机器人工作空间的数值计算

本文给出了计算任意结构形式任意自由度单链机器人工作空间的数值方法。这种方法把计算机器人工作空间的极限距离、边界曲线和边界曲面问题转化为求满足一定约束条件下的极值问题。通过选用不同的目标函数和约束条件就可以求出机器人工作空间边界曲面上的一系列特征点,把这些点连成线或面就构成了机器人的工作范围.根据上述讨论本文编制了计算机器人工作空间的程序软件 WZ,只要输入机器人的结构参数和各自由度的运动范围就可以求出机器人工作空间边界曲面上的若干点,并用绘图机绘出边界曲线。     

基于空间分解的三角网格模型求交方法

三角网格模型间的求交问题是计算机辅助设计与制造领域的关键问题之一.分析了已有空间分解技术和包围盒方法等的优缺点,并在此基础上提出了改进的空间分解求交方法. 该算法能够精确定位三角形所占的空间网格,一定程度上减少了需要求交的三角形的数量.实验的结果表明,改进的算法提高了采用空间分解进行三角网格求交的计算效率.     

裁剪后二次曲面的光线跟踪

提出了一个对裁剪后二次曲面进行光线跟踪的新方法。在该方法中引进了一个易于由世界坐标求参数的辅助参数空间，通过预处理，事先将原参数域下的边界变换到新的参数空间。这样，光线与曲面的求交仍可按二次曲面的几何参数进行，求出交点后，再将交点变换到辅助参数空间，在新的参数域中判断交点是否在裁剪过的曲面上。     

基于空间多边形三角剖分的曲面分割求交算法

针对传统曲面分割求交方法存在的平面片的选取、遗漏部分交线段以及交线间断 的问题,提出一种基于空间多边形三角剖分的曲面分割求交算法。以等深度分割方法为基础, 避免了交线不连续的问题,当分割达到一定层次时以空间多边形近似曲面片,并对空间多边形 进行三角剖分,以三角形对的交线近似空间多边形之间的交线,进而以空间多边形的交线近似 曲面片的交线,最终得到相交曲面之间的交线。利用曲面片轮廓构造出的空间多边形更加接近 曲面片的真实形状,提高了逼近精度,同时对空间多边形进行三角剖分,提高了求交精度,进 而降低了丢失交线的可能性。实验验证了该算法比传统的分割法更加精确。     

复合三角Bèzier曲面的裁剪

利用三角Ｂèｚｉｅｒ曲面片的保凸性和可分割性,解决了初始交点计算、迭代收敛等问题;通过求近曲面点、边界点跨越等过程,由一个初始交点出发跟踪计算跨越许多曲面片的整条交线;将各交点作为型值点插入曲面中,对三角网格进行局域三角化,以交线为界限进行分离,重新生成两张复合曲面,实现了裁剪的目的;基于次边界环和重新分布边界点的计算,改善了狭长三角形对整张曲面的性态影响．测试显示,上述方法简单可靠,满足了反求工程ＣＡＤ建模的要求     

基于八叉树和混合搜索树的地质曲面快速求交方法

为处理地质界面之间的空间相交关系,提出一种新的针对三角地质曲面的快速求交方法。该方法融合优化八叉树法和OBB搜索树方法,可以更快速准确地剔除远离交线的其他三角形。求交剩余的三角形得到交线,应用三角网局部重构和网格优化算法修正交线附近的三角网,最终分割交线两侧的地质曲面,完成2个地质曲面的离散化求交过程。与AABB、OBB和空间分解法相比,该方法在大数据量三角曲面求交中效率优势明显,可以快速准确处理地质模型构建和分析中的曲面求交问题,为三维地质模型自动化构建的实现提供有效支撑。     

基于AutoCAD平台的六自由度并联机器人

本文研究基于AutoCAD平台的六自由度并联机器人在姿态给定情况下工作空间(即位置工作空 间)的几何确定方法,该方法以机器人的运动学反解为基础,得出Stewart并联机器人和6-R TS并联机器人位置工作空间的边界方程,从而得出Stewart并联机器人的位置工作空 间是6个球体的交集,6-RTS并联机器人在姿态给定时其工作空间是6个相同的规则曲面体 的交集．基于AutoCAD平台,其交集以及交集的容积可以很容易的得出,该方法是确定六自 由度并联机器人工作空间的一种简单、有效方法．     

三角形域上C1连续的四次插值曲面

提出了一种在三角形域上构造C^1曲面的方法，该方法构造的曲面片由4个曲面加权平均产生，在三角形的边界上满足给定的边界曲线和一阶跨界导数．所构造的曲面可看作由一张基本曲面和三张过渡曲面构成．用三条曲线相交于一点且在交点处共面作为约束条件构造基本曲面，在三角形的内部具有较好形状和逼近精度．同边点法相比，文中方法产生的曲面形状更好；且该方法产生的曲面对四次多项式曲面是精确的，因而比Nielson的点边方法具有更高的插值精度．     

基于空间索引与碰撞检测的TIN求交算法

针对三维矿床地质模型构建及后续应用分析中的需求,提出一种基于空间索引与碰撞检测的不规则三角网(TIN)快速求交算法。通过建立TIN模型的空间格网索引,将相交测试与计算限定在映射于同一个空间格网单元内的三角形对之间,在求交计算过程中,应用包围盒碰撞检测方法快速剔除不相交三角形对,并分别采用边-面及改进的边-边求交算法计算异面与共面三角形交线,并根据交线段之间的空间邻接关系完成交线的快速分离。实验及应用结果表明,该算法效率高、运行稳定、计算结果可靠,能够满足大规模TIN快速求交计算的需要。     

多核CPU/GPU平台下的集合求交算法

提出一个多核CPU/GPU混合平台下的集合求交算法.针对CPU端求交问题,利用对数据空间局部性和中序求交的思想,给出内向求交算法和Baeza-Yates改进算法,算法速度分别提升0.79倍和1.25倍.在GPU端,提出有效搜索区间思想,通过计算GPU中每个Block在其余列表上的有效搜索区间来缩小搜索范围,进而提升求交速度,速度平均提升40％.在混合平台采用时间隐藏技术将数据预处理和输入输出操作隐藏在GPU计算过程中,结果显示系统平均速度可提升85％.     

机器人操作臂工作空间的混合计算方法

机器人操作臂工作空间的形状和体积的精确计算对于其优化问题是非常重要的。为此首先根据从关节空间到工作空间的运动映射关系,使用蒙特卡洛方法产生由点组成的三维机器人工作空间。然后,通过把这些点分解成一系列的切片,获得机器人工作空间每层的二维边界曲线;基于切片曲线,由三维重构的方法产生边界曲面。最后,用数值积分的方法计算了机器人工作空间的体积。     

Computing medial axes of generic 3D regions bounded by B-spline surfaces

A new approach is presented for computing the interior medial axes of generic regions in R³ bounded by C⁽⁴⁾-smooth parametric B-spline surfaces. The generic structure of the 3D medial axis is a set of smooth surfaces along with a singular set consisting of edge curves, branch curves, fin points and six junction points. In this work, the medial axis singular set is first computed directly from the B-spline representation using a collection of robust higher order techniques. Medial axis surfaces are computed as a time trace of the evolving self-intersection set of the boundary under the the eikonal (grassfire) flow, where the bounding surfaces are dynamically offset along the inward normal direction. The eikonal flow results in special transition points that create, modify or annihilate evolving curve fronts of the (self-) intersection set. The transition points are explicitly identified using the B-spline representation. Evolution of the (self-) intersection set is computed by adapting a method for tracking intersection curves of two different surfaces deforming over generalized offset vector fields. The proposed algorithm accurately computes connected surfaces of the medial axis as well its singular set. This presents a complete solution along with accurate topological structure.     

On the workspace boundary determination of serial manipulators with non-unilateral constraints

Broadly applicable analytical algorithms for workspace of serial manipulators with non-unilateral constraints are developed and illustrated. The Jacobian row-rank deficiency method is employed to determine the singularities of these manipulators. There are four types of singularity sets: Type I: position Jacobian singularities; Type II: instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III: domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV: coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one sub-matrix due to either of two occurrences: a Type II or a Type III singularity. All of the singular surfaces are hypersurfaces that extend internally and externally the workspace envelope. Intersecting singular surfaces identifies singular curves that partition singular surfaces into subsurfaces, and a perturbation method is used to identify regions (curve segments/surface patches) of the hypersurfaces that are on the boundary. The formulation is illustrated by implementing it to a spatial 3-degree of freedom (DOF) and a spatial 4-DOF manipulator.     

机器人灵活工作空间的边界分析

机器人灵活工作空间的分析是机器人运动学至今没有解决的一个问题.由于机器人在灵活工作空间中工作不会受到本身机构对它的限制.所以,机器人灵活工作空间的大小对于提高机器人的操作性能就显得格外重要.本文旨在解决机器人灵活工作空间边界的计算问题.首先.它分析了灵活工作空间边界的性质;其次,用一种新的方法——网络跟踪法确定了灵活工作空间在横截面内的边界;最后.提出了灵活工作空间端边界的求解方法.     

Determining interference between pairs of solids defined constructively in computer animation

This paper presents theory and implementation of a method for detecting interference between a pair of solid objects. Often at times, when performing simulations, two solids may unwittingly interpenetrate each other. The two components of the system presented in this paper are: (1) a surface representation method to model solid objects; and (2) a method for detecting interference. Body representation of a solid in this system is based upon enveloping each solid with surfaces (called positive entities). Most computer aided design (CAD) systems use solid modeling techniques to represent solid objects. Since most solid models use Boolean operations to model complex objects, a method is presented to envelop complex objects with parametric surfaces. A method for tracing intersection curves between two surfaces is also presented. Discontinuities on surfaces are defined as negative entitics in order to extend the method to complex solids. Determining interference is based upon a numerical algorithm for computing points of intersection between boundary curves and parametrized entities. The existence of segments of these curves inside the boundary of positive and negative entities is established by computing the circulation of a function around the boundary curve. Interference between two solids is then detected. No limitations are imposed on the convexity or simplicity of the boundary curves treated.     

Approximate solutions to unreachable commands in teleoperation of a robot

A method is presented for finding approximate solutions to unreachable commands for a serial link manipulator. It deals with the difficulties of joint limits and singularities in a teleoperational, task space controller. Damped least squares with dynamic weighting is used to solve the inverse Jacobian problem. Previously reported benefits of damped least squares are reviewed, and an additional benefit is demonstrated; a convergence to an approximate position when the command is outside a singularity-defined workspace boundary. The utility of damped least squares is extended by incorporating dynamic weighting matrices, allowing an approximate position to be found when the command is outside a joint-limit-defined workspace boundary. A real-time control scheme for calculating the dynamic weights and damping factor is presented. A hardware implementation, that used a six degree of freedom teleoperator, is discussed. In this implementation the approximate position solution, a new concept in dealing with workspace boundaries in teleoperation, resulted in improved operation.     

Feature based volumes for implicit intersections

The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or feature based volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualization of feature curves and modeling of surface based structures including microstructures.     

On the determination of boundaries to manipulator workspaces

The accumulation of two independent, broadly applicable formulations for determining the boundary to manipulator workspaces, presented elsewhere, are compared in this paper. Insights gained from one method are used to explain behavior exhibited in the other. Results are also compared and validated. A numerical formulation based on continuation methods is used to map curves that are on the boundary of a manipulator workspace. Analytical criteria based on row rank deficiency criteria of the manipulator's analytical Jacobian are used to map a family of one-dimensional solution curves on the boundary. The other formulation, based on a similar rank-deficiency criteria, yields analytic boundaries parametrized in terms of surface patches on the boundary. Results concerning the applicability of the numerical method to open- and closed-loop systems are compared with those limited to the open-loop for the analytical method. Conclusions regarding the behavior of the manipulator on geometric entities characterized by singular curves, higher-order bifurcation points, and surfaces inside the workspace are drawn. Applicability of both methods and their limitations are also addressed.     

A CNC interpolation algorithm for boundary machining

This paper presents an efficient and accurate algorithm for machining boundaries formed at the intersection of two surfaces, an important manufacturing problem in CNC machining. The algorithm is developed using a locus tracing technique implemented on the basis of Danielson's step selection rules. A vertical ball-end milling cutter moves along the considered boundary, in contact with the two surfaces. The algorithm guides the center of the spherical end of the cutter, to maintain exact contact (within 1 step) along the entire path. A seamless formulation is used, allowing the contact points to move freely from the ball-end to the cutter periphery and vice-versa. The surfaces forming the boundary may be implicitly or parametrically defined. The reliability of the algorithm is demonstrated for both cases, by treating a complex boundary machining example. The boundary considered is formed by the intersecting quadratic surfaces of a sphere and an elliptic hyperboloid.