Null-Space Minimization of Center of Gravity Displacementof a Redundant Aerial Manipulator

Displacements of the base during trajectory tracking are a common issue in the control of aerial manipulators. These are caused by reaction torques transferred to the base due to the manipulator motion and, in particular, to the motion of its center of gravity. We present a novel approach to reduce base displacements of a kinematically redundant aerial manipulator by using null-space projection in the inverse kinematic control. A secondary objective function minimizes the horizontal displacement of the manipulator center of gravity. We test this algorithm on different trajectories for both three and four degrees of freedom (DOF) manipulators in a simulation environment. The results comparing our algorithm with inverse kinematic control without the null-space projection show up to an 80% reduction in the end-effector position error and an average of about 56% reduction in maximum base displacement. The simulation implementation also runs faster than in real-time in our code implementation. We provide a workspace analysis based on multiple stopping criteria such as excessive base displacement, joint velocities and end-effector position error for the 3 and 4 DOF manipulators. As expected, the 4 DOF manipulator has a larger workspace

A Remark on the Renormalization Group Equation for the Penner Model

It is possible to extract values for critical couplings and gamma_string in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a ``renormalization group equation'' for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and gamma_string and is consistent with the logarithmic corrections present for g=0,1.Comment: LaTeX, 5 pages, LPTHE-Orsay-94-5

Dynamical SU(3) linear sigma model and the mixing of eta'-eta and sigma-f_0 mesons

The SU(3) linear sigma model is dynamically generated in loop-order using the nonstrange-strange basis. Only self-consistent logarithmic divergent graphs are needed, with quadratic divergent graphs replaced by SU(3) mass-shell equal splitting laws. The latter lead to an eta'-eta mixing angle of 41.84 deg which is consistent with phenomenology. Finally this above SU(3) linear sigma model in turn predicts strong decay rates which are all compatible with data.Comment: 14 pages, 1 figure, elsart; version to appear in J. Phys. G, appendix added, some typos correcte

Measurement of the Crab Nebula Spectrum Past 100 TeV with HAWC

We present TeV gamma-ray observations of the Crab Nebula, the standard reference source in ground-based gamma-ray astronomy, using data from the High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory. In this analysis we use two independent energy-estimation methods that utilize extensive air shower variables such as the core position, shower angle, and shower lateral energy distribution. In contrast, the previously published HAWC energy spectrum roughly estimated the shower energy with only the number of photomultipliers triggered. This new methodology yields a much improved energy resolution over the previous analysis and extends HAWC's ability to accurately measure gamma-ray energies well beyond 100 TeV. The energy spectrum of the Crab Nebula is well fit to a log parabola shape $\left(\frac{dN}{dE} = \phi_0 \left(E/\textrm{7 TeV}\right)^{-\alpha-\beta\ln\left(E/\textrm{7 TeV}\right)}\right)$ with emission up to at least 100 TeV. For the first estimator, a ground parameter that utilizes fits to the lateral distribution function to measure the charge density 40 meters from the shower axis, the best-fit values are $\phi_o$=(2.35$\pm$0.04$^{+0.20}_{-0.21}$)$\times$10$^{-13}$ (TeV cm$^2$ s)$^{-1}$, $\alpha$=2.79$\pm$0.02$^{+0.01}_{-0.03}$, and $\beta$=0.10$\pm$0.01$^{+0.01}_{-0.03}$. For the second estimator, a neural network which uses the charge distribution in annuli around the core and other variables, these values are $\phi_o$=(2.31$\pm$0.02$^{+0.32}_{-0.17}$)$\times$10$^{-13}$ (TeV cm$^2$ s)$^{-1}$, $\alpha$=2.73$\pm$0.02$^{+0.03}_{-0.02}$, and $\beta$=0.06$\pm$0.01$\pm$0.02. The first set of uncertainties are statistical; the second set are systematic. Both methods yield compatible results. These measurements are the highest-energy observation of a gamma-ray source to date.Comment: published in Ap

All-particle cosmic ray energy spectrum measured by the HAWC experiment from 10 to 500 TeV

We report on the measurement of the all-particle cosmic ray energy spectrum with the High Altitude Water Cherenkov (HAWC) Observatory in the energy range 10 to 500 TeV. HAWC is a ground based air-shower array deployed on the slopes of Volcan Sierra Negra in the state of Puebla, Mexico, and is sensitive to gamma rays and cosmic rays at TeV energies. The data used in this work were taken from 234 days between June 2016 to February 2017. The primary cosmic-ray energy is determined with a maximum likelihood approach using the particle density as a function of distance to the shower core. Introducing quality cuts to isolate events with shower cores landing on the array, the reconstructed energy distribution is unfolded iteratively. The measured all-particle spectrum is consistent with a broken power law with an index of $-2.49\pm0.01$ prior to a break at $(45.7\pm0.1$) TeV, followed by an index of $-2.71\pm0.01$. The spectrum also respresents a single measurement that spans the energy range between direct detection and ground based experiments. As a verification of the detector response, the energy scale and angular resolution are validated by observation of the cosmic ray Moon shadow's dependence on energy.Comment: 16 pages, 11 figures, 4 tables, submission to Physical Review

Constraining the pˉ/p\bar{p}/p Ratio in TeV Cosmic Rays with Observations of the Moon Shadow by HAWC

An indirect measurement of the antiproton flux in cosmic rays is possible as the particles undergo deflection by the geomagnetic field. This effect can be measured by studying the deficit in the flux, or shadow, created by the Moon as it absorbs cosmic rays that are headed towards the Earth. The shadow is displaced from the actual position of the Moon due to geomagnetic deflection, which is a function of the energy and charge of the cosmic rays. The displacement provides a natural tool for momentum/charge discrimination that can be used to study the composition of cosmic rays. Using 33 months of data comprising more than 80 billion cosmic rays measured by the High Altitude Water Cherenkov (HAWC) observatory, we have analyzed the Moon shadow to search for TeV antiprotons in cosmic rays. We present our first upper limits on the $\bar{p}/p$ fraction, which in the absence of any direct measurements, provide the tightest available constraints of $\sim1\%$ on the antiproton fraction for energies between 1 and 10 TeV.Comment: 10 pages, 5 figures. Accepted by Physical Review

The Sensitivity of HAWC to High-Mass Dark Matter Annihilations

The High Altitude Water Cherenkov (HAWC) observatory is a wide field-of-view detector sensitive to gamma rays of 100 GeV to a few hundred TeV. Located in central Mexico at 19 degrees North latitude and 4100 m above sea level, HAWC will observe gamma rays and cosmic rays with an array of water Cherenkov detectors. The full HAWC array is scheduled to be operational in Spring 2015. In this paper, we study the HAWC sensitivity to the gamma-ray signatures of high-mass (multi- TeV) dark matter annihilation. The HAWC observatory will be sensitive to diverse searches for dark matter annihilation, including annihilation from extended dark matter sources, the diffuse gamma-ray emission from dark matter annihilation, and gamma-ray emission from non-luminous dark matter subhalos. Here we consider the HAWC sensitivity to a subset of these sources, including dwarf galaxies, the M31 galaxy, the Virgo cluster, and the Galactic center. We simulate the HAWC response to gamma rays from these sources in several well-motivated dark matter annihilation channels. If no gamma-ray excess is observed, we show the limits HAWC can place on the dark matter cross-section from these sources. In particular, in the case of dark matter annihilation into gauge bosons, HAWC will be able to detect a narrow range of dark matter masses to cross-sections below thermal. HAWC should also be sensitive to non-thermal cross-sections for masses up to nearly 1000 TeV. The constraints placed by HAWC on the dark matter cross-section from known sources should be competitive with current limits in the mass range where HAWC has similar sensitivity. HAWC can additionally explore higher dark matter masses than are currently constrained.Comment: 15 pages, 4 figures, version to be published in PR