Natural coordinates for the computer analysis of multibody systems

In this paper we will describe a new method for the computer kinematic and dynamic analysis of a wide range of three-dimensional mechanisms or multibody systems. This method is based on a new system of non-independent coordinates that use Cartesian coordinates of points and Cartesian components of unitary vectors in order to describe the position and the motion of the system. Angular coordinates are not used. The kinematic constraint equation comes in two ways, from the rigid-body condition for each element and from the joints or kinematic pairs. The consideration of unitary vectors facilitates considerably the formulation of pair constraints when the pair is associated with a particular direction, as is the case with revolute (R), cylindrical (C), or prismatic (P) pairs. The constraint equations are quadratic in the problem coordinates and they never involve transcendental functions. The dynamic differential equations are obtained in a very simple and effective way from the theorem of virtual power. Finally, two examples will be presented.     

High-accuracy simulation of orbital dynamics: An object-oriented approach

The use of Keplerian or Equinoctial parameters instead of Cartesian coordinates as state variables in object-oriented spacecraft models is introduced in this paper. The rigid body model of the standard MultiBody library is extended by adding transformation equations from Keplerian or Equinoctial parameters to Cartesian coordinates, and by setting the former as preferred states, instead of the latter. The remaining parts of the model are left untouched, thus ensuring maximum re-usability of the model itself. The results shown in the paper demonstrate the superior accuracy and speed of computation both in the case of a point-mass gravity field, and in the case of more accurate gravity field models.     

Progress of current seamless virtual boundary method

In this paper, a current virtual boundary method, i.e., a seamless virtual boundary method (VBM) is presented. In the seamless VBM, the forcing term is added not only to the grid points near the boundary but also to the grid points inside the boundary, in order to remove unphysical oscillations near the boundary. The development of seamless VBM can be applied to solve for heat transfer and moving boundary problems in both the Cartesian and the curvilinear coordinates, and the lattice Boltzmann equation. A series of the method is validated in the typical test problems. Therefore, it is concluded that the present method is a very versatile numerical approach for solving the incompressible Navier–Stokes equations.     

The determination of implicit polynomial canonical curves

A new method is presented for identifying and comparing closed, bounded, free-form curves that are defined by even implicit polynomial (IP) equations in the X-Y Cartesian coordinates. The method provides a new expression for an IP involving a product of conic factors with unique conic factor centers. The critical points for an IP curve are also defined. The conic factor centers and the critical points are shown to be useful related points that directly map to one another under affine transformations. In particular, the explicit determination of such points implies both a canonical form for the curves and the transformation matrix which relates affine equivalent curves     

Moving grids for magnetic reconnection via Newton–Krylov methods

This paper presents a set of computationally efficient, adaptive grids for magnetic reconnection phenomenon where the current density can develop large gradients in the reconnection region. Four-field extended MagnetoHydroDynamics (MHD) equations with hyperviscosity terms are transformed so that the curvilinear coordinates replace the Cartesian coordinates as the independent variables, and moving grids' velocities are also considered in this transformed system as a part of interpolating the physical solutions from the old grid to the new grid as time advances. The curvilinear coordinates derived from the current density through the Monge–Kantorovich (MK) optimization approach help to reduce the resolution requirements during the computation.     

A recursive,numerically stable,and efficient simulation algorithm for serial robots

Traditionally, the dynamic model, i.e., the equations of motion, of a robotic system is derived from Euler–Lagrange (EL) or Newton–Euler (NE) equations. The EL equations begin with a set of generally independent generalized coordinates, whereas the NE equations are based on the Cartesian coordinates. The NE equations consider various forces and moments on the free body diagram of each link of the robotic system at hand, and, hence, require the calculation of the constrained forces and moments that eventually do not participate in the motion of the coupled system. Hence, the principle of elimination of constraint forces has been proposed in the literature. One such methodology is based on the Decoupled Natural Orthogonal Complement (DeNOC) matrices, reported elsewhere. It is shown in this paper that one can also begin with the EL equations of motion based on the kinetic and potential energies of the system, and use the DeNOC matrices to obtain the independent equations of motion. The advantage of the proposed approach is that a computationally more efficient forward dynamics algorithm for the serial robots having slender rods is obtained, which is numerically stable. The typical six-degree-of-freedom PUMA robot is considered here to illustrate the advantages of the proposed algorithm.     

Adaptive artificial viscosity for multidimensional gas dynamics for Euler variables in Cartesian coordinates

A method of adaptive artificial viscosity (AAV2D-3D) for the solution of two-and three-dimensional equations of gas dynamics for Euler variables in the Cartesian coordinates system is considered. This paper continues works [1, 2]. The computational scheme is described in detail and the results of the test case are given.     

二维空间上基于呼叫详细记录数据的用户移动性分析

针对当前基于呼叫详细记录(CDR) 研究用户移动性主要局限于移动距离、回旋半径等一维尺度,且该尺度不能准确描述移动范围的问题,提出在二维空间上用覆盖移动轨迹的凸包面积来描述用户的移动范围,用群体移动向量分析人群的移动行为。首先,设计了一种基于经纬度建立二维平面笛卡尔坐标系的方法。该方法结合墨卡托投影与半正矢公式得到散点间方位与距离,并依此确立散点在平面坐标系的坐标;然后,基于该坐标系计算了覆盖用户一天内移动轨迹的凸包及其面积,并统计其分布;最后,对所有用户的移动向量分时段作累积,分析群体移动向量在一天内的变化。实验结果表明,在180 km范围内,新坐标所计算的方位角与由墨卡托投影下确定的结果平均偏差0.037°,点间距离与由半正矢公式得到的结果平均偏差0.102%,可以很好地保持散点间的方位与距离关系。覆盖移动轨迹的凸包面积满足幂律分布,并与移动距离有较高的相关性。群体移动向量的变化展现了人群移动的潮汐现象,而且为发掘用户所在区域与周边地区的联系提供新的视角。     

Calculations of two-dimensional test problems by the method of adaptive viscosity

The paper is concerned with calculations of two-dimensional test gas dynamic problems through a new artificial viscosity grid method. A detailed account of this method is given in [1, 2]; it was extended in [3] to two and three dimensions. The equations are considered in a rectangle and in step-shaped regions using Cartesian coordinates and Euler variables, and they are closed by the gas law of ideal polytropic gas. Test problems are taken from [4–6]. A comparison of the solution of these problems as obtained by the AAV method and other methods put forward in [4–6] is made.     

Relative Finite Element Coordinates in Multibody System Simulation

In the paper a numerical approach for deriving the nonlinear explicitform dynamic equations of rigid and flexible multibody systems ispresented. The dynamic equations are obtained as Ordinary DifferentialEquations for generalized coordinates and without algebraic constraints.The Finite Element Theory is applied for discretization of flexiblebodies. The minimal set of the generalized coordinates includesindependent joint motions, as well as independent small flexibledeflections of finite element nodes. The node deflections and stiffnessmatrices are calculated with respect to the moving relative coordinatesystems of the flexible bodies. The positions and orientations ofelement and substructure coordinate systems are updated according to thenode deflections. A major step of the numerical process is the kinematicanalysis and calculation of matrices of partial derivatives of thequasi-coordinates (dependent joint motions and coordinates of points andnodes) with respect to the generalized coordinates. The inertia terms inthe dynamic equations are obtained multiplying the matrices of thepartial derivatives by the mass matrices of the rigid and flexiblebodies. Stiffness properties of flexible bodies are presented in thedynamic equations by stiff forces that depend on the generalizedrelative flexible deflections only. Several examples of large motion ofbeam structures show the effectiveness of the algorithm.     

Geometric stiffening of flexible link system with large overall motion

In the conventional hybrid-coordinate formulation, the Cartesian deformation variables are employed with a linear Cauchy strain measure. It has been found that such modeling method fails to capture the motion-induced stiffness terms and provides erroneous dynamic results in case of high rotating speed. In this paper, geometric stiffening of flexible link system is investigated. Using a non-Cartesian deformation variable, the equations of motion of each link, which include the stiffening terms, are obtained based on the virtual power principle, and forward recursive formulation is employed to derive the equations of flexible link system. Relative generalized coordinates are employed to derive the equations of motion of the link system. Numerical examples are presented to investigate the stiffening effect on large overall motion as well as deformation of the flexible link system and to testify the accuracy and efficiency of the formulation.     

PolSOM: A new method for multidimensional data visualization

In this paper, a new algorithm named polar self-organizing map (PolSOM) is proposed. PolSOM is constructed on a 2-D polar map with two variables, radius and angle, which represent data weight and feature, respectively. Compared with the traditional algorithms projecting data on a Cartesian map by using the Euclidian distance as the only variable, PolSOM not only preserves the data topology and the inter-neuron distance, it also visualizes the differences among clusters in terms of weight and feature. In PolSOM, the visualization map is divided into tori and circular sectors by radial and angular coordinates, and neurons are set on the boundary intersections of circular sectors and tori as benchmarks to attract the data with the similar attributes. Every datum is projected on the map with the polar coordinates which are trained towards the winning neuron. As a result, similar data group together, and data characteristics are reflected by their positions on the map. The simulations and comparisons with Sammon's mapping, SOM and ViSOM are provided based on four data sets. The results demonstrate the effectiveness of the PolSOM algorithm for multidimensional data visualization.     

基于球面坐标的目标定位位置的封闭解算法

针对无线传感网络WSNs(Wireless Sensor Networks)的三维目标定位问题,提出基于接收信号强度RSS(Received Signal Strength)和到达角度AoA(Angle of Arrival)混合目标定位RATL(RSS and AoA-based Target Localization algorithm)算法.RATL算法融合了RSS和AoA观察值.通过将笛卡尔坐标转换球面坐标,并充分利用AoA测量值的优势,RATL算法建立测量值与未知目标位置间的关系,进而获取简单、封闭解.相比于现在算法,RATL算法并不要求更多松驰.实验数据表明,RATL算法比同类算法的复杂度低、定位精度高.     

球面坐标下的凸组合球面参数化

球面参数化是一种应用价值很广的几何参数化方法.对于封闭且亏格为零的三角形网格,该文提出了一种新的球面参数化方法.通过引入多个球面坐标覆盖,在球面坐标系下,用凸组合方法,得到了接近线性的球面参数化求解方法.与已有的直角坐标系下的凸组合参数化方法相比,该文所提出的方法大大降低了求解方程组的非线性程度,因此求解时间大幅度降低.此外,还避免了直角坐标系下求解的多种退化情况.最后,给出了实验结果,并对凸组合球面参数化中存在的几个问题进行了讨论.     

Experiments on estimating egomotion and structure parameters using long monocular image sequences

This paper presents a simple but robust model based approach to estimating the kinematics of a moving camera and the structure of the objects in a stationary environment using long, noisy, monocular image sequences. Both batch and recursive algorithms are presented and the problem due to occlusion is addressed. The approach is based on representing the constant translational velocity and constant angular velocity of the camera motion using nine rectilinear motion parameters, which are 3-D vectors of the position of the rotation center, linear and angular velocities. The structure parameters are 3-D coordinates of the salient feature points in the inertial coordinate system. Due to redundancies in parameterization, the total number of independent parameters to be estimated is 3M+7, whereM is the number of feature points. The image plane coordinates of these feature points in each frame are first detected and matched over the frames. These noisy image coordinates serve as the input to our algorithms. Due to the nonlinear nature of perspective projection, a nonlinear least squares method is formulated for the batch algorithm, and a conjugate gradient method is then applied to find the solution. A recursive method using an Iterated Extended Kalman Filter (IEKF) for incremental estimation of motion and structure is also presented. Since the plant model is simple in our formulation, closed form solutions for the state and covariance transition equations are easily derived. Experimental results for simulated imagery as well as several real image sequences are included.The support of the Advanced Research Projects Agency (ARPA order No. 8459), the U.S. Army Topographic Engineering Center under contract DACA 76-92-C-0009, and the Department of Electrical Engineering at the University of Maryland is gratefully acknowledged.     

Optimal cross-section and configuration design of elastic-plastic structures subject to dynamic cyclic loading

This paper shows an optimal design problem with continuum variational formulation, applied to nonlinear elasticplastic structures subject to dynamic loading. The total Lagrangian procedure is used to describe the response of the structure. The direct differentiation method is used to obtain the sensitivities of the structural response that are needed to solve the optimization problem. Since unloading and reloading of the structure are allowed, the structural response is path-dependent and an additional step is needed to integrate the constitutive equations. It can be shown, consequently, that design sensitivity analysis is also path-dependent. A finite element method with implicit time integration is used to discretize the state and sensitivity equations.A mathematical programming approach is used for the optimization process. Numerical applications are performed on a 3-D truss structure, where cross-sectional areas and nodal point coordinates are treated as design variables. Optimal designs have been obtained and compared by using two different strategies: a twolevel strategy where the levels are defined according to the type of design variables, cross sectional areas or node coordinates, and optimizing simultaneously with respect to both types of design variables. Comparisons have also been made between optimal designs obtained by considering or not considering the inertial term of the structural equilibrium.     

一种基于B样条曲面的深度图像重抽样方法

银行深度图像处理中由于等角测距造成的几何失真,根据非等网格深度数据的数值特点,文中提出了一种基于B样条曲面的深度图像重抽样方法,并且与其它一些三维插值方法进行了精度比较。该文利用真实深度图像进行了重抽样实验,结果表明,基于B样条曲面的重抽样方法有效地克服了原始图像数据中存在的几何失真以及测量噪声,为后续的三维表面处理提供了更为精确的三维网格深度数据。