems were designed by coupling, and a pre-embedded high-pressure-resistant temperature sensor was designed. Finally, highprecision assembly automation, complex movement coordination of the coring device with the platform,and rotary dynamic sealing were achieved by utilizing the combination of adaptive cabin body servo control and an adaptive mechanical structure in a limited space, laying a solid foundation for the calibration of in-situ condition-preserved coring.

Easy to Calibrate:Marker-Less Calibration of Multiview Azure Kinect

Reconstructing a three-dimensional(3D)environment is an indispensable technique to make augmented reality and augmented virtuality feasible.A Kinect device is an efficient tool for reconstructing 3D environments,and using multiple Kinect devices enables the enhancement of reconstruction density and expansion of virtual spaces.To employ multiple devices simultaneously,Kinect devices need to be calibrated with respect to each other.There are several schemes available that calibrate 3D images generated frommultiple Kinect devices,including themarker detection method.In this study,we introduce a markerless calibration technique for Azure Kinect devices that avoids the drawbacks of marker detection,which directly affects calibration accuracy;it offers superior userfriendliness,efficiency,and accuracy.Further,we applied a joint tracking algorithm to approximate the calibration.Traditional methods require the information of multiple joints for calibration;however,Azure Kinect,the latest version of Kinect,requires the information of only one joint.The obtained result was further refined using the iterative closest point algorithm.We conducted several experimental tests that confirmed the enhanced efficiency and accuracy of the proposed method for multiple Kinect devices when compared to the conventional markerbased calibration.

On-orbit Geometric Calibration and Preliminary Accuracy Evaluation of GF-14 Satellite

GF-14 satellite is a new generation of sub-meter stereo surveying and mapping satellite in China,carrying dual-line array stereo mapping cameras to achieve 1∶10000 scale topographic mapping without Ground Control Points(GCPs).In fact,space-based high-precision mapping without GCPs is a challenging task that depends on the close cooperation of several payloads and links,of which on-orbit geometric calibration is one of the most critical links.In this paper,the on-orbit geometric calibration of the dual-line array cameras of GF-14 satellite was performed using the control points collected in the high-precision digital calibration field,and the calibration parameters of the dual-line array cameras were solved as a whole by alternate iterations of forward and backward intersection.On this basis,the location accuracy of the stereo images using the calibration parameters was preliminarily evaluated by using several test fields around the world.The evaluation result shows that the direct forward intersection accuracy of GF-14 satellite images without GCPs after on-orbit geometric calibration reaches 2.34 meters(RMS)in plane and 1.97 meters(RMS)in elevation.

Cross-satellite calibration of high-energy electron fluxes measured by FengYun-4A based on Arase observations

We use the High-energy Electron Experiments(HEP)instrument onboard Arase(ERG)to conduct an energy-dependent cross-satellite calibration of electron fluxes measured by the High Energy Particle Detector(HEPD)onboard FengYun-4A(FY-4A)spanning from April 1,2017,to September 30,2019.By tracing the two-dimensional magnetic positions(L,magnetic local time[MLT])of FY-4A at each time,we compare the datasets of the conjugate electron fluxes over the range of 245–894 keV in 6 energy channels for the satellite pair within different sets of L×MLT.The variations in the electron fluxes observed by FY-4A generally agree with the Arase measurements,and the percentages of the ratios of electron flux conjunctions within a factor of 2 are larger than 50%.Compared with Arase,FY-4A systematically overestimates electron fluxes at all 6 energy channels,with the corresponding calibration factors ranging from 0.67 to 0.81.After the cross-satellite calibration,the electron flux conjunctions between FY-4A and Arase show better agreement,with much smaller normalized root mean square errors.Our results provide a valuable reference for the application of FY-4A high-energy electron datasets to in-depth investigations of the Earth’s radiation belt electron dynamics.

A machine learning approach to TCAD model calibration for MOSFET

Machine learning-based surrogate models have significant advantages in terms of computing efficiency. In this paper, we present a pilot study on fast calibration using machine learning techniques. Technology computer-aided design(TCAD) is a powerful simulation tool for electronic devices. This simulation tool has been widely used in the research of radiation effects.However, calibration of TCAD models is time-consuming. In this study, we introduce a fast calibration approach for TCAD model calibration of metal–oxide–semiconductor field-effect transistors(MOSFETs). This approach utilized a machine learning-based surrogate model that was several orders of magnitude faster than the original TCAD simulation. The desired calibration results were obtained within several seconds. In this study, a fundamental model containing 26 parameters is introduced to represent the typical structure of a MOSFET. Classifications were developed to improve the efficiency of the training sample generation. Feature selection techniques were employed to identify important parameters. A surrogate model consisting of a classifier and a regressor was built. A calibration procedure based on the surrogate model was proposed and tested with three calibration goals. Our work demonstrates the feasibility of machine learning-based fast model calibrations for MOSFET. In addition, this study shows that these machine learning techniques learn patterns and correlations from data instead of employing domain expertise. This indicates that machine learning could be an alternative research approach to complement classical physics-based research.

Ground calibration of the Mars orbiter magnetometer onboard Tianwen-1

Ground calibration experiments of the Mars orbiter magnetometer(MOMAG)onboard the orbiter of Tianwen-1 were performed to determine the sensitivity,misalignment angle,and offset of the sensors.The linearity of the applied calibrated magnetic fields and the output from the sensors were confirmed to be better than 10^(-4),and the sensor axes were orthogonal to each other within 0.5 degrees.The temperature dependencies of the sensitivity and misalignment angle were examined,but no clear signatures of temperature dependencies could be seen.Sensor offset and the stability of sensor offset drift with a temperature change were also determined by the rotation method.The stability of the sensor offset drift was less than 0.01 nT/℃.The ground calibration of MOMAG determines all the calibration parameters of the sensors for accurate magnetic field measurements in orbit with the appropriate corrections.