Value Iteration Networks on Multiple Levels of Abstraction

Learning-based methods are promising to plan robot motion without performing extensive search, which is needed by many non-learning approaches. Recently, Value Iteration Networks (VINs) received much interest since---in contrast to standard CNN-based architectures---they learn goal-directed behaviors which generalize well to unseen domains. However, VINs are restricted to small and low-dimensional domains, limiting their applicability to real-world planning problems. To address this issue, we propose to extend VINs to representations with multiple levels of abstraction. While the vicinity of the robot is represented in sufficient detail, the representation gets spatially coarser with increasing distance from the robot. The information loss caused by the decreasing resolution is compensated by increasing the number of features representing a cell. We show that our approach is capable of solving significantly larger 2D grid world planning tasks than the original VIN implementation. In contrast to a multiresolution coarse-to-fine VIN implementation which does not employ additional descriptive features, our approach is capable of solving challenging environments, which demonstrates that the proposed method learns to encode useful information in the additional features. As an application for solving real-world planning tasks, we successfully employ our method to plan omnidirectional driving for a search-and-rescue robot in cluttered terrain

A representation-free description of the Kasevich-Chu interferometer: a resolution of the redshift controversy

Motivated by a recent claim by Muller et al (2010 Nature 463 926-9) that an atom interferometer can serve as an atom clock to measure the gravitational redshift with an unprecedented accuracy, we provide a representation-free description of the Kasevich-Chu interferometer based on operator algebra. We use this framework to show that the operator product determining the number of atoms at the exit ports of the interferometer is a c-number phase factor whose phase is the sum of only two phases: one is due to the acceleration of the phases of the laser pulses and the other one is due to the acceleration of the atom. This formulation brings out most clearly that this interferometer is an accelerometer or a gravimeter. Moreover, we point out that in different representations of quantum mechanics such as the position or the momentum representation the phase shift appears as though it originates from different physical phenomena. Due to this representation dependence conclusions concerning an enhanced accuracy derived in a specific representation are unfounded.German Space Agency (DLR)BMWi/DLR 50 WM 0837Alexander von Humboldt StiftungTempleton Foundation/2153

Schrödinger equation revisited

The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave

Quadrupedal Footstep Planning using Learned Motion Models of a Black-Box Controller

Legged robots are increasingly entering new domains and applications, including search and rescue, inspection, and logistics. However, for such systems to be valuable in real-world scenarios, they must be able to autonomously and robustly navigate irregular terrains. In many cases, robots that are sold on the market do not provide such abilities, being able to perform only blind locomotion. Furthermore, their controller cannot be easily modified by the end-user, requiring a new and time-consuming control synthesis. In this work, we present a fast local motion planning pipeline that extends the capabilities of a black-box walking controller that is only able to track high-level reference velocities. More precisely, we learn a set of motion models for such a controller that maps high-level velocity commands to Center of Mass (CoM) and footstep motions. We then integrate these models with a variant of the A star algorithm to plan the CoM trajectory, footstep sequences, and corresponding high-level velocity commands based on visual information, allowing the quadruped to safely traverse irregular terrains at demand

Proper time in atom interferometers: Diffractive versus specular mirrors

We compare a conventional Mach-Zehnder light-pulse atom interferometer based on diffractive mirrors with one that uses specular reflection. In contrast to diffractive mirrors that generate a symmetric configuration, specular mirrors realized, for example, by evanescent fields lead under the influence of gravity to an asymmetric geometry. In such an arrangement the interferometer phase contains nonrelativistic signatures of proper time.Comment: 7 pages, 1 figure, 1 tabl

Do subterranean mammals use the Earth’s magnetic field as a heading indicator to dig straight tunnels?

Subterranean rodents are able to dig long straight tunnels. Keeping the course of such “runways” is important in the context of optimal foraging strategies and natal or mating dispersal. These tunnels are built in the course of a long time, and in social species, by several animals. Although the ability to keep the course of digging has already been described in the 1950s, its proximate mechanism could still not be satisfactorily explained. Here, we analyzed the directional orientation of 68 burrow systems in five subterranean rodent species (Fukomys anselli, F. mechowii, Heliophobius argenteocinereus, Spalax galili, and Ctenomys talarum) on the base of detailed maps of burrow systems charted within the framework of other studies and provided to us. The directional orientation of the vast majority of all evaluated burrow systems on the individual level (94%) showed a significant deviation from a random distribution. The second order statistics (averaging mean vectors of all the studied burrow systems of a respective species) revealed significant deviations from random distribution with a prevalence of north–south (H. argenteocinereus), NNW–SSE (C. talarum), and NE–SW (Fukomys mole-rats) oriented tunnels. Burrow systems of S. galili were randomly oriented. We suggest that the Earth’s magnetic field acts as a common heading indicator, facilitating to keep the course of digging. This study provides a field test and further evidence for magnetoreception and its biological meaning in subterranean mammals. Furthermore, it lays the foundation for future field experiments