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Imagine that we have a piece of matter that can change its physical properties like its shape, density, conductivity, or color in a programmable fashion based on either user input or autonomous sensing. This is the vision behind what is commonly known as programmable matter. Envisioning systems of nano-sensors devices,

Imagine that we have a piece of matter that can change its physical properties like its shape, density, conductivity, or color in a programmable fashion based on either user input or autonomous sensing. This is the vision behind what is commonly known as programmable matter. Envisioning systems of nano-sensors devices, programmable matter consists of systems of simple computational elements, called particles, that can establish and release bonds, compute, and can actively move in a self-organized way. In this dissertation the feasibility of solving fundamental problems relevant for programmable matter is investigated. As a model for such self-organizing particle systems (SOPS), the geometric amoebot model is introduced. In this model, particles only have local information and have modest computational power. They achieve locomotion by expanding and contracting, which resembles the behavior of amoeba. Under this model, efficient local-control algorithms for the leader election problem in SOPS are presented. As a central problem for programmable matter, shape formation problems are then studied. The limitations of solving the leader election problem and the shape formation problem on a more general version of the amoebot model are also discussed. The \smart paint" problem is also studied which aims at having the particles self-organize in order to uniformly coat the surface of an object of arbitrary shape and size, forming multiple coating layers if necessary. A Universal Coating algorithm is presented and shown to be asymptotically worst-case optimal both in terms of time with high probability and work. In particular, the algorithm always terminates within a linear number of rounds with high probability. A linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information is presented, which implies that the proposed algorithm is also optimal in a competitive sense. Simulation results show that the competitive ratio of the proposed algorithm may be better than linear in practice. Developed algorithms utilize only local control, require only constant-size memory particles, and are asymptotically optimal in terms of the total number of particle movements needed to reach the desired shape configuration.
ContributorsDerakhshandeh, Zahra (Author) / Richa, Andrea (Thesis advisor) / Sen, Arunabha (Thesis advisor) / Xue, Guoliang (Committee member) / Scheideler, Christian (Committee member) / Arizona State University (Publisher)
Created2017
Description
The world is filled with systems of entities that collaborate in motion, both natural and engineered. These cooperative distributed systems are capable of sophisticated emergent behavior arising from the comparatively simple interactions of their members. A model system for emergent collective behavior is programmable matter, a physical substance capable of

The world is filled with systems of entities that collaborate in motion, both natural and engineered. These cooperative distributed systems are capable of sophisticated emergent behavior arising from the comparatively simple interactions of their members. A model system for emergent collective behavior is programmable matter, a physical substance capable of autonomously changing its properties in response to user input or environmental stimuli. This dissertation studies distributed and stochastic algorithms that control the local behaviors of individual modules of programmable matter to induce complex collective behavior at the macroscale. It consists of four parts. In the first, the canonical amoebot model of programmable matter is proposed. A key goal of this model is to bring algorithmic theory closer to the physical realities of programmable matter hardware, especially with respect to concurrency and energy distribution. Two protocols are presented that together extend sequential, energy-agnostic algorithms to the more realistic concurrent, energy-constrained setting without sacrificing correctness, assuming the original algorithms satisfy certain conventions. In the second part, stateful distributed algorithms using amoebot memory and communication are presented for leader election, object coating, convex hull formation, and hexagon formation. The first three algorithms are proven to have linear runtimes when assuming a simplified sequential setting. The final algorithm for hexagon formation is instead proven to be correct under unfair asynchronous adversarial activation, the most general of all adversarial activation models. In the third part, distributed algorithms are combined with ideas from statistical physics and Markov chain design to replace algorithm reliance on memory and communication with biased random decisions, gaining inherent self-stabilizing and fault-tolerant properties. Using this stochastic approach, algorithms for compression, shortcut bridging, and separation are designed and analyzed. Finally, a two-pronged approach to "programming" physical ensembles is presented. This approach leverages the physics of local interactions to pair theoretical abstractions of self-organizing particle systems with experimental robot systems of active granular matter that intentionally lack digital computation and communication. By physically embodying the salient features of an algorithm in robot design, the algorithm's theoretical analysis can predict the robot ensemble's behavior. This approach is applied to phototaxing, aggregation, dispersion, and object transport.
ContributorsDaymude, Joshua (Author) / Richa, Andréa W (Thesis advisor) / Scheideler, Christian (Committee member) / Randall, Dana (Committee member) / Pavlic, Theodore (Committee member) / Gil, Stephanie (Committee member) / Arizona State University (Publisher)
Created2021