Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space. The vehicle’s model is established on the matrix Lie group SE(3), which describes the configuration of rigid bodies globally and uniquely. We focus on the kinematic model of the underactuated vehicle, which features an underactuation form that has no sway and heave velocity. To compensate for the lack of these two velocities, we construct additional rotation matrices to generate a motion of rotation coupled with translation. Then, the state feedback is designed with the help of the logarithmic map, and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction. Later, the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance. Finally, simulation examples are provided to verify the effectiveness of the stabilization controller.      

A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

基于差分进化算法的手眼标定方法

针对眼在手机器人视觉系统的手眼标定问题，提出了一种基于差分进化算法的手眼标定方法。首先建立了眼在手机器人视觉系统手眼标定的数学模型，通过李群李代数理论，将手眼标定问题转化为误差函数的优化问题，同时保证了优化问题的最优解落在特殊欧氏群ＳＥ（３）上。通过差分进化算法对优化问题进行求解，避免了求解过程中的局部最优问题。最后在实物平台上进行了手眼标定实验，实验结果验证了算法的可行性和有效性。     

Variational Bayesian data analysis on manifold

In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes: variational Bayesian expectation (VB-E) step and variational Bayesian maximum (VB-M) step. Moreover, the effective of different metrics for Bayesian analysis is discussed.     

带强迫项的KdV方程的非线性自伴随性和守恒律

应用非线性自伴随性的概念和伊布拉基莫夫的一般守恒律定理，研究了带强迫的KdV方程的非线性自伴随性和守恒律。首先讨论了自伴随性，结果表明这个方程具有非线性自伴随性，同时得到了这个方程的形式拉格朗日量。在对这个方程进行李对称分析之后，根据李对称的不同得到了这个方程的一些非平凡守恒律。     

Linearization through state immersion of nonlinear systems admitting Lie symmetries

In this paper, it is shown that if a nonlinear system admits a Lie symmetry that can be transformed into its Poincaré-Dulac normal form by a state diffeomorphism, then, under some technical conditions, such a nonlinear system can be immersed into a linear one. This allows us to compute in closed-form the flow, all algebraic invariant curves (through semi-invariants) of the nonlinear system, and Lyapunov functions to study stability properties.     

Lie group method: A new approach to image matching with arbitrary orientations

In this article, we develop a new method for image matching of any two images with arbitrary orientations. The idea comes from the workpiece localization in machining industry. We first describe an image as a 3D point set other than the common 2D function f(x, y), then, making the sets corresponding to the compared images form solid surfaces, we equivalently translate the matching problem into an optimization problem on the Lie group SE(3). Through developing a kind of steepest descent algorithms on a general Lie group, we present an practical algorithm for matching problem. Simulations of eye detection and face detection are presented to show the feasibility and efficiency of the proposed algorithm. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 245–252, 2010.     

基于自适应切空间的MRI图像配准

微分同胚是一种光滑可逆的变换,在MRI图像配准中可以保证图像形变后的拓扑结构保持不变,同时避免出现不合理的物理现象。为了在空间变换中获得更合理的同胚映射,高维空间中数据的非线性结构被考虑,基于流形学习方法提出一种自适应切空间的MRI图像配准算法。首先,把MRI数据构造成对称正定（SPD）的协方差矩阵,然后形成李群;接着,利用样本点邻域的局部切空间来表示李群的几何结构的非线性;接下来,在流形上用自适应邻域选择的方法形成的线性子空间去逼近局部切空间,提高切空间的局部线性化程度,从而最大限度地保留流形的局部非线性结构,得到最优的同胚映射。仿真数据和临床数据的实验结果显示,与传统的非参数微分同胚配准算法相比,该算法在高维稠密形变场上获得更高的拓扑保持度,最终提高图像配准精度。     

充电电位剩余分析及其应用

首次采用趋势分析理论处理和研究充电法中充电电位数据资料, 从理论上简单地阐述了充电电位剩余分析的特点; 并通过简单地物理模型和实例说明充电电位剩余分析的可行性和优越性;老方法新处理, 有机结合, 使充电法再现活力。     

On a new class of finite dimensional estimation algebras

We introduce a new class of solvable finite dimensional estimation algebras that contains both the linear and the Bene cases. The condition for finite dimensionality is expressed in terms of two matrices. They play an important role in understanding the structure of estimation algebras.