Some Examples of Rigid Representations

*Research partially supported by INTAS grant 97-1644.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Probabilistic position and orientation estimation of rigid objects using an RGB-D sensor

The recent emergence of low-cost RGB-D sensors has brought new opportunities for robotics by providing affordable devices that can provide synchronized images with both color and depth information. In this thesis, recent work on pose estimation utilizing RGBD sensors is reviewed. Also, a pose recognition system for rigid objects using RGB-D data is implemented. The implementation uses half-edge primitives extracted from the RGB-D images for pose estimation. The system is based on the probabilistic object representation framework by Detry et al., which utilizes Nonparametric Belief Propagation for pose inference. Experiments are performed on household objects to evaluate the performance and robustness of the system.

Representation and Detection of Shapes in Images

We present a set of techniques that can be used to represent and detect shapes in images. Our methods revolve around a particular shape representation based on the description of objects using triangulated polygons. This representation is similar to the medial axis transform and has important properties from a computational perspective. The first problem we consider is the detection of non-rigid objects in images using deformable models. We present an efficient algorithm to solve this problem in a wide range of situations, and show examples in both natural and medical images. We also consider the problem of learning an accurate non-rigid shape model for a class of objects from examples. We show how to learn good models while constraining them to the form required by the detection algorithm. Finally, we consider the problem of low-level image segmentation and grouping. We describe a stochastic grammar that generates arbitrary triangulated polygons while capturing Gestalt principles of shape regularity. This grammar is used as a prior model over random shapes in a low level algorithm that detects objects in images.

Fast 2D/3D object representation with growing neural gas

This work presents the design of a real-time system to model visual objects with the use of self-organising networks. The architecture of the system addresses multiple computer vision tasks such as image segmentation, optimal parameter estimation and object representation. We first develop a framework for building non-rigid shapes using the growth mechanism of the self-organising maps, and then we define an optimal number of nodes without overfitting or underfitting the network based on the knowledge obtained from information-theoretic considerations. We present experimental results for hands and faces, and we quantitatively evaluate the matching capabilities of the proposed method with the topographic product. The proposed method is easily extensible to 3D objects, as it offers similar features for efficient mesh reconstruction.

Fixed-boundary constituencies and the principle of equal representation in Ireland

The process of constituency boundary revision in Ireland, designed to satisfy what is perceived as a rigid requirement that a uniform deputy-population ratio be maintained across constituencies, has traditionally consumed a great deal of the time of politicians and officials. For almost two decades after a High Court ruling in 1961, the process was a political one, was highly contentious, and was marked by serious allegations of ministerial gerrymandering. The introduction in 1979 of constituency commissions made up of officials neutralised, for the most part, charges that the system had become too politicised, but it continued the process of micro-management of constituency boundaries. This article suggests that the continuing problems caused by this system – notably, the permanently changing nature of constituency boundaries and resulting difficulties of geographical identification – could be resolved by reversion to the procedure that is normal in proportional representation systems: periodic post-census allocation of seats to constituencies whose boundaries are based on those of recognised local government units and which are stable over time. This reform, replacing the principle of redistricting by the principle of reapportionment, would result in more recognisable constituencies, more predictable boundary trajectories over time, and a more efficient, fairer, and speedier process of revision.

Comparison Of Postoperative Stability Of Three Rigid Internal Fixation Techniques After Sagittal Split Ramus Osteotomy For Mandibular Advancement.

The aim of this investigation was to compare the skeletal stability of three different rigid fixation methods after mandibular advancement. Fifty-five class II malocclusion patients treated with the use of bilateral sagittal split ramus osteotomy and mandibular advancement were selected for this retrospective study. Group 1 (n = 17) had miniplates with monocortical screws, Group 2 (n = 16) had bicortical screws and Group 3 (n = 22) had the osteotomy fixed by means of the hybrid technique. Cephalograms were taken preoperatively, 1 week within the postoperative care period, and 6 months after the orthognathic surgery. Linear and angular changes of the cephalometric landmarks of the chin region were measured at each period, and the changes at each cephalometric landmark were determined for the time gaps. Postoperative changes in the mandibular shape were analyzed to determine the stability of fixation methods. There was minimum difference in the relapse of the mandibular advancement among the three groups. Statistical analysis showed no significant difference in postoperative stability. However, a positive correlation between the amount of advancement and the amount of postoperative relapse was demonstrated by the linear multiple regression test (p < 0.05). It can be concluded that all techniques can be used to obtain stable postoperative results in mandibular advancement after 6 months.

Proposição e avaliação de um modelo de representação dos membros superiores e escapula durante a marcha humana

Universidade Estadual de Campinas . Faculdade de Educação Física

Analise de marcha : protocolo experimental a partir de variaveis cinematicas e antropometricas

Universidade Estadual de Campinas . Faculdade de Educação Física

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.

Methods of imagetic information representation

The aim of this paper is to highlight some of the methods of imagetic information representation, reviewing the literature of the area and proposing a model of methodology adapted to Brazilian museums. An elaboration of a methodology of imagetic information representation is developed based on Brazilian characteristics of information treatment in order to adapt it to museums. Finally, spreadsheets that show this methodology are presented.

The game inside the school: a representation of 5(th) graders physical education classes

Since the beginning of Physical Education entrance in the brazilin public schools, the game has been frequently used as content, and in the course of time that practice seems to be intensified. In spite of many approaches of different purposes to justify its pedagogic usefulness, the game has been used as an indiscriminate way due to the fascination that it provides to the students. The present study searches for a description and analysis of children`s (10-12 years old) attitudes behaviors in games, on Physical Education classes, inside a public school. The study was accomplished with the researcher also attending as a teacher (action research). For the accomplishment of the study 55 children were filmed in four different games, of different kinds (exposed, transformed, and spontaneous). The classes` description and analysis were focused in the attitude axis and it was defined four topics for the discussion: Conflicts, Respect of rules, Expressiveness, and Competitiveness. The relationship between the individual with the game and its culture were pointed as the main characteristics in the configuration of the ludicrous activity atmosphere. It was also possible to observe specific situations of this relationship, once the games were limited to the social games (Piaget category), in a school atmosphere where children have students roles. Due to the obtained results, the study proposes a reflexive practice in which the students notice their own attitudes and try to adapt the game to their needs and not he other way around. In this perspective, the teacher has an important mediator roll, once he will be responsible to point out the students` difficulties and promote discussions in favor to provide teamwork.

Experimental results on the nonlinear H(infinity) control via quasi-LPV representation and game theory for wheeled mobile robots

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear H(infinity) approaches. Two nonlinear H(infinity) controllers that guarantee induced L(2)-norm, between input (disturbances) and output signals, bounded by an attenuation level gamma, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

Analysis of a semi-rigid connection for precast concrete

This paper presents a study of a specific type of beam-to-column connection for precast concrete structures. Furthermore, an analytical model to determine the strength and the stiffness of the connection, based on test results of two prototypes, is proposed. To evaluate the influence of the strength and stiffness of the connection on the behaviour of the structure, the results of numerical simulations of a typical multi-storey building with semi-rigid connections are also presented and compared with the results using pinned and rigid connections. The main conclusions are: (a) the proposed design model can reasonably evaluate the studied connection strength; (b) the evaluation of strength is more accurate than that of stiffness; (c) for a typical structure, it is possible to increase the number of storeys of the structure from two to four with lower horizontal displacement at the top, and only a small increase of the column base bending moment by replacing the pinned connections with semi-rigid ones; and (d) although there is significant uncertainty in the connection stiffness, the results show that the displacements at the top of the structure, and the column base moments present low susceptibility deviations to this parameter.

A solid-like FEM for geometrically non-linear 3D frames

This study presents a solid-like finite element formulation to solve geometric non-linear three-dimensional inhomogeneous frames. To achieve the desired representation, unconstrained vectors are used instead of the classic rigid director triad; as a consequence, the resulting formulation does not use finite rotation schemes. High order curved elements with any cross section are developed using a full three-dimensional constitutive elastic relation. Warping and variable thickness strain modes are introduced to avoid locking. The warping mode is solved numerically in FEM pre-processing computational code, which is coupled to the main program. The extra calculations are relatively small when the number of finite elements. with the same cross section, increases. The warping mode is based on a 2D free torsion (Saint-Venant) problem that considers inhomogeneous material. A scheme that automatically generates shape functions and its derivatives allow the use of any degree of approximation for the developed frame element. General examples are solved to check the objectivity, path independence, locking free behavior, generality and accuracy of the proposed formulation. (C) 2009 Elsevier B.V. All rights reserved.