233,765 research outputs found
Position and Orientation Estimation of a Rigid Body: Rigid Body Localization
Rigid body localization refers to a problem of estimating the position of a
rigid body along with its orientation using anchors. We consider a setup in
which a few sensors are mounted on a rigid body. The absolute position of the
rigid body is not known, but, the relative position of the sensors or the
topology of the sensors on the rigid body is known. We express the absolute
position of the sensors as an affine function of the Stiefel manifold and
propose a simple least-squares (LS) estimator as well as a constrained total
least-squares (CTLS) estimator to jointly estimate the orientation and the
position of the rigid body. To account for the perturbations of the sensors, we
also propose a constrained total least-squares (CTLS) estimator. Analytical
closed-form solutions for the proposed estimators are provided. Simulations are
used to corroborate and analyze the performance of the proposed estimators.Comment: 4 pages and 1 reference page; 3 Figures; In Proc. of ICASSP 201
Some quadratic equations in the free group of rank 2
For a given quadratic equation with any number of unknowns in any free group
F, with right-hand side an arbitrary element of F, an algorithm for solving the
problem of the existence of a solution was given by Culler. The problem has
been studied by the authors for parametric families of quadratic equations
arising from continuous maps between closed surfaces, with certain conjugation
factors as the parameters running through the group F. In particular, for a
one-parameter family of quadratic equations in the free group F_2 of rank 2,
corresponding to maps of absolute degree 2 between closed surfaces of Euler
characteristic 0, the problem of the existence of faithful solutions has been
solved in terms of the value of the self-intersection index mu: F_2 --> Z[F_2]
on the conjugation parameter. The present paper investigates the existence of
faithful, or non-faithful, solutions of similar families of quadratic equations
corresponding to maps of absolute degree 0.Comment: This is the version published by Geometry & Topology Monographs on 29
April 200
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms
This is the sequel to the author's previous paper which gives an extension of
Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main result of this
paper asserts the following. Whenever the Seiberg-Witten invariants are defined
over a closed minimal 4-manifold X, they are equivalent modulo 2 to
"near-symplectic" Gromov invariants in the presence of certain self-dual
harmonic 2-forms on X. A version for non-minimal 4-manifolds is also proved. A
corollary to circle-valued Morse theory on 3-manifolds is also announced,
recovering a result of Hutchings-Lee-Turaev about the 3-dimensional
Seiberg-Witten invariants.Comment: 41 pages. Comments desired; to be submitte
Dirac Quantisation Conditions and Kaluza-Klein Reduction
We present the form of the Dirac quantisation condition for the p-form
charges carried by p-brane solutions of supergravity theories. This condition
agrees precisely with the conditions obtained in lower dimensions, as is
necessary for consistency with Kaluza-klein dimensional reduction. These
considerations also determine the charge lattice of BPS soliton states, which
proves to be a universal modulus-independent lattice when the charges are
defined to be the canonical charges corresponding to the quantum supergravity
symmetry groups.Comment: 40 pages, Late
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