Keep Rollin' - Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots

We show dynamic locomotion strategies for wheeled quadrupedal robots, which combine the advantages of both walking and driving. The developed optimization framework tightly integrates the additional degrees of freedom introduced by the wheels. Our approach relies on a zero-moment point based motion optimization which continuously updates reference trajectories. The reference motions are tracked by a hierarchical whole-body controller which computes optimal generalized accelerations and contact forces by solving a sequence of prioritized tasks including the nonholonomic rolling constraints. Our approach has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled including the non-steerable wheels attached to its legs. We conducted experiments on flat and inclined terrains as well as over steps, whereby we show that integrating the wheels into the motion control and planning framework results in intuitive motion trajectories, which enable more robust and dynamic locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4 m/s and a reduction of the cost of transport by 83 % we prove the superiority of wheeled-legged robots compared to their legged counterparts.Comment: IEEE Robotics and Automation Letter

The Soft X-ray Spectrum from NGC 1068 Observed with LETGS on Chandra

Using the combined spectral and spatial resolving power of the Low Energy Transmission Grating (LETGS) on board Chandra, we obtain separate spectra from the bright central source of NGC 1068 (Primary region), and from a fainter bright spot 4" to the NE (Secondary region). Both spectra are dominated by line emission from H- and He-like ions of C through S, and from Fe L-shell ions, but also include narrow radiative recombination continua, indicating that most of the soft X-ray emission arises in low-temperature (kT few eV) photoionized plasma. We confirm the conclusions of Kinkhabwala et al. (2002), based on XMM-Newton RGS observations, that the entire nuclear spectrum can be explained by recombination/radiative cascade following photoionization, and radiative decay following photoexcitation, with no evidence for hot, collisionally ionized plasma. In addition, this model also provides an excellent fit to the spectrum of the Secondary region, albeit with radial column densities a factor of three lower, as would be expected given its distance from the source of the ionizing continuum. The remarkable overlap and kinematical agreement of the optical and X-ray line emission, coupled with the need for a distribution of ionization parameter to explain the X-ray spectra, collectively imply the presence of a distribution of densities (over a few orders of magnitude) at each radius in the ionization cone. Relative abundances of all elements are consistent with Solar abundance, except for N, which is 2-3 times Solar. The long wavelength spectrum beyond 30 A is rich of L-shell transitions of Mg, Si, S, and Ar, and M-shell transitions of Fe. The velocity dispersion decreases with increasing ionization parameter, as deduced from these long wavelength lines and the Fe-L shell lines.Comment: 12 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Euler number of Instanton Moduli space and Seiberg-Witten invariants

We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish. The partition function is the sum of Euler number of instanton moduli space when it is possible to apply the vanishing theorem. And we get a relation of Euler number labeled by the instanton number $k$ with Seiberg-Witten invariants, too. All calculation in this paper is done without assuming duality.Comment: LaTeX, 34 page

The Ionized Stellar Wind in Vela X-1 During Eclipse

We present a first analysis of a high resolution X-ray spectrum of the ionized stellar wind of Vela X-1 during eclipse. The data were obtained with the High Energy Transmission Grating Spectrometer onboard the Chandra X-ray Observatory. The spectrum is resolved into emission lines with fluxes between 0.02 and 1.04x10^4 ph/cm^2/s. We identify lines from a variety of charge states, including fluorescence lines from cold material, a warm photoionized wind. We can exclude signatures from collisionally ionized plasmas. For the first time we identify fluorescence lines from L-shell ions from lower Z elements. We also detect radiative recombination continua from a kT = 10 eV (1.2 x 10^5 K) photoionized optically thin gas. The fluorescence line fluxes infer the existence of optically thick and clumped matter within or outside the warm photoionized plasma.Comment: 4 pages, 2 figures, accepted by ApJ letter

Noncommutative Moduli for Multi-Instantons

There exists a recursive algorithm for constructing BPST-type multi-instantons on commutative R^4. When deformed noncommutatively, however, it becomes difficult to write down non-singular instanton configurations with topological charge greater than one in explicit form. We circumvent this difficulty by allowing for the translational instanton moduli to become noncommutative as well. This makes possible the ADHM construction of 't Hooft multi-instanton solutions with everywhere self-dual field strengths on noncommutative R^4.Comment: 1+9 pages; v2: reference added, published versio