Realization of orientation interpolation of 6-axis articulated robot using quaternion

In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.

Circular Interpolation Algorithms of 5-Axis Simultaneous CNC System

Spatial circular arc can be machined conveniently by a 5-axis NC machine tool.Based on the data sampling method,circular interpolation in two-dimensional plane is discussed briefly.The key is to solve the problem of circular center ex- pressed in the workpiece coordinate system by means of the transformation matrix.Circular interpolation in three-dimensional space is analyzed in detail.The method of undetermined coefficient is used to solve the center of the spatial circle and the method of coor- dinate transformation is used to transform the spatial circle into the XY-plane.Circular arc in three-dimensional space can be ma- chined by the positional 5-axis machining and the conical surface can be machined by the continuous 5-axis machining.The velocity control is presented to avoid the feedrate fluctuation.The interpolation algorithms are tested by a simulation example and the inter- polation algorithms are proved feasible.The algorithms are applied to the 5-axis CNC system software.

Realization Methodology of a 5-axis Spline Interpolator in an Open CNC System

By making use of the advantages of non-uniform rational B-spline （NURBS） curves to represent spatial curves, an instruction format with double NURBS curves suitable for 5-axis coordinated real-time interpolation is presented to replace the current 5-axis coordinated linear interpolation method defective in low-speed, low-accuracy and enormous numerical control （NC） files in sculptured surface machining. A generation procedure of the NC files with the presented format is introduced and the method to realize the interpolation in an open computer numerical control （CNC） system is developed by ourselves. These illustrated the feasibility of the proposed method and its capability of avoiding all the shortages of 5-axis linear interpolation method.

Nominal Model-Based Sliding Mode Control with Backstepping for 3-Axis Flight Table

Based on nominal model, a novel global sliding mode controller （GSMC） with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.

A Real-time NURBS Surface Interpolator for 5-axis Surface Machining

A real-time non-uniform rational B-spline （NURBS） surface interpolator is proposed and 5-axis machining method with a flat-end cutter is discussed. With the Taylor expansion and the coordinate transformation, the algorithms of NURBS interpolation, cutter effective machining radius, cutter offsetting and.inverse kinematics are deduced and implemented, respectively. Different from the conventional free-form surface machining, the proposed interpolator can real-time generate the motion commands of computer numerical control （CNC） machines with CC feedrate, rather than that of CL. An example part surface is demonstrated and the results of simulation show that the proposed method can be applied in actual 5-axis surface machining.

Stiffness of Postural Alignment System Based on 3-Axis Actuators for Large Aircraft Components

Aircraft digital flexible assembly fixture and technologies are widely used in developed countries, while the traditional jig-based assembly mode is still used in China. The application study of aircraft digital flexible assembly system is just beginning in our country recently. To meet the requirements of automated posture alignment and join in digital assembly system for large aircraft components, a novel fitting fixture called 3-axis actuator is developed. On the basis of the actuators, three kinds of posture alignment system for large aircraft components are proposed, including the non-redundant system, the redundant actuating system, and the redundant leg system, and their constitutions and properties are introduced. Through deriving the feeding transmission stiffness model of single actuator and analyzing the inverse kinematics of these systems, the relationship between the external force and the changes of position and orientation of large aircraft component is obtained, and then the postural alignment stiffness models are established. With the method mentioned above, the postural alignment stiffness of three systems is computed by using the algebraic formulate, and the results show that redundant properties can increase system＇s postural alignment stiffness. As an example, a optimized layout of the assembly system for a given model of aircraft is developed, the results of application show that the layout has many advantages, such as high accuracy, stiffness, stability, reliability, efficiency and flexible, which can satisfy the requirement of aircraft digital assembly system well. The proposed study of postural alignment stiffness for different systems can supply the theoretic support for the optimization layout design of aircraft digital assembly system, and contribute to evaluate the system working performance of systems.

QFT Robust Control Design for 3-Axis Flight Table Servo System with Large Friction

The 3-axis flight table is an important device and a typical high performanceposition and speed servo system used in the hardware-in-the-loop simulation of flight controlsystem. Friction force and uncertainty are the main characteristics in the 3-axis flight table servosystem. Based on the description of dynamic and static model of a nonlinear Stribeck frictionmodel, and taking account of the practical uncertainties of 3-axis flight table servo system, theQFT controller is designed. Simulation and realtime results are presented.

3D Medical Image Interpolation Based on Parametric Cubic Convolution

In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter,which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.

Hybrid 3D printed three-axis force sensor aided by machine learning decoupling

Identification of magnitude and orientation for spatially applied loading is highly desired in the fields of not only the machinery components but also human-machine interaction.Despite the fact that the 3-axis force sensor with different structures has been proposed to measure the spatial force,there are still some common limitations including the multi-step manufacturing-assembly processes and complicated testing of decoupling calibration.Here,we propose a rapid fabrication strategy with low-cost to achieve high-precision 3-axis force sensors.The sensor is designed to compose of structural Maltese cross base and sensing units.It is directly fabricated within one step by a hybrid 3D printing technology combining deposition modeling(FDM)with direct-ink-writing(DIW).In particular,a machine learning(ML)model is used to convert the strain signal to the force components.Instead of a mount of calibration tests,this ML model is trained by sufficient simulation data based on programmed batch finite element modeling.This sensor is capable of continuously identifying a spatial force with varying magnitude and orientation,which successfully quantify the applied force of traditional Chinese medicine physiotherapy including Gua Sha and massage.This work provides insight for design and rapid fabrication of multi-axis force sensors,as well as potential applications.

Three-Dimensional Modeling of the Retinal Vascular Tree via Fractal Interpolation

In recent years,the three dimensional reconstruction of vascular structures in the field of medical research has been extensively developed.Several studies describe the various numerical methods to numerical modeling of vascular structures in near-reality.However,the current approaches remain too expensive in terms of storage capacity.Therefore,it is necessary to find the right balance between the relevance of information and storage space.This article adopts two sets of human retinal blood vessel data in 3D to proceed with data reduction in the first part and then via 3D fractal reconstruction,recreate them in a second part.The results show that the reduction rate obtained is between 66%and 95%as a function of the tolerance rate.Depending on the number of iterations used,the 3D blood vessel model is successful at reconstruction with an average error of 0.19 to 5.73 percent between the original picture and the reconstructed image.

基于OCO-2/OCO-3数据的山东省CO_(2)柱浓度特征分析

基于OCO-2/OCO-3卫星数据,通过空间插值的方法,分季节模拟山东省CO_(2)柱浓度的时空分布特征,并对模拟结果进行了验证。结果表明:观测值与模拟值之间有较高的相关性,大部分误差值在±1 ppm之间。山东省CO_(2)柱浓度年均值为415.06 ppm,空间上各季节差异明显,整体上呈现中部和南部浓度较低、西北浓度偏高的特征;时间上表现为冬季浓度高、夏季浓度低的趋势。

Building 3-D Human Data Based on Handed Measurement and CNN

3-dimension(3-D)printing technology is growing strongly with many applications,one of which is the garment industry.The application of human body models to the garment industry is necessary to respond to the increasing personalization demand and still guarantee aesthetics.This paper proposes amethod to construct 3-D human models by applying deep learning.We calculate the location of the main slices of the human body,including the neck,chest,belly,buttocks,and the rings of the extremities,using pre-existing information.Then,on the positioning frame,we find the key points(fixed and unaltered)of these key slices and update these points tomatch the current parameters.To add points to a star slice,we use a deep learning model tomimic the form of the human body at that slice position.We use interpolation to produce sub-slices of different body sections based on the main slices to create complete body parts morphologically.We combine all slices to construct a full 3-D representation of the human body.

一类含参的C^(3)连续单位四元数插值样条曲线

为调控单位四元数样条曲线的局部形状,以方便刚体关键帧动画设计,提出一种基于欧氏空间中含参七次多项式的单位四元数样条曲线.该样条曲线满足C^(3)连续性并能自动插值任意给定的一系列关键帧方向,同时样条曲线的形状可局部调控.通过数值实验具体分析了参数的改变对样条曲线形状的影响.

基于细化等值面拓扑的病灶切片三维重建方法

脑组织病灶切片的三维重构对于了解神经胶质神经瘤状态具有重要意义,可用于鉴别诊断、手术模拟等。移动立方体(MC)算法是经典的多边形曲面重建算法,具有简单易实现的优点,但其存在低效且梯级现象明显的情况。针对该问题,本研究提出一种细化等值面拓扑的病灶切片空间堆叠重建方法(SSR-RI),旨在实现拓扑构形与运行效率的优化。SSR-RI通过构建空间坐标系对磁共振图像(MRI)切片邻近图进行处理,为了改善双线性插值法中图像分量易受损的问题,提出一种自适应空间插值法,根据灰度值变化自适应选择插值点,对周围进行扩充。在结合等法线顶点的基础上,设计了一种细化等值面提取方式的堆叠重建方法,以提高堆叠速度,并减少梯级问题。为了进一步优化SSR-RI的三维重建效果,提出一种改进的局部反射光照法(PR)以绘制三维病变,利用镜面颜色反射(SCR)与镜面指数(SE)对重建体进行渲染优化。使用公开脑肿瘤分割数据集BraTS的618例病例开展三维重建实验,以验证所提出方法性能。实验结果显示,所提算法的重建时间只需2.124 s,F-score值达到0.845,SSIM值达到0.81,相较于MC算法减少了38%的重建时间,F-score值和SSIM值分别提高了30.89%和38.4%。重构体序列间结构紧密,视觉效果更富立体感和纹理感,有效地提高了三维重建的绘制效率。

基于改进PSO-GSA算法的时间最优轨迹规划

传统3-5-3多项式插值轨迹规划算法速度和加速度规划过于保守,与机械臂运动极限条件相差较远,没有充分发挥其运动性能,从而导致机械臂完成任务的时间增长。针对上述问题,本文提出一种基于改进PSO-GSA算法的3-5-3多项式插值轨迹规划算法。首先引入自适应惯性权重与动态学习因子对PSO-GSA算法进行改进,然后使用改进算法对3-5-3多项式插值算法进行时间优化。在优化过程中,关节速度超速时的粒子组使用了与不超速时不同的适应度函数,引导粒子组朝关节速度减小的方向靠拢,加快了算法收敛速度。仿真结果表明,改进的PSO-GSA算法相比原算法及一些同类算法收敛速度更快、搜索精度更高、不易陷入局部最优。对3-5-3多项式插值轨迹规划法进行时间优化后相比优化前运行时间缩短了22.9%,得到的轨迹满足速度限制且平滑稳定,运行更加安全高效。

基于空间插值的不规则海洋地质样品测试分析数据聚类算法研究

海洋地质调查中获取大量海洋沉积物柱状样样品测试分析数据,样品测试分析目的不同导致柱状样数据采样深度不同,由此造成地质取样数据在三维空间上呈现不规则散点状分布。传统聚类算法无法在三维空间上对此类不规则散点数据进行聚类分析。对此,文章设计了一种基于空间插值的不规则地质样品测试分析数据聚类算法,有效地将三维样品测试分析散点数据降为二维数据后进行聚类分析,本算法较好地解决了地质体中试验测试数据的不均衡性问题,为海洋地质大数据分析提供了基础技术方法。

Integration of a 5-axis Spline Interpolation Controller in an Open CNC System

A 5-axis controller with curve interpolation function is developed to satisfy high-speed and high-precision computer numerical control (CNC) machining of machine parts with complex shapes in the authors-devised open CNC system. The instruction for- mat of this interpolation method and the generation procedure of the numerical control (NC) files are introduced. The interpola- tion curves of both position vectors and orientation vectors constructed by the controller are C2 continuous and independent of machin...

SRTM 3与ASTER GDEM数据处理及应用进展

从SRTM 3与ASTER GDEM的版本演化、质量评价、插补方法和数据应用现状等方面系统介绍了两种重要地形数据源。SRTM 3从2003年6月公开发布至今共4个重要版本,ASTER GDEM自2009年6月公开发布至今共两个重要版本;考虑数据源和数据处理技术,并辅以等高线分析、地形属性可视化、地形属性频率直方图分析等技术,认为SRTM 3和ASTER GDEM数据质量较高,在许多领域的应用中SRTM 3优于1∶25万地形图、ASTERGDEM则堪比1∶5万地形图数据。目前,SRTM 3与ASTER GDEM数据空洞及异常区域插补方法可以相互借鉴,其方法主要有两种:一是利用空缺区域周围数据直接插值;二是借助辅助数据填补空缺区域,并对接边处平滑处理。SRTM 3与ASTER GDEM目前已成功应用于水文学、工程开发、地质与灾害评估等诸多领域,提出了对两种数据进一步研究的工作展望。

3D electrical structure of porphyry copper deposit:A case study of Shaxi copper deposit

Located in Lu-Zong ore concentration area, middle-lower Yangtze metallogenic belt, ShaXi porphyry copper deposit is a typical hydrothermal deposit. To investigate the distribution of deep ore bodies and spatial characteristics of host structures, an AMT survey was conducted in mining area. Eighteen pseudo-2D resistivity sections were constructed through careful processing and inversion. These sections clearly show resistivity difference between the Silurian sandstones formation and quartz diorite porphyry and this porphyry copper formation was controlled by the highly resistive anticlines. Using 3D block Kxiging interpolation method and 3D visualization techniques, we constructed a detailed 3D resistivity model of quartz diorite porphyry which shows the shape and spatial distribution of deep ore bodies. This case study can serve as a good example for future ore prospecting in and around this mining area.

插值法在药物联合作用评价模型的应用研究

目的探讨插值法构建联合作用模型,结合等效线图法,评价二元混合药物联合作用效果。方法以人乳腺癌MDA-MB-231细胞为受试细胞株,测定5氟尿嘧啶[(5-fluorouracil,5-FU),浓度设为2、4、8、16、32、64μmol/L]和3-溴丙酮酸[(3-Bromopyruvic acid,3-BrPA),浓度设为20、40、80、160、320、640μmol/L]单一及混合后联合作用人乳腺癌MDA-MB-231细胞24 h,采用CCK-8法检测药物对MDA-MB-231细胞增殖的影响。采用多元统计法评价混合药物整体联合作用。插值法计算混合药物整体联合作用函数表达式,并绘制联合作用曲面以及30%、50%效应下的浓度加和等效线与置信区间;利用等高线与联合作用曲面得到30%、50%效应的观测等效线。结果5-FU、3-BrPA单一作用MDA-MB-231细胞增殖有抑制作用。5-FU的IC_(30)和IC_(50)分别为9.48μmol/L(95%C I:6.79~12.61)和37.96μmol/L(95%CI:27.19~60.83);3-BrPA的IC_(30)和IC_(50)分别为150.54μmol/L(95%CI:120.19~187.92)和410.07μmol/L(95%CI:316.25~575.94)。Bartlett检验显示3×3和6×6混合药物组数据方差无显著差异(P>0.05),交互效应图中曲线无明显相交,判断联合作用表现为相加作用。30%效应的观测等效线位于浓度加和等效线置信区间内,表现为相加作用;50%效应的观测等效线位于浓度加和等效线置信区间内以及下方,表现为相加作用,并可能存在协同作用。结论插值法与等效线图法构建的观测等效线可评价二元混合药物联合作用效果,为联合作用评价提供新的途径。