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Affine Connection

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Jochen Trumpf – One of the best experts on this subject based on the ideXlab platform.

  • discrete update pose filter on the special euclidean group se 3
    Conference on Decision and Control, 2019
    Co-Authors: Mohammad Zamani, Jochen Trumpf
    Abstract:

    This paper proposes two variants of the Geometric Approximate Minimum Energy (GAME) filter on the Special Euclidean Group SE(3) in the case that exteroceptive measurements are obtained in discrete time. Continuous-discrete versions of the GAME filter are provided that near-continuously predict pose and its covariance using high frequency interoceptive measurements and then update these estimates utilizing low frequency exteroceptive measurements obtained in discrete time. The two variants of the proposed filter are differentiated in their derivation due to the choice of Affine Connection used on SE(3). The proposed discrete update filters are derived based on first principles of deterministic minimum-energy filtering extended for discrete time measurements and derived directly on SE(3). The performance of the proposed filters is demonstrated and compared in simulations with a short discussion of practical implications of the choice of Affine Connection.

  • CDC – Discrete update pose filter on the special Euclidean group SE(3)
    2019 IEEE 58th Conference on Decision and Control (CDC), 2019
    Co-Authors: Mohammad Zamani, Jochen Trumpf
    Abstract:

    This paper proposes two variants of the Geometric Approximate Minimum Energy (GAME) filter on the Special Euclidean Group SE(3) in the case that exteroceptive measurements are obtained in discrete time. Continuous-discrete versions of the GAME filter are provided that near-continuously predict pose and its covariance using high frequency interoceptive measurements and then update these estimates utilizing low frequency exteroceptive measurements obtained in discrete time. The two variants of the proposed filter are differentiated in their derivation due to the choice of Affine Connection used on SE(3). The proposed discrete update filters are derived based on first principles of deterministic minimum-energy filtering extended for discrete time measurements and derived directly on SE(3). The performance of the proposed filters is demonstrated and compared in simulations with a short discussion of practical implications of the choice of Affine Connection.

Mohammad Zamani – One of the best experts on this subject based on the ideXlab platform.

  • discrete update pose filter on the special euclidean group se 3
    Conference on Decision and Control, 2019
    Co-Authors: Mohammad Zamani, Jochen Trumpf
    Abstract:

    This paper proposes two variants of the Geometric Approximate Minimum Energy (GAME) filter on the Special Euclidean Group SE(3) in the case that exteroceptive measurements are obtained in discrete time. Continuous-discrete versions of the GAME filter are provided that near-continuously predict pose and its covariance using high frequency interoceptive measurements and then update these estimates utilizing low frequency exteroceptive measurements obtained in discrete time. The two variants of the proposed filter are differentiated in their derivation due to the choice of Affine Connection used on SE(3). The proposed discrete update filters are derived based on first principles of deterministic minimum-energy filtering extended for discrete time measurements and derived directly on SE(3). The performance of the proposed filters is demonstrated and compared in simulations with a short discussion of practical implications of the choice of Affine Connection.

  • CDC – Discrete update pose filter on the special Euclidean group SE(3)
    2019 IEEE 58th Conference on Decision and Control (CDC), 2019
    Co-Authors: Mohammad Zamani, Jochen Trumpf
    Abstract:

    This paper proposes two variants of the Geometric Approximate Minimum Energy (GAME) filter on the Special Euclidean Group SE(3) in the case that exteroceptive measurements are obtained in discrete time. Continuous-discrete versions of the GAME filter are provided that near-continuously predict pose and its covariance using high frequency interoceptive measurements and then update these estimates utilizing low frequency exteroceptive measurements obtained in discrete time. The two variants of the proposed filter are differentiated in their derivation due to the choice of Affine Connection used on SE(3). The proposed discrete update filters are derived based on first principles of deterministic minimum-energy filtering extended for discrete time measurements and derived directly on SE(3). The performance of the proposed filters is demonstrated and compared in simulations with a short discussion of practical implications of the choice of Affine Connection.

Josef Mikeš – One of the best experts on this subject based on the ideXlab platform.

  • Almost Geodesics and Special Affine Connection
    Results in Mathematics, 2020
    Co-Authors: Olga Belova, Josef Mikeš
    Abstract:

    In the present paper we continue to study almost geodesic curves and determine in $${\mathbb {R}}^n$$ the form of curves $${\mathcal {C}}$$ for which every image under an $$(n-1)$$ -dimensional algebraic torus is also an almost geodesic with respect to an Affine Connection $$\nabla $$ with constant coefficients. We also calculate explicitly the components of $$\nabla $$ . For the explicit calculation of the form of curves $${\mathcal {C}}$$ in the n-dimensional real space $${\mathbb {R}}^n$$ that are almost geodesics with respect to an Affine Connection $$\nabla $$ , we can suppose that with $${{\mathcal {C}}}$$ all images of $${{\mathcal {C}}}$$ under a real $$(n-1)$$ -dimensional algebraic torus are also almost geodesics. This implies that the determination of $${{\mathcal {C}}}$$ becomes an algebraic problem. Here we use E. Beltrami’s result that a differentiable curve is a local geodesic with respect to an Affine Connection $$\nabla $$ precisely if it is a solution of an abelian differential equation with coefficients that are functions of the components of $$\nabla $$ . Now we consider the special case for the Connection $$\nabla $$ in which every curve is almost geodesic with respect to $$\nabla $$ .

  • On canonical F-planar mappings of spaces with Affine Connection
    Filomat, 2019
    Co-Authors: Volodymyr Berezovski, Josef Mikeš, Patrik Peška, Lenka Rýparová
    Abstract:

    In this paper we study the theory of F-planar mappings of spaces with Affine Connection. We obtained condition, which preserved the curvature tensor. We also studied canonical F-planar mappings of space with Affine Connection onto symmetric spaces. In this case, the main equations have the partial differential Cauchy type form in covariant derivatives. We got the set of substantial real parameters on which depends the general solution of that PDE?s system.

  • Rotary mappings of spaces with Affine Connection
    Filomat, 2019
    Co-Authors: Josef Mikeš, Lenka Rýparová
    Abstract:

    This paper concerns with rotary mappings of two-dimensional spaces with an Affine Connection onto (pseudo-) Riemannian spaces. The results obtained in the theory of rotary mappings are further developed. We prove that any (pseudo-) Riemannian space admits rotary mapping. There are also presented certain properties from which yields the existence of these rotary mappings.

Takesi Saito – One of the best experts on this subject based on the ideXlab platform.

  • Affine Connections and topological conformal field theories on higher-genus Riemann surfaces. II: Bosonic strings and related models
    Progress of Theoretical Physics, 1993
    Co-Authors: Takesi Saito
    Abstract:

    The topological conformal algebra for the models of bosonic string type is considered on an arbitrary higher-genus Riemann surface M. Associated with the U(1) anomaly the Affine Connection is automatically introduced into the algebra. The Affine Connection always appears in the form of covariant derivatives, so that it guarantees coordinate-independence of the algebra. Since our Affine Connection is meromorphic on M, the theorem that a globally defined holomorphic Affine Connection is admitted only on a torus is not applicable to our case. One may use it on general Riemann surfaces of genus g ≥ 1 in the form of covariant derivatives

  • Affine Connections and Two-Dimensional Topological Gravity on a Torus
    Progress of Theoretical Physics, 1993
    Co-Authors: Takesi Saito
    Abstract:

    The topological conformal algebra for topological gravity is considered on higher-genus Riemann surfaces. Associated with the U(1) anomaly the Affine Connection is automatically introduced into the algebra. The Affine Connection guarantees coordinate-independence of the algebra. Since the Affine Connection is admitted only on a torus, the algebra with the Affine Connection can be defined only on the same surface. The U(1) anomaly d is given by d= −2−2y, where y is a parameter contained in the model. However, the value of y is fixed to be y = 0 from the condition that the algebra is coordinate-independent. Some types of topological gravity are excluded on a torus

  • Affine Connections and Topological Conformal Field Theories on Higher-Genus Riemann Surfaces
    Progress of Theoretical Physics, 1993
    Co-Authors: Takesi Saito
    Abstract:

    We consider a topological conformal algebra on a higher·genus Riemann surface S. Associated with the U(l) anomaly it is required to introduce an Affine Connection into the algebra in order to render the algebra coordinate· independent. Since a compact Riemann surface admits Affine connec­ tions if and only if the surface has genus one, the topological conformal algebra with the U(l) anomaly on S is valid only on a torus. The supersymmetric ghost system is used to realize such an algebra. We actually construct the Affine Connection and give its transformation law under a conformal transformation. When there is ITO U(l) anomaly, the corresponding topological confor­ mal algebra does not contain the Affine Connection and is admitted on Riemann surfaces with any genus.

Dan Dumitru – One of the best experts on this subject based on the ideXlab platform.

  • Special multiply Einstein warped products with an Affine Connection
    International Journal of Geometric Methods in Modern Physics, 2018
    Co-Authors: Dan Dumitru
    Abstract:

    The aim of this paper is to study special multiply Einstein warped products having an Affine Connection. Let [Formula: see text] be a multiply warped product such that [Formula: see text] is an open interval, [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] for every [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] an Affine Connection on [Formula: see text] We compute the warping functions that make [Formula: see text] an Einstein space in the following cases: (a) [Formula: see text] is a semi-symmetric metric/non-metric Connection and all the fibers are Ricci flat. (b) [Formula: see text] is a quarter-symmetric metric/non-metric Connection and all the fibers are Ricci flat.

  • Special multiply Einstein warped products with an Affine Connection
    International Journal of Geometric Methods in Modern Physics, 2018
    Co-Authors: Dan Dumitru
    Abstract:

    The aim of this paper is to study special multiply Einstein warped products having an Affine Connection. Let M = I ×f1F1 ×⋯ ×fmFm be a multiply warped product such that I ⊂ ℝ is an open interval, d…