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
Robotic swarms can potentially perform complicated tasks such as exploration and mapping at large space and time scales in a parallel and robust fashion. This thesis presents strategies for mapping environmental features of interest – specifically obstacles, collision-free paths, generating a metric map and estimating scalar density fields– in an unknown domain using data obtained by a swarm of resource-constrained robots. First, an approach was developed for mapping a single obstacle using a swarm of point-mass robots with both directed and random motion. The swarm population dynamics are modeled by a set of advection-diffusion-reaction partial differential equations (PDEs) in which a spatially-dependent indicator function marks the presence or absence of the obstacle in the domain. The indicator function is estimated by solving an optimization problem with PDEs as constraints. Second, a methodology for constructing a topological map of an unknown environment was proposed, which indicates collision-free paths for navigation, from data collected by a swarm of finite-sized robots. As an initial step, the number of topological features in the domain was quantified by applying tools from algebraic topology, to a probability function over the explored region that indicates the presence of obstacles. A topological map of the domain is then generated using a graph-based wave propagation algorithm. This approach is further extended, enabling the technique to construct a metric map of an unknown domain with obstacles using uncertain position data collected by a swarm of resource-constrained robots, filtered using intensity measurements of an external signal. Next, a distributed method was developed to construct the occupancy grid map of an unknown environment using a swarm of inexpensive robots or mobile sensors with limited communication. In addition to this, an exploration strategy which combines information theoretic ideas with Levy walks was also proposed. Finally, the problem of reconstructing a two-dimensional scalar field using observations from a subset of a sensor network in which each node communicates its local measurements to its neighboring nodes was addressed. This problem reduces to estimating the initial condition of a large interconnected system with first-order linear dynamics, which can be solved as an optimization problem.
ContributorsRamachandran, Ragesh Kumar (Author) / Berman, Spring M (Thesis advisor) / Mignolet, Marc (Committee member) / Artemiadis, Panagiotis (Committee member) / Marvi, Hamid (Committee member) / Robinson, Michael (Committee member) / Arizona State University (Publisher)
Created2018
Description
The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with the number of agents. One scalable approach to characterizing the behavior of a multi-agent system is possible when the agents' states evolve over time according to a Markov process. In this case, the density of agents over space and time is governed by a set of difference or differential equations known as a {\it mean-field model}, whose parameters determine the stochastic control policies of the individual agents. These models often have the advantage of being easier to analyze than the individual agent dynamics. Mean-field models have been used to describe the behavior of chemical reaction networks, biological collectives such as social insect colonies, and more recently, swarms of robots that, like natural swarms, consist of hundreds or thousands of agents that are individually limited in capability but can coordinate to achieve a particular collective goal.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
ContributorsBiswal, Shiba (Author) / Berman, Spring (Thesis advisor) / Fainekos, Georgios (Committee member) / Lanchier, Nicolas (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2020
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