Student-oriented program for introductory robotics education

The aim of the paper is to present a software package for teaching introductory robotics. One of two simple manipulators (Cartesian or cylindrical coordinates) can be chosen and joined control algorithms (PID or adaptive one) together with pointed models of acutators and sensors. Computer simulation is available in an easy way for the model parameters determined. The simulation results can be displayed as graph functions, tables or as the animal of manipulators considered.     

Model reference adaptive impedance control in Cartesian coordinates for physical human–robot interaction

In this paper, a nonlinear model reference adaptive impedance controller is proposed and tested. The controller provides asymptotic tracking of a reference impedance model for the robot end-effector in Cartesian coordinates applicable to rehabilitation robotics or any other human–robot interactions such as haptic systems. The controller uses the parameters of a desired stable reference model which is the target impedance for the robot’s end-effector. It also considers uncertainties in the model parameters of the robot. The asymptotic tracking is proven using Lyapunov stability theorem. Moreover, the adaptation law is proposed in joint space for reducing the complexity of its calculations; however, the controller and the stability proof are all presented in Cartesian coordinates. Using simulations and experiments on a two DOFs robot, the effectiveness of the proposed controller is investigated.     

Averaging on Manifolds by Embedding Algorithm

We will propose a new algorithm for finding critical points of cost functions defined on a differential manifold. We will lift the initial cost function to a manifold that can be embedded in a Riemannian manifold (Euclidean space) and will construct a vector field defined on the ambient space whose restriction to the embedded manifold is the gradient vector field of the lifted cost function. The advantage of this method is that it allows us to do computations in Cartesian coordinates instead of using local coordinates and covariant derivatives on the initial manifold. We will exemplify the algorithm in the case of SO(3) averaging problems and will rediscover a few well known results that appear in literature.     

Twenty-five years of natural coordinates

In the early eighties, the author and co-workers created and further developed the natural coordinates to describe the motion of 2-D and 3-D multibody systems. Natural coordinates do not need angles or angular parameters to define orientation, leading to constant inertia matrices and to the simplest form of the constraint equations. Natural coordinates are composed by the Cartesian coordinates of some points and the Cartesian components of some unit vectors distributed on the different bodies of the system. The points and vectors can be located in the joints, being shared by contiguous bodies, decreasing or even eliminating the need to set joint constraints and reducing the total number of variables. However, other authors prefer not to share variables in order to get even simpler equations and to keep a bigger decoupling of equations, which is preferable in some cases. In this paper the history of natural coordinates is reviewed, as well as the main contributions coming from other research groups. In the second part of the paper some application areas in which natural coordinates can be particularly advantageous are examined. Commemorative Contribution.     

A flux-coordinate independent field-aligned approach to plasma turbulence simulations

This work illustrates a new approach to field-aligned coordinates for plasma turbulence simulations which is not based on flux variables. The method employs standard Cartesian or polar coordinates to discretize the fields. Parallel derivatives are computed directly along a coordinate that follows the local field, and poloidal derivatives are computed in the original Cartesian frame. Several advantages of this approach are presented. The tests on a drift-wave model demonstrate that the method is well suited to exploit the flute property of small parallel gradients by minimizing the number of degrees of freedom needed to treat a given problem in an accurate and efficient manner.     

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.     

Performance of automatic differentiation tools in the dynamic simulation of multibody systems

Within the multibody systems literature, few attempts have been made to use automatic differentiation for solving forward multibody dynamics and evaluating its computational efficiency. The most relevant implementations are found in the sensitivity analysis field, but they rarely address automatic differentiation issues in depth. This paper presents a thorough analysis of automatic differentiation tools in the time integration of multibody systems. To that end, a penalty formulation is implemented. First, open-chain generalized positions and velocities are computed recursively, while using Cartesian coordinates to define local geometry. Second, the equations of motion are implicitly integrated by using the trapezoidal rule and a Newton–Raphson iteration. Third, velocity and acceleration projections are carried out to enforce kinematic constraints. For the computation of Newton–Raphson’s tangent matrix, instead of using numerical or analytical differentiation, automatic differentiation is implemented here. Specifically, the source-to-source transformation tool ADIC2 and the operator overloading tool ADOL-C are employed, in both dense and sparse modes. The theoretical approach is backed with the numerical analysis of a 1-DOF spatial four-bar mechanism, three different configurations of a 15-DOF multiple four-bar linkage, and a 16-DOF coach maneuver. Numerical and automatic differentiation are compared in terms of their computational efficiency and accuracy. Overall, we provide a global perspective of the efficiency of automatic differentiation in the field of multibody system dynamics.     

Simplification and acceleration of crystal energy calculations under constant pressure

It is recommended that in crystal energy calculations under constant pressure one replaces the lattice parameters as independent variables by the six non-zero elements of the matrix that transforms fractional coordinates into Cartesian coordinates.     

Generation algorithm of grid model for complex terrain based on geodetic coordinate data transformation

Grid model construction is one of the preconditions for computational fluid dynamics (CFD) simulation. As many environmental accidents or unfavorable incidents occur in complex real terrain circumstances, corresponding grid model generation algorithm for scenario simulation has become a hot research field. The digital elevation model (DEM) is common for three-dimensional terrain modeling. DEM data usually consist of a certain number of geodetic coordinates, however, CFD preprocessing platform can't identify geodetic coordinates directly. In this paper, firstly an algorithm of coordinate transformation was proposed, which could convert geodetic coordinates to Cartesian coordinates in the form of length (x), width (y) and height (z). Secondly, another algorithm that generates a complex real terrain grid model was recommended based on the algorithm mentioned previously, which could import converted terrain data into a gridding platform for constructing the CFD terrain grid model. Experiments’ results showed that the terrain grid algorithm obtained through the combination of the two algorithms is highly geometrically consistent with real terrain. The algorithm provided by this study could give a more reliable and convenient basis for the application of CFD fine simulation in real complex terrain.     

REVLD: A coarse-grained model for polymers

A new model for polymers is presented. REVLD (Rigid, Excluded Volume, Langevin Dynamics) is similar to the coarse-grained, bead spring model for linear chains except that the inter-bead distance is rigidly constrained instead of using an inter-bead potential to encapsulate the connectivity. Static and dynamic results support that REVLD accurately reproduces the single-chain behavior of real polymers known from experiment, theory, and published data from existing models. Additionally, a time step can be used that is at least comparable to simulations using a FENE potential without introducing any computational overhead for accessing longer time scale modes. REVLD, and more simply the idea of using constraints in Cartesian coordinates for large simulations, was made computationally viable through the recent development of the algorithm MILC SHAKE. We expect it to improve established techniques and aid in the development of new models of import to large scale simulations that were not practicable before.     

Robust digital image watermarking method against geometrical attacks

This paper proposes a new image watermarking scheme which is robust to RST attacks with cropping by improving Fourier–Mellin transform based watermarking (FMW). The proposed scheme reorders and modifies function blocks of FMW for improvement of realization and performance. Unlike FMW, our method uses log-polar map (LPM) in the spatial domain for scaling invariance, while translation invariance is provided by the use of an invariant centroid (IC) as the origin of LPM. IC is a gravity center of a central area on gray scale image that is invariant although an image is attacked by RST. For this, its calculation method is proposed. Also since LPM includes the property which transforms rotation of Cartesian coordinates system into a cyclic shift, 2-D DFT is performed on the LPM image and the magnitude spectrum extracted to provide a domain that is rotation invariant. The resulting domain, which is invariant to RST, is then used as the watermark-embedding domain. Furthermore, to prevent the watermarked image from degrading due to the coordinate system conversion, only LPM image of watermark signal is inverse mapped to Cartesian coordinates and add to the original image. Experimental results demonstrate that the proposed scheme is robust to RST attacks.     

A procedure to find equivalences among dynamic models of planar biped robots

In this paper, a method to find equivalences among dynamic models is presented. The models are given in different generalized coordinates for the same mechanical system. This novel method is valid for planar biped robots, i.e., those whose motions are executed only in a plane. We show that no matter which generalized coordinates are used to get the dynamic models, there is always an equivalence among them by using a particular input matrix. We exhibit some advantages of getting the dynamic model using absolute coordinates instead of relative coordinates, and we show how to calculate the input matrix for getting the equivalence between these models. Because of its simplicity, a compass-like biped robot model is used as example to explain in detail the novel procedure. In order to appreciate the benefits of the proposed procedure in biped robots of high degrees of freedom, we also present the equivalence between two dynamic models for the single support phase of a 5 degrees of freedom biped robot using absolute coordinates and relative ones.     

Cartesian control of robots without dynamic model and observer design

Most control algorithms for rigid robots are given in joint coordinates. However, since the task to be accomplished is expressed in Cartesian coordinates, inverse kinematics has to be computed in order to implement the control law. Alternatively, one can develop the necessary theory directly in workspace coordinates. This has the disadvantage of a more complex robot model. In this paper, a control-observer scheme is given to achieve exact Cartesian tracking without the knowledge of the manipulator dynamics nor computing inverse kinematics. Also, only joint measurements are used.     

Deployment and control of flexible solar array system considering joint friction

It is well known that the traditional modeling theories adopt the Cartesian coordinates to establish the dynamic equation of solar array system. The order of this equation is often very high, which is inconvenient for controller design. The Cartesian coordinates are difficult to be measured in practice. In this paper, the joint coordinates are used as generalized variables to establish the dynamic equation of the solar array system. The single direction recursive construction method and the Jourdain’s velocity variation principle are used in modeling the system. The order of the established equation is lower, and the joint coordinates are easily measured in practice. Besides the dynamics modeling, joint friction and control design are extensively studied in this paper too. A three-dimensional revolute joint model is introduced, and the contribution of joint friction to the dynamic equation of the system is deduced. A fuzzy PD controller is designed to eliminate the drift of spacecraft caused by the deployment of solar array. In the end of this paper, numerical simulations are carried out to analyze the deployment dynamics and control effect of the solar array system with friction.     

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。     

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.     

利用三载流方环进行均匀磁场仿真

为实现较大范围的高精度三分量均匀磁场的仿真,解决圆环实现较困难的问题,对利用三正方形载流线圈仿真均匀磁场进行了研究.通过对正方形线框的标量位按直角坐标的幂展开式进行分析和数值计算,给出了利用共轴三正方形载流线圈仿真均匀磁场的最佳参数.利用Matlab仿真该参数,显示其可以在相当范围内实现精确的均匀磁场.在此基础上建立了一个三分量的均匀磁场模拟实验系统,实验结果表明该方案可以实现较大范围高精度三分量均匀磁场仿真.     

Differential geometry images: remeshing and morphing with local shape preservation

In this paper, we propose a novel conception of differential geometry images (DGIM), encapsulating differential coordinates to traditional geometry images. DGIM preserves the local geometric characteristics in many graphics applications, such as model remeshing and morphing. The traditional geometry images using Cartesian coordinates require normal maps for correctly rendering models, because they neglect the existence of local geometric details in the image structure, which leads us to compute the normals and curvatures imprecisely. Using our differential geometry images, normals can be reconstructed easily and correctly thereafter normal maps are no longer required. In addition, DGIM can be easily applied to mesh morphing due to its regular topology and well-preserved local details. In this paper, we also demonstrate a variety of plausible mesh morphing results based on DGIM in shape space.     

Features in Continuous Parallel Coordinates

Continuous Parallel Coordinates (CPC) are a contemporary visualization technique in order to combine several scalar fields, given over a common domain. They facilitate a continuous view for parallel coordinates by considering a smooth scalar field instead of a finite number of straight lines. We show that there are feature curves in CPC which appear to be the dominant structures of a CPC. We present methods to extract and classify them and demonstrate their usefulness to enhance the visualization of CPCs. In particular, we show that these feature curves are related to discontinuities in Continuous Scatterplots (CSP). We show this by exploiting a curve-curve duality between parallel and Cartesian coordinates, which is a generalization of the well-known point-line duality. Furthermore, we illustrate the theoretical considerations. Concluding, we discuss relations and aspects of the CPC's/CSP's features concerning the data analysis.