Many proposals have already been made for realizing programmable matter, ranging from shape-changing molecules, DNA tiles, and synthetic cells to reconfigurable modular robotics. Envisioning systems of nano-sensors devices, we are particularly interested in programmable matter consisting of systems of simple computational elements, called particles, that can establish and release bonds and can actively move in a self-organized way, and in shape formation problems relevant for programmable matter in those self-organizing particle systems (SOPS). In this paper, we present a general algorithmic framework for shape formation problems in SOPS, and show direct applications of this framework to the problems of having the particle system self-organize to form a hexagonal or triangular shape. Our algorithms utilize only local control, require only constant-size memory particles, and are asymptotically optimal both in terms of the total number of movements needed to reach the desired shape configuration.
In the area of it is usually assumed that there is a collection of autonomous robots that have limited sensing, and communication ranges, and that can freely move in a given area. They follow a variety of goals, including for example shape formation problems (e.g., @cite_16 @cite_1 ). Surveys of recent results in swarm robotics can be found in @cite_3 @cite_17 . While the analytical techniques developed in the area of swarm robotics and natural swarms are of some relevance for this work, the individual units in those systems have more powerful communication and processing capabilities than in the systems we consider.
@cite_16 @cite_1 @cite_3 @cite_17
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From an engineering point of view, the problem of coordinating a set of autonomous, mobile robots for the purpose of cooperatively performing a task has been studied extensively over the past decade. In contrast, in this paper we aim to understand the fundamental algorithmic limitations on what a set of autonomous mobile robots can or cannot achieve. We therefore study a hard task for a set of weak robots. The task is for the robots in the plane to form any arbitrary pattern that is given in advance. This task is fundamental in the sense that if the robots can form any pattern, they can agree on their respective roles in a subsequent, coordinated action. The robots are weak in several aspects. They are anonymous; they cannot explicitly communicate with each other, but only observe the positions of the others; they cannot remember the past; they operate in a very strong form of asynchronicity. We show that the tasks that such a system of robots can perform depend strongly on their common agreement about their environment, i.e. the readings of their environment sensors. If the robots have no common agreement about their environment, they cannot form an arbitrary pattern. If each robot has a compass needle that indicates North (the robot world is a flat surface, and compass needles are parallel), then any odd number of robots can form an arbitrary pattern, but an even number cannot (in the worst case). If each robot has two independent compass needles, say North and East, then any set of robots can form any pattern. When individuals swarm, they must somehow communicate to direct collective motion. Swarms of robots need to deal with outliers, such as robots that move more slowly than the rest. created a large swarm of programmed robots that can form collaborations using only local information. The robots could communicate only with nearby members, within about three times their diameter. They were able to assemble into complex preprogrammed shapes. If the robots' formation hit snags when they bumped into one another or because of an outlier, additional algorithms guided them to rectify their collective movements. @PARASPLIT Science , this issue p. [795][1] @PARASPLIT [1]: lookup volpage 345 795?iss=6198 Distributed algorithms for multi-robot systems rely on network communications to share information. However, the motion of the robots changes the network topology, which affects the information presented to the algorithm. For an algorithm to produce accurate output, robots need to communicate rapidly enough to keep the network topology correlated to their physical configuration. Infrequent communications will cause most multi-robot distributed algorithms to produce less accurate results, and cause some algorithms to stop working altogether. The central theme of this work is that algorithm accuracy, communications bandwidth, and physical robot speed are related. This thesis has three main contributions: First, I develop a prototypical multi-robot application and computational model, propose a set of complexity metrics to evaluate distributed algorithm performance on multi-robot systems, and introduce the idea of the robot speed ratio, a dimensionless measure of robot speed relative to message speed in networks that rely on multi-hop communication. The robot speed ratio captures key relationships between communications bandwidth, mobility, and algorithm accuracy, and can be used at design time to trade off between them. I use this speed ratio to evaluate the performance of existing distributed algorithms for multi-hop communication and navigation. Second, I present a definition of boundaries in multi-robot systems, and develop new distributed algorithms to detect and characterize them. Finally, I define the problem of dynamic task assignment, and present four distributed algorithms that solve this problem, each representing a different trade-off between accuracy, running time, and communication resources. All the algorithms presented in this work are provably correct under ideal conditions and produce verifiable real-world performance. They are self-stabilizing and robust to communications failures, population changes, and other errors. All the algorithms were tested on a swarm of 112 robots. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)