雅克比矩阵近似更新的三维装配约束求解研究

提出了三维装配约束求解中雅克比矩阵近似更新的方法。该方法通过对 迭代过程中满秩以及行秩秩亏雅克比矩阵进行近似更新,提高了约束求解的效率。首先在非 线性迭代求解过程中添加雅克比矩阵及其逆矩阵近似更新的公式;然后给出使用近似更新公 式需要满足的限制条件;最后通过对奇异点扰动算法的描述介绍迭代求解过程中雅克比矩阵 发生行秩秩亏的处理办法。文中提出的策略与算法已在三维装配约束求解引擎CBABench 中实现,给出的实例表明本文提出的方法效果显著。     

面向矩阵秩函数准确估计的自表示子空间聚类方法

传统子空间聚类方法通常使用矩阵核范数代替矩阵秩函数进行低秩矩阵恢复,然而在目标优化过程中主要关注低秩矩阵大奇异值的影响,容易导致矩阵秩估计不准确的问题。为此,在分析矩阵奇异值长尾分布特点基础上,提出使用基于截断Schatten-p范数的低秩子空间聚类模型。该模型充分考虑小奇异值对低秩矩阵恢复过程的贡献,利用小奇异值信息拟合矩阵奇异值的长尾分布,通过对矩阵秩函数进行准确估计以提升子空间聚类性能。实验结果表明,与现有加权核范数子空间聚类WNNM-LRR和近邻约束子空间聚类BDR算法相比,在Extended Yale B数据集上的聚类准确性分别提升了11%和8%,所提方法能够更好地拟合数据奇异值分布以及生成准确的相似度矩阵。     

空间几何对象相对位置的新安全判定方法

针对空间几何对象相对位置判定问题提出一种新的解决方案,也就是运用矩阵秩的概念和一般矩阵求和的安全两方计算协议秘密判定空间几何对象相对位置问题.关于此问题,之前罗永龙教授设计了对应成比例判定协议,而文中则利用矩阵秩的概念和一般矩阵求和的安全两方计算协议设计了一些基础的空间几何对象相对位置安全判定协议.运用此协议解决了空间中的平面与平面位置关系问题、平面与直线位置关系问题和直线与直线位置关系问题.提出的新安全判定方法不久解决了空间几何对象相对位置判定问题,也将在其他安全多方计算问题中起到重要作用.     

基于列约束的低秩矩阵恢复方法

由于在成像过程中出现遮挡现象,图像矩阵的元素有缺失。在正投影相机模型下,提出一种基于列约束的低秩矩阵恢复方法。该方法利用图像矩阵是一个低秩矩阵从而图像序列具有冗余性的特性,利用奇异值分解由图像矩阵的列空间构造出一个投影矩阵,得到图像矩阵的列所满足的约束条件,将缺失元素的恢复转化为迭代求解二次型的极值问题,利用它恢复出图像矩阵的缺失元素。该方法从理论上能够保证收敛到全局最小值。仿真实验表明,此方法具有收敛速度快,恢复精度高等优点。     

基于稀疏与低秩的核磁共振图像重构算法

已有的基于压缩感知的核磁共振图像重构算法仅利用了数据的稀疏性或矩阵的低秩性,并没有充分利用图像数据的相关性先验知识.针对这一问题,提出了一种新型的应用于二维核磁共振图像重建的算法模型.与传统的单一利用原始数据的稀疏性或矩阵低秩性进行重建的方法不同,该方法同时利用了图像数据的稀疏性与矩阵的低秩性.矩阵低秩部分使用应用赤池信息量准则的奇异值分解阈值方法,数据稀疏部分使用全变分作为稀疏变换基.实验结果表明,该方法在相同的采样率下与应用赤池信息量准则的奇异值分解阈值方法、全变分方法和奇异值分解阈值方法相比大大提升了重建图像的质量.     

线性系统能控性、能观测性的数值判断

本文讨论数字计算机判断线性、时不变系统能控性,能观测性的问题。引入了矩阵数值秩的概念以及通过奇异值判断矩阵数值秩的方法。在此基础上给出了线性系统能控性、能观测性数值判断的概念和方法。以Schuler平台的初始对准问题为例说明了这一方法。利用奇异值扰动的性质,进行了系统能控性,能观测性的鲁棒性分析。     

低秩–稀疏与全变分表示的运动目标检测方法

针对含有动态背景的运动目标检测问题,本文提出了一种低秩–稀疏与全变分表示的运动目标检测方法.提出方法以鲁棒主成分分析(RPCA)为基础,利用三维全变分对运动目标约束,去除动态背景的干扰;同时利用低秩矩阵在正交子空间下系数的群稀疏性来加速低秩矩阵的秩最小化,弥补全变分计算量大的问题,平衡整体运行速度.实验结果表明,该方法不仅能准确检测复杂背景下的运动目标,而且还保持了较快的运行速度.     

一种基于中心矩和相关系数阈值的SVD重构算法

传统的奇异值分解(SVD)去噪框架中,有效秩阶次是影响去噪效果的关键因素,对此提出一种无须选择有效秩阶次的SVD重构算法以进一步增强去噪性能.针对Hankel矩阵结构确定问题,引入中心矩的概念重新确定矩阵结构,从而减少SVD计算量;提出相关系数阈值选择有用分量实现信号重构,可最大程度保留原始信号的信息.应用该方法对一台电力变压器实测极化电流进行去噪处理.实验结果表明,该方法去噪性能优于传统SVD方法,且不需要选择有效秩阶次,信号有效分量损失较小,在强噪声背景下也能取得较好的去噪效果.     

基于数据矩阵的多个窄带信号频率和波达方向同时估计

以矩阵奇异值分解的性能研究为基础,针对等矩线阵提出了一种多个窄带信号波达方向和频率的同时估计方法。该方法用采集到的数据矩阵在最小二乘意义下低秩近似无噪数据矩阵,并根据信号的窄带假设构造了可用ESPRIT型方法求解待测参数的矩阵结构,频率和方向可自动配对,计算量较小。计算机模拟实验证实了该方法所作近似的有效性,显示了其高分辨率特性和在短数据条件下的鲁棒性。     

广义区间动力系统脉冲模存在性判据

系统有无脉冲行为直接影响到系统性质,本文针对广义区间动力系统首先给出了区间矩阵奇异值变化范围的判定定理,然后得到判别区间矩阵秩的变化范围的充分条件,进而得到判别广义区间动力系统具有脉冲模的判据.     

Identification and resolution of structural and algorithmic singularity in redundancy control of serial manipulations

A major difficulty that has haunted most researchers in the process of optimal redundancy resolution of robotic manipulators is the instability observed in even very simple numerical simulations. This numerical instability is not related to the structurally singular configurations of the manipulators, and in the literature has been referred to as “algorithmic singularity,” “artificial singularity,” or “unavoidable singularity.” In this work, conditions on both structural and algorithmic singularities are studied based on the Singular Value Decomposition of the Jacobian matrix, and, hence, a singularity-free control algorithm for redundant manipulators is developed and resolved as the Lagrange problem of optimal control. It is shown that many well-known methods for optimal redundant manipulation in the literature, including the Extended Jacobian Technique, most of constraint function-based methods, and most of the previously reported methods on global optimization techniques, are all special cases of the formulation provided here. Further, the necessary conditions of the global optimality for this general formulation are derived in explicit form and the source of “algorithmic singularity” is rigorously identified and resolved. © 2995 John Wiley & Sons, Inc.     

Local Analysis of Singular Configurations of Open and Closed Loop Manipulators

The paper gives a general approach to the local analysis of singularconfigurations of both serial and parallel manipulators. For all possiblecases the maximum rank deficiency of the manipulator Jacobian is given andshown never to exceed 4. This is the equivalent to the maximum number oflinear dependent constraint equations for kinematic loops. Singularconfigurations of serial/parallel manipulators are roughly classified withrespect to the active and passive joints. An algorithm is presented whichdetermines the singular motion of a mechanism. This algorithm is purelyalgebraic and involves at maximum three steps. It is based on theinstantaneous screw system of the considered mechanism. It is shown thatfourth order analysis is always sufficient to locally characterize theconfiguration space manifold in singular points. Thus the singular set canlocally be approximated by a hypersurface of maximum degree 4. The approachcan easily be implemented in existing simulation tools Finally theminimum number of joints is given that a serialmanipulator must activate in order to escape from a singular configuration.     

A closed-loop jacobian transpose scheme for solving the inverse kinematics of nonredundant and redundant wrists

The solution of the inverse kinematic problem is of the utmost importance in robotic manipulator control. This article proposes a closed-loop scheme for solving the inverse kinematic problem for nonredundant and redundant wrists based on the computation of the Jacobian transpose. The manipulability measure is suitably introduced as a constraint for redundant wrists, by taking advantage of the null space of the Jacobian matrix. The resulting algorithm provides a computational tool to solve a specified orientation trajectory into a joint trajectory. Numerical results with two spherical wrists show the excellent performance of the scheme.     

A direct algorithm for continuous path control of manipulators

This paper presents an algorithm for positioning and orientation of the hand for a redundant or non-redundant manipulator along a continuous path in space. This algorithm minimizes the distance between the actual position of the tip of the end-effector and the desired path. The algorithm does not use the Jacobian matrix for the inverse kinematics of the robot. It takes full advantage of the resolution of the joint drives, avoids singularity problems, and can be used for both redundant manipulators. The algorithm can be used in any situation where continuus motion of the end-effector is required in an open loop mode.     

Singularity-free simulation of closed loop multibody systems by using null space of Jacobian matrix

Numerical simulation of closed loop multibody systems is associated with numerical solution of equations of motion which are, in general, in the form of DAE’s index-3 systems. For assuring continuous simulation, one should overcome some difficulties such as stabilization of the constraint equations, singular configuration of the system. In this paper, the system equations of motion with the Lagrange multipliers is rewritten by introducing generalized reaction forces. The combination with the condition of ideality of constraints leads to the system of equations which can be solved by numerical techniques smoothly, even over singular positions. Based on the new criterion of ideality of constraints, which relates generalized reaction forces and the null space matrix of Jacobian matrix, it is possible also to remove reaction forces and use only the reduced system of equations with null space matrix for passing singular positions. In order to prevent the constraint equations from the accumulated errors of integral time, the method of position and velocity projection has been exploited. Some numerical experiments are carried out to verify the proposed approach.     

三维几何约束求解的变分算法

研究了运动学变分原理在三维几何约束求解中的应用,提出了变分求解算法．该算法采用相对坐标,将求解域从笛卡儿空间转换到相对坐标空间．对于约束开环,依次选取相对坐标即可获得满足几何约束的刚体位姿;对于约束闭环,通过切断闭环铰,将约束闭环转化为等价的广义开环与切断铰约束代数方程,其切断铰约束代数方程的相对坐标雅克比矩阵解析式可通过变分关系显式获得．最后通过实例验证,说明该算法具有较高的求解效率与稳定性．     

机器人运动学反解中的奇异点处理

本文研究机器人运动学反解中的奇异点处理问题，给出了机器人微分运动Ｊａｃｏｂｉａｎ矩阵Ｊ（ｑ）条件数的一个上界，并在此基础上提出机器人关节速度阻尼伪逆解方法中阻尼系数的一种自适应调整方法，该方法可以保证在奇异点附近伪逆解的稳定性。     

三维装配几何约束组合的分类求解策略

针对两个刚体之间的三维几何约束求解问题,依据几何约束的参数结构 分析了角度约束和距离约束的解耦性,给出了角度约束和距离约束可解耦求解的条件;然后 对两个刚体之间的几何约束进行组合分析,总结出约束度不小于2 的几何约束构成的组合只 有几十种,且均可采用几何推理方法进行求解;最后阐述了附加方向约束、冗余约束和矛盾 约束对数值求解的不利影响,提出了三维几何约束组合的分类求解策略,并用实例验证了该 求解策略的有效性。     

基于等价类划分的配置求解与解释计算

基于约束的配置模型中会有一些变量之间不存在任何直接或间接的约束关系,这样的变量之间进行约束传播不会互相影响取值.基于配置问题的这一特点,提出了一种等价类划分的思想,用于构造产品模型时的预处理技术,可以有效地将原问题划分为若干子问题,证明了这些子问题可以分别处理.分别采用两种回溯策略对求解效率进行了测试,结果表明能够有效地提高求解效率.最后,等价类划分方法与计算解释的QUICKXPLAIN算法集成计算冲突解释,测试结果表明,经过等价类划分后,同样可以有效地提高计算解释的效率.