10 research outputs found
Blending techniques in Curve and Surface constructions
Source at https://www.geofo.no/geofoN.html. <p
Path Planning For Persistent Surveillance Applications Using Fixed-Wing Unmanned Aerial Vehicles
This thesis addresses coordinated path planning for fixed-wing Unmanned Aerial Vehicles
(UAVs) engaged in persistent surveillance missions. While uniquely suited to this mission,
fixed wing vehicles have maneuver constraints that can limit their performance in this role.
Current technology vehicles are capable of long duration flight with a minimal acoustic
footprint while carrying an array of cameras and sensors. Both military tactical and civilian
safety applications can benefit from this technology. We make three main contributions:
C1 A sequential path planner that generates a C2 flight plan to persistently acquire a
covering set of data over a user designated area of interest. The planner features the
following innovations:
• A path length abstraction that embeds kino-dynamic motion constraints to estimate feasible path length
• A Traveling Salesman-type planner to generate a covering set route based on the path length abstraction
• A smooth path generator that provides C2 routes that satisfy user specified curvature constraints
C2 A set of algorithms to coordinate multiple UAVs, including mission commencement
from arbitrary locations to the start of a coordinated mission and de-confliction of
paths to avoid collisions with other vehicles and fixed obstacles
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C3 A numerically robust toolbox of spline-based algorithms tailored for vehicle routing
validated through flight test experiments on multiple platforms. A variety of tests
and platforms are discussed.
The algorithms presented are based on a technical approach with approximately equal
emphasis on analysis, computation, dynamic simulation, and flight test experimentation.
Our planner (C1) directly takes into account vehicle maneuverability and agility constraints
that could otherwise render simple solutions infeasible. This is especially important when
surveillance objectives elevate the importance of optimized paths. Researchers have devel
oped a diverse range of solutions for persistent surveillance applications but few directly
address dynamic maneuver constraints.
The key feature of C1 is a two stage sequential solution that discretizes the problem so that
graph search techniques can be combined with parametric polynomial curve generation.
A method to abstract the kino-dynamics of the aerial platforms is then presented so that
a graph search solution can be adapted for this application. An A* Traveling Salesman
Problem (TSP) algorithm is developed to search the discretized space using the abstract
distance metric to acquire more data or avoid obstacles. Results of the graph search are
then transcribed into smooth paths based on vehicle maneuver constraints. A complete
solution for a single vehicle periodic tour of the area is developed using the results of the
graph search algorithm. To execute the mission, we present a simultaneous arrival algorithm
(C2) to coordinate execution by multiple vehicles to satisfy data refresh requirements and
to ensure there are no collisions at any of the path intersections.
We present a toolbox of spline-based algorithms (C3) to streamline the development of C2
continuous paths with numerical stability. These tools are applied to an aerial persistent
surveillance application to illustrate their utility. Comparisons with other parametric poly
nomial approaches are highlighted to underscore the benefits of the B-spline framework.
Performance limits with respect to feasibility constraints are documented
Low dimensional dualities:Matrix models, two-dimensional quantum gravity & black holes
This thesis focuses on low dimensional dualities as tractable models to explore two-dimensional de Sitter space and black holes. The first two chapters review, discuss and explore the framework for a novel attempt to create a connection between de Sitter space and the conjectured duality between matrix models and two-dimensional quantum gravity. The hope is that this could pave a path toward understanding the so far unknown microscopic picture of our Universe. In the last chapter we address fundamental problems about the microscopic picture of black holes through a low dimensional duality dubbed the near-AdS2/near-CFT1 correspondence
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
Second International Workshop on Harmonic Oscillators
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory
Safety and Reliability - Safe Societies in a Changing World
The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management
- mathematical methods in reliability and safety
- risk assessment
- risk management
- system reliability
- uncertainty analysis
- digitalization and big data
- prognostics and system health management
- occupational safety
- accident and incident modeling
- maintenance modeling and applications
- simulation for safety and reliability analysis
- dynamic risk and barrier management
- organizational factors and safety culture
- human factors and human reliability
- resilience engineering
- structural reliability
- natural hazards
- security
- economic analysis in risk managemen