Programmable matter systems are composed of small, intelligent modules able to form a variety of macroscale objects with specific material properties in response to external commands or stimuli. While many programmable matter systems have been proposed in fiction, (Barbapapa, Changelings from Star Trek, the Terminator, and Transformers), and academia, a lack of suitable hardware and accompanying algorithms prevents their full realization. With this thesis research, we aim to create a system of miniature modules that can form arbitrary structures on demand. We develop autonomous 12mm cubic modules capable of bonding to, and communicating with, four of their immediate neighbors. These modules are among the smallest autonomous modular robots capable of sensing, communication, computation, and actuation. The modules employ unique electropermanent magnet connectors. The four connectors in each module enable the modules to communicate and share power with their nearest neighbors. These solid-state connectors are strong enough for a single inter-module connection to support the weight of 80 other modules. The connectors only consume power when switching on or off; they have no static power consumption. We implement a number of low-level communication and control algorithms which manage information transfer between neighboring modules. These algorithms ensure that messages are delivered reliably despite challenging conditions. They monitor the state of all communication links and are able to reroute messages around broken communication links to ensure that they reach their intended destinations. In order to accomplish our long-standing goal of programmatic shape formation, we also develop a suite of provably-correct distributed algorithms that allow complex shape formation. The distributed duplication algorithm that we present allows the system to duplicate any passive object that is submerged in a collection of programmable matter modules. The algorithm runs on the processors inside the modules and requires no external intervention. It requires 0(1) storage and O(n) inter-module messages per module, where n is the number of modules in the system. The algorithm can both magnify and produce multiple copies of the submerged object. A programmable matter system is a large network of autonomous processors, so these algorithms have applicability in a variety of routing, sensor network, and distributed computing applications. While our hardware system provides a 50-module test-bed for the algorithms, we show, by using a unique simulator, that the algorithms are capable of operating in much larger environments. Finally, we perform hundreds of experiments using both the simulator and hardware to show how the algorithms and hardware operate in practice.
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