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

Piloted evaluation of a control allocation technique to recover from pilot-induced oscillations

This paper describes the maturation of a control allocation technique designed to assist pilots in recovery from pilot-induced oscillations. The control allocation technique to recover from pilot-induced oscillations is designed to enable next-generation high-efficiency aircraft designs. Energy-efficient next-generation aircraft require feedback control strategies that will enable lowering the actuator rate limit requirements for optimal airframe design. A common issue on aircraft with actuator rate limitations is they are susceptible to pilot-induced oscillations caused by the phase lag between the pilot inputs and control surface response. The control allocation technique to recover from pilot-induced oscillations uses real-time optimization for control allocation to eliminate phase lag in the system caused by control surface rate limiting. System impacts of the control allocator were assessed through a piloted simulation evaluation of a nonlinear aircraft model in the NASA Ames Research Center's Vertical Motion Simulator. Results indicate that the control allocation technique to recover from pilot-induced oscillations helps reduce oscillatory behavior introduced by control surface rate limiting, including the pilot-induced oscillation tendencies reported by pilots

On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations

The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical stability and convergence are presented. Comparisons are made between the present schemes in terms of accuracy and computational efficiency for solving problems with severe internal and boundary gradients. The present study shows that the fourth-order compact ADI scheme is stable and efficient

The Political Economy of Failure: The Euro as an International Currency

How do international currencies get established and consolidated? What domestic and international political foundations support an international currency? And what kinds of macro-economic flows enable an international currency? In this essay we consider these perennial questions of modern IPE scholarship in reverse order to ask whether the euro could ever have become, or seek to become, a true international currency rivalling the US dollar, used not only for passive foreign exchange reserves but also as a major commercial currency outside the EU. We argue that the EU lacks the will, the ideas and the capacity to promote the euro into the status of an international currency. In this article, we concentrate on this final issue of capacity, as the will and ideas issues have already been well explored. Capacity is an issue coeval with, if not prior to, the first two issues. The EU's current institutional arrangements and its economic geography create macro-economic consequences that diminish the euro's capacity to operate as a top currency. These conflicts go beyond the well-recognized issue that the euro-zone is not an optimum currency area. Examining the euro's debilities sheds light not only on the euro's (in)capacity to rival the dollar as an international currency, but also on the future of both the euro and the dollar in the aftermath of the euro-zone crisis

Projected WIMP sensitivity of the LUX-ZEPLIN dark matter experiment

LUX-ZEPLIN (LZ) is a next-generation dark matter direct detection experiment that will operate 4850 feet underground at the Sanford Underground Research Facility (SURF) in Lead, South Dakota, USA. Using a two-phase xenon detector with an active mass of 7 tonnes, LZ will search primarily for low-energy interactions with weakly interacting massive particles (WIMPs), which are hypothesized to make up the dark matter in our galactic halo. In this paper, the projected WIMP sensitivity of LZ is presented based on the latest background estimates and simulations of the detector. For a 1000 live day run using a 5.6-tonne fiducial mass, LZ is projected to exclude at 90% confidence level spin-independent WIMP-nucleon cross sections above 1.4 × 10-48cm2 for a 40 GeV/c2 mass WIMP. Additionally, a 5σ discovery potential is projected, reaching cross sections below the exclusion limits of recent experiments. For spin-dependent WIMP-neutron(-proton) scattering, a sensitivity of 2.3 × 10−43 cm2 (7.1 × 10−42 cm2) for a 40 GeV/c2 mass WIMP is expected. With underground installation well underway, LZ is on track for commissioning at SURF in 2020

Space Telescope and Optical Reverberation Mapping Project. VII. Understanding the Ultraviolet Anomaly in NGC 5548 with X-Ray Spectroscopy

During the Space Telescope and Optical Reverberation Mapping Project observations of NGC 5548, the continuum and emission-line variability became decorrelated during the second half of the six-month-long observing campaign. Here we present Swift and Chandra X-ray spectra of NGC 5548 obtained as part of the campaign. The Swift spectra show that excess flux (relative to a power-law continuum) in the soft X-ray band appears before the start of the anomalous emission-line behavior, peaks during the period of the anomaly, and then declines. This is a model-independent result suggesting that the soft excess is related to the anomaly. We divide the Swift data into on- and off-anomaly spectra to characterize the soft excess via spectral fitting. The cause of the spectral differences is likely due to a change in the intrinsic spectrum rather than to variable obscuration or partial covering. The Chandra spectra have lower signal-to-noise ratios, but are consistent with the Swift data. Our preferred model of the soft excess is emission from an optically thick, warm Comptonizing corona, the effective optical depth of which increases during the anomaly. This model simultaneously explains all three observations: the UV emission-line flux decrease, the soft-excess increase, and the emission-line anomaly

A muon-track reconstruction exploiting stochastic losses for large-scale Cherenkov detectors

IceCube is a cubic-kilometer Cherenkov telescope operating at the South Pole. The main goal of IceCube is the detection of astrophysical neutrinos and the identification of their sources. High-energy muon neutrinos are observed via the secondary muons produced in charge current interactions with nuclei in the ice. Currently, the best performing muon track directional reconstruction is based on a maximum likelihood method using the arrival time distribution of Cherenkov photons registered by the experiment\u27s photomultipliers. A known systematic shortcoming of the prevailing method is to assume a continuous energy loss along the muon track. However at energies >1 TeV the light yield from muons is dominated by stochastic showers. This paper discusses a generalized ansatz where the expected arrival time distribution is parametrized by a stochastic muon energy loss pattern. This more realistic parametrization of the loss profile leads to an improvement of the muon angular resolution of up to 20% for through-going tracks and up to a factor 2 for starting tracks over existing algorithms. Additionally, the procedure to estimate the directional reconstruction uncertainty has been improved to be more robust against numerical errors

The Physics of Star Cluster Formation and Evolution

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00689-4.Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work.Peer reviewe