Integrating rotation and angular velocity from curvature

The problem of integrating the rotational vector from a given angular velocity vector is met in such diverse fields as the navigation, robotics, computer graphics, optical tracking and non-linear dynamics of flexible beams. For example, if the numerical formulation of non-linear dynamics of flexible beams is based on the interpolation of curvature, one needs to derive the rotation from the assumed curvature field. The relation between the angular velocity and the rotation is described by the first-order quasi-linear differential equation. If the rotation is given, the related angular velocity is obtained by the differentiation. By contrast, if the angular velocity is given, the related rotations are obtained by the integration. The exact closed-form solution for the rotation is only possible if the angular velocity is constant in time. In dynamics of non-linear flexible spatial beams, the problem of integrating rotations from a given angular velocity becomes even more complex because both the angular velocity and the curvature need simultaneously be integrated and are both functions of space and time. As the angular velocity and the curvature are assumed to be analytic functions, they must satisfy certain integrability conditions to assure the unique rotation is obtained from the two differential equations. The objective of the present paper is to derive approximate, yet closed-form solutions of the following problem: for a given curvature vector, determine both the rotation and the angular velocity. In order to avoid the singularity of kinematic relations, the quaternions are used for the parametrization of rotations, and the integrations are partly performed in the four-dimensional quaternion space. The resulting closed-form expressions for the rotational and angular velocity quaternions are ready to be used in the finite-element formulations of the dynamics of flexible spatial beams as interpolating functions. The present novel solution is assessed by comparisons of the numerical results with analytical solutions for variety of oscillating curvature functions, as well as with the solutions of the quaternion-based midpoint integrator and the Runge–Kutta-based Crouch–Grossman geometrical methods CG3 and CG4.     

SIFT算法在点云配准中的应用

提出一种精确有效的点云配准算法。通过对图像进行SIFT特征检测与匹配来获得特征点与匹配关系,用RANSAC算法剔除误匹配点,然后由映射关系获取三维对应特征点,采用投票法来进一步剔除误匹配点。在由单位四元数法获得点云初始位置关系的基础上,采用基于特征点的改进ICP算法来实现精确配准。通过实验验证,该算法在点云配准中具有速度快和稳定性好的特点。     

Hermite Interpolation of Solid Orientations with Circular Blending Quaternion Curves

Construction methods are presented that generate Hermite interpolation quaternion curves on SO(3). Two circular curves C₁(t) and C₂(t), 0 ≤ t ≤ 1, are generated that interpolate two orientations q₁ and q₂, and have boundary angular velocities: C₁′(0) = ω₁ and C₂′(1) = ω₂, respectively. They are smoothly blended together on SO(3) to generate a Hermite quaternion curve Q(t) ∈ SO(3), 0 ≤ t ≤ 1, which satisfies the boundary conditions: Q(0) = q₁, Q(1) = ₂, Q′(0) = ω₁, and Q′ (1) = ω₂.     

飞行器大迎角运动新模型及应用

首次提出了既适应小迎角又适应大迎角飞行的切换新模型。理论分析和实际应用结果表明，使用大迎角切换新模型，可以给出状态估计和气动导数辨识更准确的结果。     

四元数矩阵的右特征值与三种奇异值的一些不等式

给出了四元数矩阵的右特征值与三种奇异值的一些不等式。这些结果推广、改进了ＭｉｃｈａｅｌＩ．Ｇｉｌ，Ｔ．Ａｎｄｏ和Ｃ．Ｋ．Ｌｉ的相应结论。     

示教机械臂姿态解算改进方法仿真研究

在示教机械臂姿态解算精度优化的研究中,针对使用单组传感器进行数据融合,姿态解算的传统方法中存在的精度低,稳定性差的问题,设计了一种组合MEMS传感器的姿态解算方法。将六组传感器安装于载体坐标系三个轴上,分别测量两组传感器数据。以传感器量测数据与四元数估计数据的向量积代替姿态角误差作为互补滤波器的输入量,分别利用模糊控制器和PI控制器,根据互补滤波原理调节陀螺仪输出量。通过拓展卡尔曼滤波器进行姿态估计,得到更精确的四元数,进而转化为姿态角。仿真结果表明,在静态和动态情况下,多组传感器组合调节后的姿态角数据相比单组传感器PI调节在姿态角精度和系统稳定性上有进一步提高。     

从运动捕获数据中提取关键帧

在四元数表示下导出了两个旋转之间差异的一种简单形式,将人体各关节上总的旋转变化作为帧间距,设计了一种从运动捕获数据中提取关键帧的高效算法,通过向量的线性插值和四元数的球面线性插值重建了原始动画。实验表明,该算法具有很好的数据压缩效果,而且提取出的关键帧在视觉上对原始动画具有概括力。     

利用n维参数L系统构造超复数空间广义M-J集

利用n维参数L系统描述了超复数空间广义Mandelbrot集和Julia集,给出了描述算法和实验所得图形,并对四元数广义M-J集的动力学特征进行了理论上的分析和探讨.经过实验发现,四元数广义M-J集在保留了复平面M-J集特征的基础上,还有一些特殊的性质,如广义M集在三维虚轴截面上的拓扑结构等同于球体,四元数Julia集在参数c同模同实部的情况下保持着结构的一致性.实验结果表明,n维参数L系统字母表较为简洁,包含信息量大,可以有效的描述诸如广义M-J集和四元数广义M-J集的分形集.     

四元数量子力学中一类特征值反问题及其应用

本文研究了四元数量子力学中一类要求其解是正规或可对角化四元数矩阵的特征值反问题。并给出了其有解的充要条件和通解的表达式。讨论了四元数量子力学中带有谱约束的最小二乘解反问题,得到了此问题有解的充分条件。最后给出了数值算法和数值例子。     

Automatic Key-Frame Extraction from Optical Motion Capture Data

Optical motion capture is an increasingly popular animation technique. In the last few years, plenty of methods have been proposed for key-frame extraction of motion capture data, and it is a common method to extract key-frame using quaternion. Here, one main difficulty is due to the fact that previous algorithms often need to manually set various parameters. In addition, it is problematic to predefine the appropriate threshold without knowing the data content. In this paper, we present a novel adaptive threshold-based extraction method. Key-frame can be found according to quaternion distance. We propose a simple and efficient algorithm to extract key-frame from a motion sequence based on adaptive threshold. It is convenient with no need to predefine parameters to meet certain compression ratio. Experimental results of many motion captures with different traits demonstrate good performance of the proposed algorithm. Our experiments show that one can typically cut down the process of extraction from several minutes to a couple of seconds.