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

On the Progenitors of Core-Collapse Supernovae

Theory holds that a star born with an initial mass between about 8 and 140 times the mass of the Sun will end its life through the catastrophic gravitational collapse of its iron core to a neutron star or black hole. This core collapse process is thought to usually be accompanied by the ejection of the star's envelope as a supernova. This established theory is now being tested observationally, with over three dozen core-collapse supernovae having had the properties of their progenitor stars directly measured through the examination of high-resolution images taken prior to the explosion. Here I review what has been learned from these studies and briefly examine the potential impact on stellar evolution theory, the existence of "failed supernovae", and our understanding of the core-collapse explosion mechanism.Comment: 7 Pages, invited review accepted for publication by Astrophysics and Space Science (special HEDLA 2010 issue

Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams

Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research aimed at establishing and solving dynamic models purged of any artificial nonlinearity by taking advantage of symmetry properties underlying the use of Lie groups. The geometric constructions needed for reduction are presented in the context of the "covariant" approach.Comment: Submitted to GSI2013 - Geometric Science of Informatio

Novel Transversity Properties in Semi-Inclusive Deep Inelastic Scattering

The $T$-odd distribution functions contributing to transversity properties of the nucleon and their role in fueling nontrivial contributions to azimuthal asymmetries in semi-inclusive deep inelastic scattering are investigated. We use a dynamical model to evaluate these quantities in terms of HERMES kinematics.Comment: 5 pages revtex; 5 eps figures. References added. To appear as a Rapid Communication in Physical Review

Design, synthesis, and biological evaluation of aryl piperazines with potential as antidiabetic agents via the stimulation of glucose uptake and inhibition of NADH:ubiquinone oxidoreductase

The management of blood glucose levels and the avoidance of diabetic hyperglycemia are common objectives of many therapies in the treatment of diabetes. An aryl piperazine compound 3a (RTC1) has been described as a promoter of glucose uptake, in part through a cellular mechanism that involves inhibition of NADH:ubiquinone oxidoreductase. We report herein the synthesis of 41 derivatives of 3a (RTC1) and a systematic structure-activity-relationship study where a number of compounds were shown to effectively stimulate glucose uptake in vitro and inhibit NADH:ubiquinone oxidoreductase. The hit compound 3a (RTC1) remained the most efficacious with a 2.57 fold increase in glucose uptake compared to vehicle control and micromolar inhibition of NADH:ubiquinone oxidoreductase (IC50 = 27 μM). In vitro DMPK and in vivo PK studies are also described, where results suggest that 3a (RTC1) would not be expected to provoke adverse drug-drug interactions, yet be readily metabolised, avoid rapid excretion, with a short half-life, and have good tissue distribution. The overall results indicate that aryl piperazines, and 3a (RTC1) in particular, have potential as effective agents for the treatment of diabetes

A mechanism for the T-odd pion fragmentation function

We consider a simple rescattering mechanism to calculate a leading twist $T$-odd pion fragmentation function, a favored candidate for filtering the transversity properties of the nucleon. We evaluate the single spin azimuthal asymmetry for a transversely polarized target in semi-inclusive deep inelastic scattering (for HERMES kinematics). Additionally, we calculate the double $T$-odd $\cos2\phi$ asymmetry in this framework.Comment: 6 pages revtex, 7 eps figures, references added and updated in this published versio

PTF11iqb: cool supergiant mass-loss that bridges the gap between Type IIn and normal supernovae

The supernova (SN) PTF11iqb was initially classified as a Type IIn event caught very early after explosion. It showed narrow Wolf–Rayet (WR) spectral features on day 2 (as in SN 1998S and SN 2013cu), but the narrow emission weakened quickly and the spectrum morphed to resemble Types II-L and II-P. At late times, H? exhibited a complex, multipeaked profile reminiscent of SN 1998S. In terms of spectroscopic evolution, we find that PTF11iqb was a near twin of SN 1998S, although with somewhat weaker interaction with circumstellar material (CSM) at early times, and stronger interaction at late times. We interpret the spectral changes as caused by early interaction with asymmetric CSM that is quickly (by day 20) enveloped by the expanding SN ejecta photosphere, but then revealed again after the end of the plateau when the photosphere recedes. The light curve can be matched with a simple model for CSM interaction (with a mass-loss rate of roughly 10?4 M? yr?1) added to the light curve of a normal SN II-P. The underlying plateau requires a progenitor with an extended hydrogen envelope like a red supergiant at the moment of explosion, consistent with the slow wind speed (<80?km?s?1) inferred from narrow H? emission. The cool supergiant progenitor is significant because PTF11iqb showed WR features in its early spectrum – meaning that the presence of such WR features does not necessarily indicate a WR-like progenitor. Overall, PTF11iqb bridges SNe IIn with weaker pre-SN mass-loss seen in SNe II-L and II-P, implying a continuum between these types

PTF11iqb: cool supergiant mass-loss that bridges the gap between Type IIn and normal supernovae

The supernova (SN) PTF11iqb was initially classified as a Type IIn event caught very early after explosion. It showed narrow Wolf–Rayet (WR) spectral features on day 2 (as in SN 1998S and SN 2013cu), but the narrow emission weakened quickly and the spectrum morphed to resemble Types II-L and II-P. At late times, H? exhibited a complex, multipeaked profile reminiscent of SN 1998S. In terms of spectroscopic evolution, we find that PTF11iqb was a near twin of SN 1998S, although with somewhat weaker interaction with circumstellar material (CSM) at early times, and stronger interaction at late times. We interpret the spectral changes as caused by early interaction with asymmetric CSM that is quickly (by day 20) enveloped by the expanding SN ejecta photosphere, but then revealed again after the end of the plateau when the photosphere recedes. The light curve can be matched with a simple model for CSM interaction (with a mass-loss rate of roughly 10?4 M? yr?1) added to the light curve of a normal SN II-P. The underlying plateau requires a progenitor with an extended hydrogen envelope like a red supergiant at the moment of explosion, consistent with the slow wind speed (<80?km?s?1) inferred from narrow H? emission. The cool supergiant progenitor is significant because PTF11iqb showed WR features in its early spectrum – meaning that the presence of such WR features does not necessarily indicate a WR-like progenitor. Overall, PTF11iqb bridges SNe IIn with weaker pre-SN mass-loss seen in SNe II-L and II-P, implying a continuum between these types

Backward diode composed of a metallic and semiconducting nanotube

The conditions necessary for a nanotube junction connecting a metallic and semiconducting nanotube to rectify the current are theoretically investigated. A tight binding model is used for the analysis, which includes the Hartree-Fock approximation and the Green's function method. It is found that the junction has a behavior similar to the backward diode if the gate electrode is located nearby and the Fermi level of the semiconducting tube is near the gap. Such a junction would be advantageous since the required length for the rectification could be reduced.Comment: 4 pages, RevTeX, uses epsf.st