CDDT: Fast Approximate 2D Ray Casting for Accelerated Localization

Localization is an essential component for autonomous robots. A well-established localization approach combines ray casting with a particle filter, leading to a computationally expensive algorithm that is difficult to run on resource-constrained mobile robots. We present a novel data structure called the Compressed Directional Distance Transform for accelerating ray casting in two dimensional occupancy grid maps. Our approach allows online map updates, and near constant time ray casting performance for a fixed size map, in contrast with other methods which exhibit poor worst case performance. Our experimental results show that the proposed algorithm approximates the performance characteristics of reading from a three dimensional lookup table of ray cast solutions while requiring two orders of magnitude less memory and precomputation. This results in a particle filter algorithm which can maintain 2500 particles with 61 ray casts per particle at 40Hz, using a single CPU thread onboard a mobile robot.Comment: 8 pages, 14 figures, ICRA versio

Observation of accelerating parabolic beams

We report the first observation of accelerating parabolic beams. These accelerating parabolic beams are similar to the Airy beams because they exhibit the unusual ability to remain diffraction-free while having a quadratic transverse shift during propagation. The amplitude and phase masks required to generate these beams are encoded onto a single liquid crystal display. Experimental results agree well with theory

Accelerating Reinforcement Learning by Composing Solutions of Automatically Identified Subtasks

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The system achieves much of its power by transferring parts of previously learned solutions rather than a single complete solution. The system exploits strong features in the multi-dimensional function produced by reinforcement learning in solving a particular task. These features are stable and easy to recognize early in the learning process. They generate a partitioning of the state space and thus the function. The partition is represented as a graph. This is used to index and compose functions stored in a case base to form a close approximation to the solution of the new task. Experiments demonstrate that function composition often produces more than an order of magnitude increase in learning rate compared to a basic reinforcement learning algorithm

Non-Paraxial Accelerating Beams

We present the spatially accelerating solutions of the Maxwell equations. Such non-paraxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams. For both TE and TM polarizations, the beams exhibit shape-preserving bending with sub-wavelength features, and the Poynting vector of the main lobe displays a turn of more than 90 degrees. We show that these accelerating beams are self-healing, analyze their properties, and compare to the paraxial Airy beams. Finally, we present the new family of periodic accelerating beams which can be constructed from our solutions

Manipulating light at distance by a metasurface using momentum transformation

A momentum conservation approach is introduced to manipulate light at distance using metasurfaces. Given a specified field existing on one side of the metasurface and specified desired field transmitted from the opposite side, a general momentum boundary condition is established, which determines the amplitude, phase and polarization transformation to be induced by the metasurface. This approach, named momentum transformation, enables a systematic way to synthesize metasurfaces with complete control over the reflected and transmitted fields. Several synthesis illustrative examples are provided: a vortex hypergeometric-Gaussian beam and a "delayed-start" accelerated beam for Fresnel region manipulation, and a pencil beam radiator and a holographic repeater for Frauenhofer region manipulation

Radially Self-Accelerating Beams

We report on optical non-paraxial beams that exhibit a self-accelerating behavior in radial direction. Our theory shows that those beams are solutions to the full scalar Helmholtz equation and that they continuously evolve on spiraling trajectories. We provide a detailed insight into the theoretical origin of the beams and verify our findings on an experimental basis

Accelerating and abruptly-autofocusing beam waves in the Fresnel zone of antenna arrays

We introduce the concept of spatially accelerating (curved) beam waves in the Fresnel region of properly designed antenna arrays. These are transversely localized EM waves that propagate in free space in a diffraction-resisting manner, while at the same time laterally shifting their amplitude pattern along a curved trajectory. The proposed beams are the radiowave analogue of Airy and related accelerating optical waves, which, in contrast to their optical counterparts, are produced by the interference of discrete radiating elements rather than by the evolution of a continuous wavefront. Two dyadic array configurations are proposed comprising 2D line antennas: linear phased arrays with a power-law phase variation and curved power-law arrays with in-phase radiating elements. Through analysis and numerical simulations, the formation of broadside accelerating beams with power-law trajectories is studied versus the array parameters. Furthermore, the abrupt autofocusing effect, that occurs when beams of this kind interfere with opposite acceleration, is investigated. The concept and the related antenna setups can be of use in radar and wireless communications applications