基于螺旋理论的新型三自由度移动并联机器人奇异性分析

采用螺旋理论及线性几何学方法对具有3支链5关节（P-4R）的三自由度纯移动并联机器人的奇异性进行了分析和总结．研究了该并联机器人的结构奇异性以及主动关节（驱动关节）的配置的奇异性，并采用线性几何学图解形式直观地给出其处于奇异时的形位，为进一步研究其动力学、运动学性质奠定了基础．     

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。     

改进的Hestenes SVD方法及其并行计算和在并联机器人中的应用

提出一种改进的Hestenes SVD处理方法,显著减少了矩阵奇异值分解计算的循环轮次数和正交化次数,也方便和加快了矩阵的求(伪)逆运算过程.研究了两种分别基于行划分和列划分策略的改进Hestenes SVD方法的并行计算方案,并对算法性能进行了分析.针对目前并联机器人计算需求不断扩大的特点,以6自由度并联机器人一、二阶影响系数矩阵为算例对改进Hestenes SVD方法及其并行算法进行了实验.结果表明该算法可大幅度提高矩阵奇异值分解的效率,益于基于大量影响系数矩阵运算的并联机器人运动学、动力学性能分析和实时控制.相关方法也适用于具有类似矩阵处理的其他诸多工程领域.     

农田信息采集机器人机构设计与奇异性分析

提出一种四轮并联机构的新型农田信息采集机器人．结构和越障原理分析结果表明,该机器人具有较 强的地形适应能力．为了研究机器人的奇异位形,根据雅可比矩阵的定义和D-H 矩阵法直接求出雅可比矩阵的解析 表达．根据机构的奇异性分类,利用动力学分析软件ADAMS 仿真得到了各奇异位形的精确位置和运动特点,与理 论分析相一致．根据以上分析设计的机器人物理样机能有效避免奇异位形．     

基于小波变换的图像纹理奇异性检测方法的研究

介绍了一种用于图像纹理奇异性检测的二维数字滤波器的设计,该滤波器是基于离散小波变换设计的。它具有纹理树状结构的多分辨分析特性。用一阶及二阶的微分方法进行奇异点的估计与合并,可应用于图像纹理奇异性检测。     

基于小波变换的图像纹理奇异性检测方法的研究

介绍了一种用于图像纹理奇异性检测的二维数字滤波器的设计，该滤波器是基于离散小波变换设计的。它具有纹理树状结构的多分辨分析特性。用一阶及二阶的微分方法进行奇异点的估计与合并。可应用于图像纹理奇异性检测．     

首系数奇异的二阶系统解耦

针对首系数奇异的二阶系统的解耦问题,提出了一种奇异二阶系统的同谱构造解耦方法。引入了对逆二阶系统,将难以描述的二阶系统无穷大特征值转化为其对逆二阶系统的零特征值来加以描述,分析了奇异二阶系统可对角化应该满足的条件及其相应的证明,并且给出了一种具体的奇异二阶系统的同谱构造解耦方法,从而实现了奇异二阶系统解耦,即将奇异二阶系统的3个参数矩阵同时对角化。数值试验中将一个三自由度的奇异质量弹簧二阶系统解耦成3个无关的单自由度二阶子系统,而且解耦前后系统不仅保持了相同的有限特征值及其重复度结构,还保持了相同的无限特征值及其重复度结构。工程应用前景十分广泛。     

机械系统的快速有限时间跟踪控制及其在航天器交会中的应用

针对一类具有匹配干扰的二阶机械系统,本文研究了快速有限时间跟踪控制问题.结合有限时间反步法和非奇异快速终端滑模,本文提出了一种新的快速有限时间控制律,并给出了控制器参数所需满足的充分条件以保证系统的快速有限时间稳定性.进一步地,在一定情形下,所设计的快速有限时间控制律能够退化为经典的反步法、有限时间控制律和非奇异快速终端滑模控制律.最终,将所设计的控制律应用于航天器交会系统,数值仿真结果验证了所提方法的有效性.     

机械系统的快速有限时间跟踪控制及其在航天器交会中的应用（英文）

针对一类具有匹配干扰的二阶机械系统,本文研究了快速有限时间跟踪控制问题.结合有限时间反步法和非奇异快速终端滑模,本文提出了一种新的快速有限时间控制律,并给出了控制器参数所需满足的充分条件以保证系统的快速有限时间稳定性.进一步地,在一定情形下,所设计的快速有限时间控制律能够退化为经典的反步法、有限时间控制律和非奇异快速终端滑模控制律.最终,将所设计的控制律应用于航天器交会系统,数值仿真结果验证了所提方法的有效性.     

并联6—SPS机器人的影响系数及其应用

本文根据并联机构的特点,对位置反解直接求导,建立了并联6-SPS 机器人的一、二阶影响系数矩阵,解决了速度分析和加速度分析问题.为机器人的误差分析和动力学分析奠定了基础.所得的一、二阶影响系数矩阵的形式简单统一,特别实用于计算机计算.最后给出了实例计算.     

Singularities affect dynamics of learning in neuromanifolds

The parameter spaces of hierarchical systems such as multilayer perceptrons include singularities due to the symmetry and degeneration of hidden units. A parameter space forms a geometrical manifold, called the neuromanifold in the case of neural networks. Such a model is identified with a statistical model, and a Riemannian metric is given by the Fisher information matrix. However, the matrix degenerates at singularities. Such a singular structure is ubiquitous not only in multilayer perceptrons but also in the gaussian mixture probability densities, ARMA time-series model, and many other cases. The standard statistical paradigm of the Cramér-Rao theorem does not hold, and the singularity gives rise to strange behaviors in parameter estimation, hypothesis testing, Bayesian inference, model selection, and in particular, the dynamics of learning from examples. Prevailing theories so far have not paid much attention to the problem caused by singularity, relying only on ordinary statistical theories developed for regular (nonsingular) models. Only recently have researchers remarked on the effects of singularity, and theories are now being developed.This article gives an overview of the phenomena caused by the singularities of statistical manifolds related to multilayer perceptrons and gaussian mixtures. We demonstrate our recent results on these problems. Simple toy models are also used to show explicit solutions. We explain that the maximum likelihood estimator is no longer subject to the gaussian distribution even asymptotically, because the Fisher information matrix degenerates, that the model selection criteria such as AIC, BIC, and MDL fail to hold in these models, that a smooth Bayesian prior becomes singular in such models, and that the trajectories of dynamics of learning are strongly affected by the singularity, causing plateaus or slow manifolds in the parameter space. The natural gradient method is shown to perform well because it takes the singular geometrical structure into account. The generalization error and the training error are studied in some examples.     

The Singularity Principle and Property of Stewart Parallel Manipulator

Based on the kinematic relationship of rigid body, this paper presents a new principle and method to analyze the singularity of a Stewart parallel manipulator. We study the sufficient and necessary condition that three velocities of three non‐collinear points in a body can determine a screw motion. All singularities of the Stewart parallel mechanism are classified into three different linear‐complex singularities. The various algebraic and geometrical properties as well as kinematics ones are analyzed in detail in different singular configurations. With the condition above, the singularity loci and distribution characteristics of a 3/6—Stewart parallel manipulator for some orientations of the mobile are studied in an oblique plane and in three‐dimensional space. © 2003 Wiley Periodicals, Inc.     

Degeneracy conditions of the dynamic model of parallel robots

Despite their well-known advantages in terms of higher intrinsic rigidity, larger payload-to-weight ratio, and higher velocity and acceleration capacities, parallel robots have drawbacks. Among them, the most important one is surely the presence of singularities in the workspace, which divide the workspace into different aspects (each aspect corresponding to one or more assembly modes) and near which the performance is considerably reduced.In order to increase the reachable workspace of parallel robots, a promising solution consists in the definition of optimal trajectories passing through the singularities to change either the leg working modes or the robot assembly modes. Previous works on the field have shown that it is possible to define optimal trajectories that allow the passing through the robot type 2 singularities. Such trajectories must respect a physical criterion that can be obtained through the analysis of the degeneracy conditions of the parallel robot inverse dynamic model.However, the mentioned works were not complete: they lacked a degeneracy condition of the parallel robot inverse dynamic model, which is not due to type 2 singularity anymore, but to a serial singularity. Crossing a serial singularity is appealing as in that case we can change the robot leg working mode and then potentially access to other workspace zones. This absence is due to the fact that the authors used a reduced dynamic model, which was not taking into account all link dynamic parameters.The present paper aims to fill this gap by providing a complete study of the degeneracy conditions of the parallel robot dynamic model and by demonstrating that it is possible to cross the type 2, but also serial singularity, by defining trajectories that respect some given criteria obtained from the analysis of the degeneracy of the robot dynamic model. It also aims to demonstrate that the serial singularities have impacts on the robot effort transmission, which is a point that is usually bypassed in the literature. All theoretical developments are validated through simulations and experiments.     

基于Bayes决策的奇异点检测

针对奇异信号中奇异点的检测和定位问题,提出了一个新的信号奇异点检测方法。根据脉冲奇异点的特点,首先将脉冲奇异点的检测建模为一个分类问题：信号中的脉冲奇异点为一类,非脉冲奇异点为另一类。然后,基于Bayes决策和Neyman-Pearson准则,在限定脉冲奇异点漏检概率的情况下,导出了两类点之间的分界面。据此设计了一个新的脉冲奇异点检测方法--基于Bayes决策的脉冲奇异点检测(BDPSD)方法。模拟及真实信号上的实验结果表明,与基于小波变换的模极大法相比,BDPSD方法在检测质量和定位精度方面都有很大的改善,证明BDPSD是一个有效、可行的信号奇异点检测方法。     

工业CT图像中小间隙裂纹的亚像素测量方法

工业部件内部小间隙裂纹测量是公认的技术难题,研究工件断面CT图像中小间隙裂纹的测量方法,使之达到亚像素精度。脊波变换是近年在小波变换基础上发展起来的新的分析方法,脊波变换对于图像中的线状奇异性（如边缘、裂纹等）较敏感,且它对图像中的点状噪声有抑制作用。在利用脊波变换检测工业CT图像中工件裂纹边缘的基础上,对小间隙裂纹的平均宽度进行亚像素测量。而工业CT图像成像时存在的点扩散效应,使测得裂纹宽度较真实的要宽些。因此采用宽度收缩的方法获得裂纹平均宽度并进行尺寸标定。实际工业CT图像的实验结果表明,该方法的测量精度能够达到亚像素级精度,可应用于工业CT图像中的小间隙裂纹测量,也可应用于其他类型图像。     

Implicitization,parameterization and singularity computation of Steiner surfaces using moving surfaces

A Steiner surface is a quadratically parameterizable surface without base points. To make Steiner surfaces more applicable in Computer Aided Geometric Design and Geometric Modeling, this paper discusses implicitization, parameterization and singularity computation of Steiner surfaces using the moving surface technique. For implicitization, we prove that there exist two linearly independent moving planes with total degree one in the parametric variables. From this fact, the implicit equation of a Steiner surface can be expressed as a 3×3 determinant. The inversion formula and singularities for the Steiner surface can also be easily computed from the moving planes. For parameterization, we first compute the singularities of a Steiner surface in implicit form. Based on the singularities, we can find some special moving planes, from which a quadratic parameterization of the Steiner surface can be retrieved.     

Enlarging parallel robot workspace through Type-2 singularity crossing

In order to increase the reachable workspace of parallel robots, a promising solution consists of the definition of optimal trajectories that ensure the non-degeneracy of the dynamic model in the Type 2 (or parallel) singularity. However, this assumes that the control law can perfectly track the desired trajectory, which is impossible due to modeling errors.This paper proposes a robust multi-model approach allowing parallel robots to cross Type 2 singularities. The main idea is to shift near singularities to a simplified dynamic model that can never degenerate. The two main contributions are the definition of an optimal trajectory crossing Type 2 singularities and the multi-model control law allowing to track this trajectory. The proposed control law is validated experimentally through a Five-bar planar mechanism.     

A Note on Some Phase Differencing Algorithms for Disparity Estimation

Disparity can be estimated from the local phase differences between a pair of stereo images after Gabor filterings. In this paper, some phase differencing algorithms are discussed from the point of view of numerical computation. They are all categorised as certain types of Newton iterations, hence are restricted by the preconditions of Newton iterations. Furthermore, a numerical sensitivity analysis is made for phase computation near its singularity points without referring to any specific filtering method. It makes clear that the numerical instability has its roots in the singularities of the phase functions themselves rather than in their derivatives, therefore severe errors cannot be properly reduced by Newton iterations. Hence, the singularity problem must be carefully treated for any disparity estimation using phase differencing techniques. In the case of foveal vision, such as target detection or vergence control, the central parts of scenes are of interest. A shift-trials algorithm is proposed to contain the effects of singularities instead of relying on detection and removal of singularity neighbourhoods through local computation. This algorithm directly tackles the singularity problem by posing the local disparity estimations as a minimisation of the phase differences of the left and right views in terms of a global matching residual norm. By a direct search for solution, no numerical derivative is needed, phase singularity can be tolerated and robust results are thus produced.     

信号Lipschitz奇异性的计算与分析

该文从Lipschitz奇异性的定义出发,根据信号与噪声的奇异性指数α的不同,推导出了小波变换系数点是噪声点还是信号点的判别法,也为计算Lipschitz指数提供了一个简单可靠的方法。仿真结果证明,该方法对于信号去噪能起到良好的效果。