Trajectory generation for cooperating robots

Includes bibliographical references (page 302).This paper derives a formulation for on-line trajectory generation for two robots cooperating to perform an assembly task. The two robots are treated as a single redundant system. A Jacobian is formulated that relates the joint rates of the entire system to the relative motion of one of the hands with respect to the other. The minimum norm solution of this relative Jacobian equation results in a set of joint rates which perform the cooperative task. In addition to the cooperative task, secondary goals, which include obstacle and joint limit avoidance, are specified using velocities in the null space of the relative Jacobian. This formulation also allows the robots to be controlled in parallel on independent tasks

Sphere rolling on the surface of a cone

We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We exhibit that the only circular of the system orbit is stable and furthermore show that all its solutions can be found using an analogy with central force problems. We also discuss the case of motion with no gravitational field, that is, of motion on a freely falling cone.Comment: 12 pages, 2 figures, to be published in Eur J Phy

[The Impact of Nuclear Star Formation on Gas Inflow to AGN

Our adaptive optics observations of nearby AGN at spatial resolutions as small as 0.085arcsec show strong evidence for recent, but no longer active, nuclear star formation. We begin by describing observations that highlight two contrasting methods by which gas can flow into the central tens of parsecs. Gas accumulation in this region will inevitably lead to a starburst, and we discuss the evidence for such events. We then turn to the impact of stellar evolution on the further inflow of gas by combining a phenomenological approach with analytical modelling and hydrodynamic simulations. These complementary perspectives paint a picture in which all the processes are ultimately regulated by the mass accretion rate into the central hundred parsecs, and the ensuing starburst that occurs there. The resulting supernovae delay accretion by generating a starburst wind, which leaves behind a clumpy interstellar medium. This provides an ideal environment for slower stellar outflows to accrete inwards and form a dense turbulent disk on scales of a few parsecs. Such a scenario may resolve the discrepancy between the larger scale structure seen with adaptive optics and the small scale structure seen with VLTI.Comment: to appear in: Co-Evolution of Central Black Holes and Galaxies; 7 page

A Planetary Mass Companion to the K0 Giant HD 17092

We report the discovery of a substellar-mass companion to the K0-giant HD 17092 with the Hobby-Eberly Telescope. In the absence of any correlation of the observed 360-day periodicity with the standard indicators of stellar activity, the observed radial velocity variations are most plausibly explained in terms of a Keplerian motion of a planetary-mass body around the star. With the estimated stellar mass of 2.3Msun, the minimum mass of the planet is 4.6MJ. The planet's orbit is characterized by a mild eccentricity of e=0.17 and a semi-major axis of 1.3 AU. This is the tenth published detection of a planetary companion around a red giant star. Such discoveries add to our understanding of planet formation around intermediate-mass stars and they provide dynamical information on the evolution of planetary systems around post-main sequence stars.Comment: 13 pages, 3 figures, 2 tables. Submitted to Ap

WASP-14 b: Transit Timing analysis of 19 light curves

Although WASP-14 b is one of the most massive and densest exoplanets on a tight and eccentric orbit, it has never been a target of photometric follow-up monitoring or dedicated observing campaigns. We report on new photometric transit observations of WASP-14 b obtained within the framework of "Transit Timing Variations @ Young Exoplanet Transit Initiative" (TTV@YETI). We collected 19 light-curves of 13 individual transit events using six telescopes located in five observatories distributed in Europe and Asia. From light curve modelling, we determined the planetary, stellar, and geometrical properties of the system and found them in agreement with the values from the discovery paper. A test of the robustness of the transit times revealed that in case of a non-reproducible transit shape the uncertainties may be underestimated even with a wavelet-based error estimation methods. For the timing analysis we included two publicly available transit times from 2007 and 2009. The long observation period of seven years (2007-2013) allowed us to refine the transit ephemeris. We derived an orbital period 1.2 s longer and 10 times more precise than the one given in the discovery paper. We found no significant periodic signal in the timing-residuals and, hence, no evidence for TTV in the system.Comment: 12 pages, 10 figures, 7 table

Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom

We consider natural complex Hamiltonian systems with $n$ degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of degree $k>2$. The well known Morales-Ramis theorem gives the strongest known necessary conditions for the Liouville integrability of such systems. It states that for each $k$ there exists an explicitly known infinite set \scM_k\subset\Q such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) calculated at a non-zero \vd\in\C^n satisfying V'(\vd)=\vd, belong to \scM_k. The aim of this paper is, among others, to sharpen this result. Under certain genericity assumption concerning $V$ we prove the following fact. For each $k$ and $n$ there exists a finite set \scI_{n,k}\subset\scM_k such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) belong to \scI_{n,k}. We give an algorithm which allows to find sets \scI_{n,k}. We applied this results for the case $n=k=3$ and we found all integrable potentials satisfying the genericity assumption. Among them several are new and they are integrable in a highly non-trivial way. We found three potentials for which the additional first integrals are of degree 4 and 6 with respect to the momenta.Comment: 54 pages, 1 figur

Continuity of medication management in Medicaid patients with chronic comorbid conditions: An examination by mental health status

Patients with serious mental illness (SMI) often have comorbid cardiometabolic conditions (CMCs) that may increase the number of prescribers involved in treatment. This study examined whether patients with SMI (depression and schizophrenia) and comorbid CMCs experience greater discontinuity of prescribing than patients with CMCs alone

Non integrability of a self-gravitating Riemann liquid ellipsoid

We prove that the motion of a triaxial Riemann ellipsoid of homogeneous liquid without angular momentum does not possess an additional first integral which is meromorphic in position, impulsions, and the elliptic functions which appear in the potential, and thus is not integrable. We prove moreover that this system is not integrable even on a fixed energy level hypersurface.Comment: 14 pages, 8 reference