ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.
In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.
Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.
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Description
Building and optimizing a design for deformable media can be extremely costly. However, granular scaling laws enable the ability to predict system velocity and mobility
power consumption by testing at a smaller scale in the same environment. The validity of
the granular scaling laws for arbitrarily shaped wheels and screws were evaluated in
materials like silica sand and BP-1, a lunar simulant. Different wheel geometries, such as
non-grousered and straight and bihelically grousered wheels were created and tested
using 3D printed technologies. Using the granular scaling laws and the empirical data
from initial experiments, power and velocity were predicted for a larger scaled version
then experimentally validated on a dynamic mobility platform. Working with granular
media has high variability in material properties depending on initial environmental
conditions, so particular emphasis was placed on consistency in the testing methodology.
Through experiments, these scaling laws have been validated with defined use cases and
limitations.
ContributorsMcbryan, Teresa (Author) / Marvi, Hamidreza (Thesis advisor) / Berman, Spring (Committee member) / Lee, Hyunglae (Committee member) / Arizona State University (Publisher)
Created2022
Description
Modern life is full of challenging optimization problems that we unknowingly attempt to solve. For instance, a common dilemma often encountered is the decision of picking a parking spot while trying to minimize both the distance to the goal destination and time spent searching for parking; one strategy is to drive as close as possible to the goal destination but risk a penalty cost if no parking spaces can be found. Optimization problems of this class all have underlying time-varying processes that can be altered by a decision/input to minimize some cost. Such optimization problems are commonly solved by a class of methods called Dynamic Programming (DP) that breaks down a complex optimization problem into a simpler family of sub-problems. In the 1950s Richard Bellman introduced a class of DP methods that broke down Multi-Stage Optimization Problems (MSOP) into a nested sequence of ``tail problems”. Bellman showed that for any MSOP with a cost function that satisfies a condition called additive separability, the solution to the tail problem of the MSOP initialized at time-stage k>0 can be used to solve the tail problem initialized at time-stage k-1. Therefore, by recursively solving each tail problem of the MSOP, a solution to the original MSOP can be found. This dissertation extends Bellman`s theory to a broader class of MSOPs involving non-additively separable costs by introducing a new state augmentation solution method and generalizing the Bellman Equation. This dissertation also considers the analogous continuous-time counterpart to discrete-time MSOPs, called Optimal Control Problems (OCPs). OCPs can be solved by solving a nonlinear Partial Differential Equation (PDE) called the Hamilton-Jacobi-Bellman (HJB) PDE. Unfortunately, it is rarely possible to obtain an analytical solution to the HJB PDE. This dissertation proposes a method for approximately solving the HJB PDE based on Sum-Of-Squares (SOS) programming. This SOS algorithm can be used to synthesize controllers, hence solving the OCP, and also compute outer bounds of reachable sets of dynamical systems. This methodology is then extended to infinite time horizons, by proposing SOS algorithms that yield Lyapunov functions that can approximate regions of attraction and attractor sets of nonlinear dynamical systems arbitrarily well.
ContributorsJones, Morgan (Author) / Peet, Matthew M (Thesis advisor) / Nedich, Angelia (Committee member) / Kawski, Matthias (Committee member) / Mignolet, Marc (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2021
Description
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers - machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.
ContributorsKamyar, Reza (Author) / Peet, Matthew (Thesis advisor) / Berman, Spring (Committee member) / Rivera, Daniel (Committee member) / Artemiadis, Panagiotis (Committee member) / Fainekos, Georgios (Committee member) / Arizona State University (Publisher)
Created2016
Description
Vehicles traverse granular media through complex reactions with large numbers of small particles. Many approaches rely on empirical trends derived from wheeled vehicles in well-characterized media. However, the environments of numerous bodies such as Mars or the moon are primarily composed of fines called regolith which require different design considerations. This dissertation discusses research aimed at understanding the role and function of empirical, computational, and theoretical granular physics approaches as they apply to helical geometries, their envelope of applicability, and the development of new laws. First, a static Archimedes screw submerged in granular material (glass beads) is analyzed using two methods: Granular Resistive Force Theory (RFT), an empirically derived set of equations based on fluid dynamic superposition principles, and Discrete element method (DEM) simulations, a particle modeling software. Dynamic experiments further confirm the computational method with multi-body dynamics (MBD)-DEM co-simulations. Granular Scaling Laws (GSL), a set of physics relationships based on non-dimensional analysis, are utilized for the gravity-modified environments. A testing chamber to contain a lunar analogue, BP-1, is developed and built. An investigation of straight and helical grousered wheels in both silica sand and BP-1 is performed to examine general GSL applicability for lunar purposes. Mechanical power draw and velocity prediction by GSL show non-trivial but predictable deviation. BP-1 properties are characterized and applied to an MBD-DEM environment for the first time. MBD-DEM simulation results between Earth gravity and lunar gravity show good agreement with theoretical predictions for both power and velocity. The experimental deviation is further investigated and found to have a mass-dependant component driven by granular sinkage and engagement. Finally, a robust set of helical granular scaling laws (HGSL) are derived. The granular dynamics scaling of three-dimensional screw-driven mobility is reduced to a similar theory as wheeled scaling laws, provided the screw is radially continuous. The new laws are validated in BP-1 with results showing very close agreement to predictions. A gravity-variant version of these laws is validated with MBD-DEM simulations. The results of the dissertation suggest GSL, HGSL, and MBD-DEM give reasonable approximations for use in lunar environments to predict rover mobility given adequate granular engagement.
ContributorsThoesen, Andrew Lawrence (Author) / Marvi, Hamidreza (Thesis advisor) / Berman, Spring (Committee member) / Emady, Heather (Committee member) / Lee, Hyunglae (Committee member) / Klesh, Andrew (Committee member) / Arizona State University (Publisher)
Created2019