平面四连杆机构近似位姿综合的计算机模拟逼近法

平面连杆机构尺寸综合的两个基本工具是几何法和解析法，它们仅适用于规定较少的机构精确位姿数的综合。几何法简单直观，但求解精度低且重复性差；解析法求解精度高且重复性好，但求解复杂、不直观。针对两种方法的缺点，提出一种机构尺寸驱动综合方法，即连杆机构近似位姿综合的计算机模拟逼近法。首先在多个复合精确和近似位姿情况下，用CAD的几何约束和尺寸驱动技术，构造一个基本四连杆模拟机构；再根据函数、轨迹和运动综合的原则，由基本四连杆模拟机构分别构造出函数、轨迹和运动的近似位姿综合模拟机构。计算机模拟结果表明，这种方法不仅具有简捷直观、求解精度高和重复性好的优点，而且可以增加机构综合的规定位置个数，为机构的尺寸综合提供更有效的工具。     

用计算机辅助几何技术对Stephenson六杆机构近似位姿的综合

机构尺寸综合的两个基本工具是几何法和解析法，适用于位置较少的机构尺寸综合，而且解析法求解复杂和不直观．提出计算机辅助几何技术的Stephenson六杆机构近似位姿综合法．先用CAD的几何约束和尺寸驱动技术，在多个复合精确和近似位姿情况下构造一个基本六杆模拟机构，再根据轨迹和运动综合的原则，由基本六杆模拟机构分别创造出轨迹和运动的近似位姿综合模拟机构．计算机模拟结果表明，该方法不仅具有简洁直观、求解精度高和重复性好的特点，而且可以增加机构综合的规定位置个数，为机构的尺寸综合提供更有效的工具．     

用CAD约束和尺寸驱动技术分析平面机构的运动

提出用CAD约束和尺寸驱动技术分析平面机构的运动。采用CAD的几何约束、尺寸约束、尺寸方程和尺寸驱动技术，构造一些典型平面连杆模拟机构。给定输入件的驱动尺寸，确定输出件被驱动尺寸，求出输出杆件运动点的轨迹。利用CAD软件的记录功能，得到机构输出点轨迹数据；再用Excel软件拟合轨迹数据，得到轨迹拟合曲线和拟合方法；最后求解机构输出运动件的速度和加速度方程。计算机模拟结果表明，文中方法不仅具有简单、快捷、直观、求解精度高和重复性好的优点，而且可以完成复杂机构和多自由度机构的运动分析，为机构的运动分析提供更有效的工具。     

平面并联机构工作空间的三维螺旋扫描CAD求解

针对平面并联机构无奇异位置工作空间求解困难、过程繁琐、计算量大等问题，提出了基于CAD求解平面并联机构工作空间的三维螺旋扫描方法。将[n]自由度平面并联机构分解成[n]条支链进行独立分析，得到每条支链下末端执行器的可达区域，再将所有支链可达区域取交集即为平面并联机构工作空间。应用SolidWorks软件建立平面并联机构模型，进行几何特征处理，通过自动求解器求解，将求解过程图形化，快速得到同轴布局5R机构和平面3-RPR并联机构的无奇异位置工作空间。通过同轴布局5R机构的运动学实验，验证了该求解方法的可行性。     

三维服装CAD中几何约束表达及其求解技术研究

从人体及服装的特点出发,提出三维服装几何元素的概念．采用样条曲线作为基本几何元素,归纳出服装的三种约束关系,即共点、对称和自对称关系;成为约束关系形成的基础．以三种约束关系为基础,建立了面向服装的几何约束图,有效地表达了三维服装几何元素及其相互关系;实现了一种基于约束图的约束求解方法。从而完成了构造服装及对服装的交互参数化修改,文中给出了应用实例,并将参数化方法向高层次图素如样条曲线、曲面作了推广,成功地应用于以样条曲线为几何元素的参数化服装CAD系统中,运行效果良好。     

几何约束求解的去并拟合方法

依据有向图理论提出了去并拟合方法,由此导出了对于几何约束求解问题的去并拟合的并行处理及串行处理策略,进而得到了一套求解几何约束问题的完备算法。通过将该理论引入到参数化CAD的设计中,使得在算法复杂度增加不大的情况下,几何自动作图的范围大大拓宽。还将其应用于智能动态几何软件的设计中,取得了较好的结果。     

A Geometric Approach for the Theory and Applications of 3D Projective Invariants

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.     

基于图割理论和极几何约束的图像匹配算法

提出了一种基于图割理论和极几何约束的图像匹配算法。利用极几何约束对两幅待匹配图像进行矫正,使得它们的极线处在同一扫描线上,从而将二维匹配简化成一维匹配;利用基于图割的一维匹配算法获取视差数据,此时匹配中能量函数的标号是一维的,大大减少了搜索范围,并且提高了匹配的速度。     

The Motor Extended Kalman Filter: A Geometric Approach for Rigid Motion Estimation

In this paper the motor algebra for linearizing the 3D Euclidean motion of lines is used as the oretical basis for the development of a novel extended Kalman filter called the motor extended Kalman filter (MEKF). Due to its nature the MEKF can be used as online approach as opposed to batch SVD methods. The MEKF does not encounter singularities when computing the Kalman gain and it can estimate simultaneously the translation and rotation transformations. Many algorithms in the literature compute the translation and rotation transformations separately. The experimental part demonstrates that the motor extended Kalman filter is an useful approach for estimation of dynamic motion problems. We compare the MEKF with an analytical method using simulated data. We present also an application using real images of a visual guided robot manipulator; the aim of this experiment is to demonstrate how we can use the online MEKF algorithm. After the system has been calibrated, the MEKF estimates accurately the relative position of the end-effector and a 3D reference line. We believe that future vision systems being reliably calibrated will certainly make great use of the MEKF algorithm.     

Estimation of 2D Displacement Field Based on Affine Geometric Invariance and Scene Constraints

In the paper, a novel approach using affine transfer and scene constraint for estimation of 2D displacement field was developed. In this approach, we derived a system of 5 linear equations for computing corresponding point of any image point via the utilisation of affine invariant. Subsequently, the characteristics of such a linear system was thoroughly studied, and the way to obtain a reliable solution of the system via robust least squares (RLS) approach, in conjunction with total least squares technique, was proposed. In addition, through the interpretation of the approach from both geometric point of view and numerical point of view, we gave the limitation of the algorithm. The limitation was then relaxed to a certain extent by using full fundamental matrix. These findings were further verified through the experimental results.     

基于约束的装配体位置描述及求解

装配体设计是计算机辅助设计(CAD)的一个重要组成部分,本文就装配体设计中装配体位置的描述及自动求解这两个关键问题进行了深入的探讨,提出了基于约束的装配体相互位置关系的描述方法及自动求解算法.同时本文首次引入奇异矩阵的方法,较好地解决了装配体位置的约束冗余、约束不足以及病态矩阵的问题.