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.      

计算机代数系统Maple及其在机器人学上的应用

简要介绍计算机代数系统Maple功能 ,举例说明在机器人学中的应用 ,最后讨论了应用该系统应该注意的问题。利用其强大的符号计算功能使研究人员从推导公式的繁琐劳动中部分解脱 ,具有较强的现实意义     

On the Center of Generic Hecke Algebra

We knowthat the set of conjugancy class sumsof the group algebraR[W]forms a basisfor the cen-ter ofR[W]for any ringRand any finite WeylgroupW.It is knownthat thereis the Lusztig’siso-morphism between the group algebra ofWoverQ(q21)and the Hecke algebraH(W)overQ(q21),whereqis anindeterminate overQ[1].Therefore,itis natural to askif there is a“generic”analogue(or aq-analogue)of the above basis for the center ofR[W].Is there a canonical basis for the center ofthe Hecke algebraH(Sn)over…     

A 3D GIS spatial data model based on conformal geometric algebra

We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are con...     

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。     

Multichannel image contrast enhancement based on linguistic rule-based intensificators

This study follows the direct approach to image contrast enhancement, which changes the image contrast at each its pixel and is more effective than the indirect approach that deals with image histograms. However, there are only few studies following the direct approach because, by its nature, it is very complex. Additionally, it is difficult to develop an effective method since it is required to keep a balance in maintaining local and global image features while changing the contrast at each individual pixel. Moreover, raw images obtained from many sources randomly influenced by many external factors can be considered as fuzzy uncertain data. In this context, we propose a novel method to apply and immediately handle expert fuzzy linguistic knowledge of image contrast enhancement to simulate human capability in using natural language. The formalism developed in the study is based on hedge algebras considered as a theory, which can immediately handle linguistic words of variables. This allows the proposed method to produce an image contrast intensificator from a given expert linguistic rule base. A technique to preserve global as well as local image features is proposed based on a fuzzy clustering method, which is applied for the first time in this field to reveal region image features of raw images. The projections of the obtained clusters on each channel are suitably aggregated to produce a new channel image considered as input of the pixelwise defined operators proposed in this study. Many experiments are performed to demonstrate the effect of the proposed method versus the counterparts considered.     

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.     

VEST: Abstract vector calculus simplification in Mathematica

We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined standard form. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by reduction, subsequently applying these to simplify large expressions. In a companion paper Burby et al. (2013)  [12], we employ VEST in the automation of the calculation of high-order Lagrangians for the single particle guiding center system in plasma physics, a computation which illustrates its ability to handle very large expressions. VEST has been designed to be simple and intuitive to use, both for basic checking of work and more involved computations.