Improving Sampling-Based Motion Planning Using Library of Trajectories

Plánování pohybu je jedním z podstatných problémů robotiky. Tato práce kombinuje pokroky v plánování pohybu a hodnocení podobnosti objektů za účelem zrychlení plánování ve statických prostředích. První část této práce pojednává o současných metodách používaných pro hodnocení podobnosti objektů a plánování pohybu. Prostřední část popisuje, jak jsou tyto metody použity pro zrychlení plánování s využitím získaných znalostí o prostředí. V poslední části jsou navržené metody porovnány s ostatními plánovači v nezávislém testu. Námi navržené algoritmy se v experimentech ukázaly být často rychlejší v porovnání s ostatními plánovači. Také často nacházely cesty v prostředích, kde ostatní plánovače nebyly schopny cestu nalézt.Motion planning is one of the fundamental problems in robotics. This thesis combines the advances in motion planning and shape matching to improve planning speeds in static environments. The first part of this thesis covers current methods used in object similarity evaluation and motion planning. The middle part describes how these methods are used together to improve planning speeds by utilizing prior knowledge about the environment, along with additional modifications. In the last part, the proposed methods are tested against other state-of-the-art planners in an independent benchmarking facility. The proposed algorithms are shown to be faster than other planners in many cases, often finding paths in environments where the other planners are unable to

Crawling the Cosmic Network: Exploring the Morphology of Structure in the Galaxy Distribution

Although coherent large-scale structures such as filaments and walls are apparent to the eye in galaxy redshift surveys, they have so far proven difficult to characterize with computer algorithms. This paper presents a procedure that uses the eigenvalues and eigenvectors of the Hessian matrix of the galaxy density field to characterize the morphology of large-scale structure. By analysing the smoothed density field and its Hessian matrix, we can determine the types of structure - walls, filaments, or clumps - that dominate the large-scale distribution of galaxies as a function of scale. We have run the algorithm on mock galaxy distributions in a LCDM cosmological N-body simulation and the observed galaxy distributions in the Sloan Digital Sky Survey. The morphology of structure is similar between the two catalogues, both being filament-dominated on 10-20 h^{-1} Mpc smoothing scales and clump-dominated on 5 h^{-1} Mpc scales. There is evidence for walls in both distributions, but walls are not the dominant structures on scales smaller than ~25 h^{-1} Mpc. Analysis of the simulation suggests that, on a given comoving smoothing scale, structures evolve with time from walls to filaments to clumps, where those found on smaller smoothing scales are further in this progression at a given time.Comment: 37 pages, 14 figures. Accepted to MNRAS

Primordial non-Gaussianity in the large scale structure of the Universe

Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of significant non-Gaussianity would thus have profound implications for our understanding of cosmic structure formation. The large scale mass distribution in the Universe is a sensitive probe of the nature of initial conditions. Recent theoretical progress together with rapid developments in observational techniques will enable us to critically confront predictions of inflationary scenarios and set constraints as competitive as those from the Cosmic Microwave Background. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large scale structure of the Universe.Comment: 24 pages, 10 figures. To appear in the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" of Advances in Astronom

Dynamic Zoom Simulations: a fast, adaptive algorithm for simulating lightcones

The advent of a new generation of large-scale galaxy surveys is pushing cosmological numerical simulations in an uncharted territory. The simultaneous requirements of high resolution and very large volume pose serious technical challenges, due to their computational and data storage demand. In this paper, we present a novel approach dubbed Dynamic Zoom Simulations -- or DZS -- developed to tackle these issues. Our method is tailored to the production of lightcone outputs from N-body numerical simulations, which allow for a more efficient storage and post-processing compared to standard comoving snapshots, and more directly mimic the format of survey data. In DZS, the resolution of the simulation is dynamically decreased outside the lightcone surface, reducing the computational work load, while simultaneously preserving the accuracy inside the lightcone and the large-scale gravitational field. We show that our approach can achieve virtually identical results to traditional simulations at half of the computational cost for our largest box. We also forecast this speedup to increase up to a factor of 5 for larger and/or higher-resolution simulations. We assess the accuracy of the numerical integration by comparing pairs of identical simulations run with and without DZS. Deviations in the lightcone halo mass function, in the sky-projected lightcone, and in the 3D matter lightcone always remain below 0.1%. In summary, our results indicate that the DZS technique may provide a highly-valuable tool to address the technical challenges that will characterise the next generation of large-scale cosmological simulations.Comment: 17 pages, 13 figures, version accepted for publication in MNRA

Terrain Aware Traverse Planning for Mars Rovers

NASA is proposing a Mars Sample Return mission, to be completed within one Martian year, that will require enhanced autonomy to perform its duties faster, safer, and more efficiently. With its main purpose being to retrieve samples possibly tens of kilometers away, it will need to drive beyond line-of-sight to get to its target more quickly than any rovers before. This research proposes a new methodology to support a sample return mission and is divided into three compo-nents: map preparation (map of traversability, i.e., ability of a terrain to sustain the traversal of a vehicle), path planning (pre-planning and replanning), and terrain analysis. The first component aims at creating a better knowledge of terrain traversability to support planning, by predicting rover slip and drive speed along the traverse using orbital data. By overlapping slope, rock abundance and terrain types at the same location, the expected drive velocity is obtained. By combining slope and thermal data, additional information about the experienced slip is derived, indicating whether it will be low (less than 30%) or medium to high (more than 30%). The second component involves planning the traverse for one Martian day (or sol) at a time, based on the map of expected drive speed. This research proposes to plan, offline, several paths traversable in one sol. Once online, the rover chooses the fastest option (the path cost being calculated using the distance divided by the expected velocity). During its drive, the rover monitors the terrain via analysis of its experienced wheel slip and actual speed. This information is then passed along the different pre-planned paths over a given distance (e.g., 25 m) and the map of traversability is locally updated given this new knowledge. When an update occurs, the rover calculates the new time of arrival of the various paths and replans its route if necessary. When tested in a simulation study on maps of the Columbia Hills, Mars, the rover successfully updates the map given new information drawn from a modified map used as ground truth for simulation purposes and replans its traverse when needed. The third component describes a method to assess the soil in-situ in case of dangerous terrain detected during the map update, or if the monitoring is not enough to confirm the traversability predicted by the map. The rover would deploy a shear vane instrument to compute intrinsic terrain parameters, information then propagated ahead of the rover to update the map and replan if necessary. Experiments in a laboratory setting as well as in the field showed promising results, the mounted shear vane giving values close to the expected terrain parameters of the tested soils