scholarly journals Pose Changes From a Different Point of View

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Gregory S. Chirikjian ◽  
Robert Mahony ◽  
Sipu Ruan ◽  
Jochen Trumpf
Keyword(s):  
Rigid Body ◽  
Reference Frame ◽  
Semidirect Product ◽  
Group Structure ◽  
Linear Part ◽  
Point Of View ◽  
Affine Transformations ◽  
Fixed Reference ◽  
New Perspective ◽  
Direct Product Group

For more than a century, rigid-body displacements have been viewed as affine transformations described as homogeneous transformation matrices wherein the linear part is a rotation matrix. In group-theoretic terms, this classical description makes rigid-body motions a semidirect product. The distinction between a rigid-body displacement of Euclidean space and a change in pose from one reference frame to another is usually not articulated well in the literature. Here, we show that, remarkably, when changes in pose are viewed from a space-fixed reference frame, the space of pose changes can be endowed with a direct product group structure, which is different from the semidirect product structure of the space of motions. We then show how this new perspective can be applied more naturally to problems such as monitoring the state of aerial vehicles from the ground, or the cameras in a humanoid robot observing pose changes of its hands.

Pose Changes From a Different Point of View

2017 ◽  
Author(s):  
Gregory S. Chirikjian ◽  
Robert Mahony ◽  
Sipu Ruan ◽  
Jochen Trumpf
Keyword(s):  
Rigid Body ◽  
Reference Frame ◽  
Direct Product ◽  
Group Structure ◽  
Linear Part ◽  
Point Of View ◽  
Affine Transformations ◽  
Fixed Reference ◽  
New Perspective ◽  
Direct Product Group

For more than a century, rigid-body displacements have been viewed as affine transformations described as homogeneous transformation matrices wherein the linear part is a rotation matrix. In group-theoretic terms, this classical description makes rigid-body motions a semi-direct product. The distinction between a rigid-body displacement of Euclidean space and a change in pose from one reference frame to another is usually not articulated well in the literature. Here we show that, remarkably, when changes in pose are viewed from a space-fixed reference frame, the space of pose changes can be endowed with a direct product group structure, which is different from the semi-direct product structure of the space of motions. We then show how this new perspective can be applied more naturally to problems such as monitoring the state of aerial vehicles from the ground, or the cameras in a humanoid robot observing motions of its hands.

Be´zier Curves on Riemannian Manifolds and Lie Groups with Kinematics Applications

1995 ◽  
Vol 117 (1) ◽  
pp. 36-40 ◽  
Author(s):  
F. C. Park ◽  
B. Ravani
Keyword(s):  
Riemannian Manifold ◽  
Rigid Body ◽  
Lie Groups ◽  
Riemannian Manifolds ◽  
Reference Frames ◽  
Group Structure ◽  
Recursive Algorithm ◽  
Fixed Reference ◽  
Spatial Displacements ◽  
Natural Way

In this article we generalize the concept of Be´zier curves to curved spaces, and illustrate this generalization with an application in kinematics. We show how De Casteljau’s algorithm for constructing Be´zier curves can be extended in a natural way to Riemannian manifolds. We then consider a special class of Riemannian manifold, the Lie groups. Because of their group structure Lie groups admit an elegant, efficient recursive algorithm for constructing Be´zier curves. Spatial displacements of a rigid body also form a Lie group, and can therefore be interpolated (in the Be´zier sense) using this recursive algorithm. We apply this alogorithm to the kinematic problem of trajectory generation or motion interpolation for a moving rigid body. The orientation trajectory of motions generated in this way have the important property of being invariant with respect to choices of inertial and body-fixed reference frames.

Bézier Curves on Riemannian Manifolds and Lie Groups With Kinematics Applications

1994 ◽  
Author(s):  
Frank C. Park ◽  
Bahram Ravani
Keyword(s):  
Riemannian Manifold ◽  
Rigid Body ◽  
Lie Groups ◽  
Riemannian Manifolds ◽  
Group Structure ◽  
Recursive Algorithm ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Spatial Displacements ◽  
Natural Way

Abstract In this article we generalize the concept of Bézier curves to curved spaces, and illustrate this generalization with an application in kinematics. We show how De Casteljau’s algorithm for constructing Bézier curves can be extended in a natural way to Riemannian manifolds. We then consider a special class of Riemannian manifold, the Lie groups. Because of their algebraic group structure Lie groups admit an elegant, efficient recursive algorithm for constructing Bézier curves. Spatial displacements of a rigid body also form a Lie group, and can therefore be interpolated (in the Bezier sense) using this recursive algorithm. We apply this algorithm to the kinematic problem of trajectory generation or motion interpolation for a moving rigid body.

TRADITION AND INNOVATION IN MODERN KAZAKH POETRY (XX century and independence)

2021 ◽  
Vol 76 (2) ◽  
pp. 118-128
Author(s):  
Sh. Kuttybaev ◽  
◽  
Е. Abdimomynov ◽  
Keyword(s):  
20Th Century ◽  
Large Scale ◽  
Point Of View ◽  
Soviet Period ◽  
Evolutionary Development ◽  
Spiritual Values ◽  
Literary Traditions ◽  
New Perspective ◽  
National Poetry ◽  
In The Beginning

The article analyzes views on innovation in the literary science of the early twentieth century and the work of Alash representatives in an era that is a period filled with profound changes and large-scale innovations in Kazakh society. In addition, works related to freedom, enlightenment, politics, spiritual values, the position of the people as a whole and social changes are considered the idea of independence and continuity. On the way of evolutionary development of the Kazakh literature, artistic power, thematic and ideological character, substantial and stylistic features of poetry of poets in the beginning of the XX century and during the Great Patriotic War, in subsequent years and years of independence are discussed in detail. In addition, on the basis of literary traditions and novelty, the works of prominent poets of Kazakh poetry of the 20th century and Independence are considered and comprehensively characterized, i.e. internal motives, the content of life phenomena in national poetry are analyzed in close connection with the works of poets. The original vision of the traditional and differentiated in the literature of the Soviet period in the works of poets from a new perspective, from the point of view of today. In addition, the works of outstanding poets of Kazakh poetry in the period of the 20th century and independence are considered on the basis of classical tradition and novelty in literature.

scholarly journals Difficulty in implementing continuous improvement – Rasch measurement analysis

2019 ◽  
Vol 25 (6) ◽  
pp. 1228-1250 ◽  
Author(s):  
Lidia Sanchez-Ruiz ◽  
Beatriz Blanco ◽  
Emma Diaz
Keyword(s):  
Continuous Improvement ◽  
Measurement Theory ◽  
Reliability And Validity ◽  
Rasch Measurement ◽  
Point Of View ◽  
Future Research ◽  
Theoretical Point ◽  
Content Type ◽  
Level Of Difficulty ◽  
New Perspective

Purpose The purpose of this paper is to define a general and common construct in order to measure the level of difficulty companies experience when they implement continuous improvement (CI). Additionally, a rank of barriers is obtained together with a rank of companies. Design/methodology/approach In order to achieve the objective, first, a literature review is carried out to specify the domain of the construct; second, a sample of items is selected; third a survey is carried out in companies that have already implemented CI initiatives, the results being thus limited to this population; fourth, measures are purified by analysing the reliability and validity of the measurements, and finally results are obtained. The Rasch measurement theory will be used to provide a new perspective on a mature research topic. Findings It can be concluded that a new valid construct has been defined together with a rank of CI barriers, being lack of time the main barrier. A rank of companies is also obtained which is a first step in the development of future research studies. Practical implications Managers are provided with a better understanding of the barriers that can obstruct CI implementation. Thus, the rank of CI barriers guides managers through the most common and important obstacles so that they will be able to plan better CI strategies. In addition, the rank of companies allows each company to undertake a benchmarking exercise. Originality/value This work proposes a new way of analysing the difficulty in implementing CI as a continuum, rather than as independent barriers. From a theoretical point of view, it defines a new construct and offers a rank of CI barriers together with a rank of companies based on their level of difficulty when implementing CI initiatives. This is something new, as previous studies were mainly focussed on the items side. From a practical point of view, this study offers the surveyed companies the opportunity to see how they are positioned with respect to the other companies. Moreover, this rank of companies is the foundation on which to develop further studies with a practical orientation in the future.

scholarly journals A CRITICAL ANALYSIS OF THE COSMOLOGICAL IMPLEMENTATION OF LOOP QUANTUM GRAVITY

2012 ◽  
Vol 27 (07) ◽  
pp. 1250032 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Critical Discussion ◽  
Point Of View ◽  
Graph Structure ◽  
Quantum Geometry ◽  
Cosmological Problem ◽  
New Perspective ◽  
Made In

This papers offers a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG) theory. Revising recent issues in preserving SU(2) symmetry when quantizing the isotropic Universe, we trace a new perspective in approaching the cosmological problem within quantum geometry. The cosmological sector of LQG is reviewed and a critical point of view on LQC is presented. It is outlined how a polymer-like scale for quantum cosmology can be predicted from a proper fundamental graph underlying the homogeneous and isotropic continuous picture. However, such a minimum scale does not coincide with the choice made in LQC. Finally, the perspectives towards a consistent cosmological LQG model based on such a graph structure are discussed.

Screw-Retained Implant-Supported Fixed Dental Restorations: A Rational Method to Overcome Esthetic Issues with the Screw-Access Hole

2021 ◽  
Vol 7 (4) ◽  
Author(s):  
Etienne O ◽  
◽  
Waltmann E ◽  
Serfaty R ◽  
◽  
...  
Keyword(s):  
Bacterial Contamination ◽  
Point Of View ◽  
Dental Restoration ◽  
Rational Method ◽  
Rational Analysis ◽  
Dental Restorations ◽  
Access Hole ◽  
Functional Point ◽  
New Perspective ◽  
Materials Used

Achieving both esthetics and a perfect seal of the screw-access hole in a screw-retained implant-supported fixed dental restoration is a great challenge. From a functional point of view, a perfect seal needs to be obtained to prevent bacterial contamination along the screw access canal and the occlusion shall be addressed. Such a challenging procedure has to be based on a rational analysis of the different materials used. Screw-retained zirconia-based restorations offer a new perspective for esthetic and biocompatible results. The aim of this article is to describe an easy and reproducible clinical procedure to esthetically seal the screw-access hole of screw-retained implant-supported fixed dental restorations.

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