6,758 research outputs found
Image based visual servoing using algebraic curves applied to shape alignment
Visual servoing schemes generally employ various image features (points, lines, moments etc.) in their control formulation. This paper presents a novel method for using boundary information in visual servoing. Object boundaries are
modeled by algebraic equations and decomposed as a unique sum of product of lines. We propose that these lines can be used to extract useful features for visual servoing purposes. In this paper, intersection of these lines are used as point features in visual servoing. Simulations are performed with a 6 DOF Puma
560 robot using Matlab Robotics Toolbox for the alignment of a free-form object. Also, experiments are realized with a 2 DOF SCARA direct drive robot. Both simulation and experimental results are quite promising and show potential of our new method
Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras
Darboux coordinates are constructed on rational coadjoint orbits of the
positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by
the values of the spectral parameters at the divisors corresponding to
eigenvector line bundles over the associated spectral curves, defined within a
given matrix representation. A Liouville generating function is obtained in
completely separated form and shown, through the Liouville-Arnold integration
method, to lead to the Abel map linearization of all Hamiltonian flows induced
by the spectral invariants. Serre duality is used to define a natural
symplectic structure on the space of line bundles of suitable degree over a
permissible class of spectral curves, and this is shown to be equivalent to the
Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general
construction is given for or , with
reductions to orbits of subalgebras determined as invariant fixed point sets
under involutive automorphisms. The case is shown to reproduce
the classical integration methods for finite dimensional systems defined on
quadrics, as well as the quasi-periodic solutions of the cubically nonlinear
Schr\"odinger equation. For , the method is applied to the
computation of quasi-periodic solutions of the two component coupled nonlinear
Schr\"odinger equation.Comment: 61 pg
Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles
Athermal lattice gases of particles with first neighbor exclusion have been
studied for a long time as simple models exhibiting a fluid-solid transition.
At low concentration the particles occupy randomly both sublattices, but as the
concentration is increased one of the sublattices is occupied preferentially.
Here we study a mixed lattice gas with excluded volume interactions only in the
grand-canonical formalism with two kinds of particles: small ones, which occupy
a single lattice site and large ones, which occupy one site and its first
neighbors. We solve the model on a Bethe lattice of arbitrary coordination
number . In the parameter space defined by the activities of both particles.
At low values of the activity of small particles () we find a continuous
transition from the fluid to the solid phase as the activity of large particles
() is increased. At higher values of the transition becomes
discontinuous, both regimes are separated by a tricritical point. The critical
line has a negative slope at and displays a minimum before reaching the
tricritical point, so that a reentrant behavior is observed for constant values
of in the region of low density of small particles. The isobaric curves
of the total density of particles as a function of (or ) show a
minimum in the fluid phase.Comment: 18 pages, 5 figures, 1 tabl
A complex ray-tracing tool for high-frequency mean-field flow interaction effects in jets
This paper presents a complex ray-tracing tool for the calculation of high-frequency Green’s functions in 3D mean field jet flows. For a generic problem, the ray solution suffers from three main deficiencies: multiplicity of solutions, singularities at caustics, and the determining of complex solutions. The purpose of this paper is to generalize, combine and apply existing stationary media methods to moving media scenarios. Multiplicities are dealt with using an equivalent two-point boundary-value problem, whilst non-uniformities at caustics are corrected using diffraction catastrophes. Complex rays are found using a combination of imaginary perturbations, an assumption of caustic stability, and analytic continuation of the receiver curve. To demonstrate this method, the ray tool is compared against a high-frequency modal solution of Lilley’s equation for an off-axis point source. This solution is representative of high-frequency source positions in real jets and is rich in caustic structures. A full utilization of the ray tool is shown to provide excellent results<br/
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