6,216 research outputs found
Geometry-aware Manipulability Learning, Tracking and Transfer
Body posture influences human and robots performance in manipulation tasks,
as appropriate poses facilitate motion or force exertion along different axes.
In robotics, manipulability ellipsoids arise as a powerful descriptor to
analyze, control and design the robot dexterity as a function of the
articulatory joint configuration. This descriptor can be designed according to
different task requirements, such as tracking a desired position or apply a
specific force. In this context, this paper presents a novel
\emph{manipulability transfer} framework, a method that allows robots to learn
and reproduce manipulability ellipsoids from expert demonstrations. The
proposed learning scheme is built on a tensor-based formulation of a Gaussian
mixture model that takes into account that manipulability ellipsoids lie on the
manifold of symmetric positive definite matrices. Learning is coupled with a
geometry-aware tracking controller allowing robots to follow a desired profile
of manipulability ellipsoids. Extensive evaluations in simulation with
redundant manipulators, a robotic hand and humanoids agents, as well as an
experiment with two real dual-arm systems validate the feasibility of the
approach.Comment: Accepted for publication in the Intl. Journal of Robotics Research
(IJRR). Website: https://sites.google.com/view/manipulability. Code:
https://github.com/NoemieJaquier/Manipulability. 24 pages, 20 figures, 3
tables, 4 appendice
Gauge invariant finite size spectrum of the giant magnon
It is shown that the finite size corrections to the spectrum of the giant
magnon solution of classical string theory, computed using the uniform
light-cone gauge, are gauge invariant and have physical meaning. This is seen
in two ways: from a general argument where the single magnon is made gauge
invariant by putting it on an orbifold as a wrapped state obeying the level
matching condition as well as all other constraints, and by an explicit
calculation where it is shown that physical quantum numbers do not depend on
the uniform light-cone gauge parameter. The resulting finite size effects are
exponentially small in the -charge and the exponent (but not the prefactor)
agrees with gauge theory computations using the integrable Hubbard model.Comment: 12 pages, some clarifications, references adde
BCJ duality and double copy in the closed string sector
This paper is focused on the loop-level understanding of the
Bern-Carrasco-Johansson double copy procedure that relates the integrands of
gauge theory and gravity scattering amplitudes. At four points, the first
non-trivial example of that construction is one-loop amplitudes in N=2
super-Yang-Mills theory and the symmetric realization of N=4 matter-coupled
supergravity. Our approach is to use both field and string theory in parallel
to analyze these amplitudes. The closed string provides a natural framework to
analyze the BCJ construction, in which the left- and right-moving sectors
separately create the color and kinematics at the integrand level. At tree
level, in a five-point example, we show that the Mafra-Schlotterer-Stieberger
procedure gives a new direct proof of the color-kinematics double copy. We
outline the extension of that argument to n points. At loop level, the
field-theoretic BCJ construction of N=2 SYM amplitudes introduces new terms,
unexpected from the string theory perspective. We discuss to what extent we can
relate them to the terms coming from the interactions between left- and
right-movers in the string-theoretic gravity construction.Comment: 46 pages, 8 figures, 2 tables; v3 significantly revised published
versio
Second Quantization of the Wilson Loop
Treating the QCD Wilson loop as amplitude for the propagation of the first
quantized particle we develop the second quantization of the same propagation.
The operator of the particle position (the endpoint of the
"open string") is introduced as a limit of the large Hermitean matrix. We
then derive the set of equations for the expectation values of the vertex
operators \VEV{ V(k_1)\dots V(k_n)} . The remarkable property of these
equations is that they can be expanded at small momenta (less than the QCD mass
scale), and solved for expansion coefficients. This provides the relations for
multiple commutators of position operator, which can be used to construct this
operator. We employ the noncommutative probability theory and find the
expansion of the operator in terms of products of creation
operators . In general, there are some free parameters left
in this expansion. In two dimensions we fix parameters uniquely from the
symplectic invariance. The Fock space of our theory is much smaller than that
of perturbative QCD, where the creation and annihilation operators were
labelled by continuous momenta. In our case this is a space generated by creation operators. The corresponding states are given by all sentences made
of the four letter words. We discuss the implication of this construction for
the mass spectra of mesons and glueballs.Comment: 41 pages, latex, 3 figures and 3 Mathematica files uuencode
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