1,692 research outputs found
Optimal path planning for nonholonomic robotics systems via parametric optimisation
Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping
Frequency shifting of pulsed narrow-band laser light in a multipass Raman cell
A multipass cell is described which allows efficient stimulated Raman frequency shifting for low pump laser intensities and low gas pressures. The latter is important for Raman shifting of narrow-band Fourier-transform limited light pulses (Îv=75 MHz). It is shown that frequency broadening of the Raman shifted light can be largely avoided in the Dicke narrowing regime at low pressures. For 75 MHz pump pulses and an H2 density of 2.5 amagat we found a negligible broadening to 90 MHz of the stimulated Stokes light. This is far below the value of 250 MHz expected from spontaneous emission. The narrow-band Stokes pulses achieved in CO2 enabled us to measure the pressure shift coefficient (-0.71Ă10-2 cm-1/amagat) of this gas. It is demonstrated, for the example of benzene, that our technique provides a very practical light source for high resolution molecular spectroscopy
Process mapping of laser surface modification of AISI 316L stainless steel for biomedical applications
A 1.5-kW CO2 laser in pulsed mode at 3 kHz was used to investigate the effects of varied laser process parameters and resulting morphology of AISI 316L stainless steel. Irradiance and residence time were varied between 7.9 to 23.6 MW/cm2 and 50 to 167 ”s respectively. A strong correlation between irradiance, residence time, depth of processing and roughness of processed steel was established. The high depth of altered microstructure and increased roughness were linked to higher levels of both irradiance and residence times. Energy fluence and surface temperature models were used to predict levels of melting occurring on the surface through the analysis of roughness and depth of the region processed. Microstructural images captured by the SEM revealed significant grain structure changes at higher irradiances, but due to increased residence times, limited to the laser in use, the hardness values were not improved
Topological Defects, Orientational Order, and Depinning of the Electron Solid in a Random Potential
We report on the results of molecular dynamics simulation (MD) studies of the
classical two-dimensional electron crystal in the presence disorder. Our study
is motivated by recent experiments on this system in modulation doped
semiconductor systems in very strong magnetic fields, where the magnetic length
is much smaller than the average interelectron spacing , as well as by
recent studies of electrons on the surface of helium. We investigate the low
temperature state of this system using a simulated annealing method. We find
that the low temperature state of the system always has isolated dislocations,
even at the weakest disorder levels investigated. We also find evidence for a
transition from a hexatic glass to an isotropic glass as the disorder is
increased. The former is characterized by quasi-long range orientational order,
and the absence of disclination defects in the low temperature state, and the
latter by short range orientational order and the presence of these defects.
The threshold electric field is also studied as a function of the disorder
strength, and is shown to have a characteristic signature of the transition.
Finally, the qualitative behavior of the electron flow in the depinned state is
shown to change continuously from an elastic flow to a channel-like, plastic
flow as the disorder strength is increased.Comment: 31 pages, RevTex 3.0, 15 figures upon request, accepted for
publication in Phys. Rev. B., HAF94MD
Moving glass phase of driven lattices
We study periodic lattices, such as vortex lattices, driven by an external
force in a random pinning potential. We show that effects of static disorder
persist even at large velocity. It results in a novel moving glass state with
topological order analogous to the static Bragg glass. The lattice flows
through well-defined, elastically coupled, {\it % static} channels. We predict
barriers to transverse motion resulting in finite transverse critical current.
Experimental tests of the theory are proposed.Comment: Revised version, shortened, 8 pages, REVTeX, no figure
Strangeness Enhancement in and Interactions at SPS Energies
The systematics of strangeness enhancement is calculated using the HIJING and
VENUS models and compared to recent data on , and
collisions at CERN/SPS energies (). The HIJING model is used to
perform a {\em linear} extrapolation from to . VENUS is used to
estimate the effects of final state cascading and possible non-conventional
production mechanisms. This comparison shows that the large enhancement of
strangeness observed in collisions, interpreted previously as possible
evidence for quark-gluon plasma formation, has its origins in non-equilibrium
dynamics of few nucleon systems. % Strangeness enhancement %is therefore traced
back to the change in the production dynamics %from to minimum bias
and central collisions. A factor of two enhancement of at
mid-rapidity is indicated by recent data, where on the average {\em one}
projectile nucleon interacts with only {\em two} target nucleons. There appears
to be another factor of two enhancement in the light ion reaction relative
to , when on the average only two projectile nucleons interact with two
target ones.Comment: 29 pages, 8 figures in uuencoded postscript fil
First-principles study of lattice instabilities in the ferromagnetic martensite NiMnGa
The phonon dispersion relations and elastic constants for ferromagnetic
NiMnGa in the cubic and tetragonally distorted Heusler structures are
computed using density-functional and density-functional perturbation theory
within the spin-polarized generalized-gradient approximation. For
, the TA tranverse acoustic branch along and
symmetry-related directions displays a dynamical instability at a wavevector
that depends on . Through examination of the Fermi-surface nesting and
electron-phonon coupling, this is identified as a Kohn anomaly. In the parent
cubic phase the computed tetragonal shear elastic constant,
C=(CC)/2, is close to zero, indicating a marginal
elastic instability towards a uniform tetragonal distortion. We conclude that
the cubic Heusler structure is unstable against a family of energy-lowering
distortions produced by the coupling between a uniform tetragonal distortion
and the corresponding modulation. The computed relation between the
ratio and the modulation wavevector is in excellent agreement with
structural data on the premartensitic ( = 1) and martensitic ( =
0.94) phases of NiMnGa.Comment: submitted to Phys. Rev.
Fractional reaction-diffusion equations
In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b)
derived solutions of a number of fractional kinetic equations in terms of
generalized Mittag-Leffler functions which provide the extension of the work of
Haubold and Mathai (1995, 2000). The subject of the present paper is to
investigate the solution of a fractional reaction-diffusion equation. The
results derived are of general nature and include the results reported earlier
by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for
anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for
reaction-diffusion systems with L\'evy flights. The solution has been developed
in terms of the H-function in a compact form with the help of Laplace and
Fourier transforms. Most of the results obtained are in a form suitable for
numerical computation.Comment: LaTeX, 17 pages, corrected typo
The Horizontal Component of Photospheric Plasma Flows During the Emergence of Active Regions on the Sun
The dynamics of horizontal plasma flows during the first hours of the
emergence of active region magnetic flux in the solar photosphere have been
analyzed using SOHO/MDI data. Four active regions emerging near the solar limb
have been considered. It has been found that extended regions of Doppler
velocities with different signs are formed in the first hours of the magnetic
flux emergence in the horizontal velocity field. The flows observed are
directly connected with the emerging magnetic flux; they form at the beginning
of the emergence of active regions and are present for a few hours. The Doppler
velocities of flows observed increase gradually and reach their peak values
4-12 hours after the start of the magnetic flux emergence. The peak values of
the mean (inside the +/-500 m/s isolines) and maximum Doppler velocities are
800-970 m/s and 1410-1700 m/s, respectively. The Doppler velocities observed
substantially exceed the separation velocities of the photospheric magnetic
flux outer boundaries. The asymmetry was detected between velocity structures
of leading and following polarities. Doppler velocity structures located in a
region of leading magnetic polarity are more powerful and exist longer than
those in regions of following polarity. The Doppler velocity asymmetry between
the velocity structures of opposite sign reaches its peak values soon after the
emergence begins and then gradually drops within 7-12 hours. The peak values of
asymmetry for the mean and maximal Doppler velocities reach 240-460 m/s and
710-940 m/s, respectively. An interpretation of the observable flow of
photospheric plasma is given.Comment: 20 pages, 10 figures, 3 tables. The results of article were presented
at the ESPM-13 (12-16 September 2011, Rhodes, Greece, Abstract Book p. 102,
P.4.12,
http://astro.academyofathens.gr/espm13/documents/ESPM13_abstract_programme_book.pdf
Geometric Approach to Pontryagin's Maximum Principle
Since the second half of the 20th century, Pontryagin's Maximum Principle has
been widely discussed and used as a method to solve optimal control problems in
medicine, robotics, finance, engineering, astronomy. Here, we focus on the
proof and on the understanding of this Principle, using as much geometric ideas
and geometric tools as possible. This approach provides a better and clearer
understanding of the Principle and, in particular, of the role of the abnormal
extremals. These extremals are interesting because they do not depend on the
cost function, but only on the control system. Moreover, they were discarded as
solutions until the nineties, when examples of strict abnormal optimal curves
were found. In order to give a detailed exposition of the proof, the paper is
mostly self\textendash{}contained, which forces us to consider different areas
in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page
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