25,125 research outputs found
Shape Formation by Programmable Particles
Shape formation (or pattern formation) is a basic distributed problem for systems of compu- tational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter, where entities are assumed to be small and with severely limited capabilities. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessella- tion of the plane and have limited computational power (they have constant memory), strictly local interaction and communication capabilities (only with particles in neighboring nodes of the grid), and limited motorial capabilities (from a grid node to an empty neighboring node); their activation is controlled by an adversarial scheduler. Recent investigations have shown how, start- ing from a well-structured configuration in which the particles form a (not necessarily complete) triangle, the particles can form a large class of shapes. This result has been established under several assumptions: agreement on the clockwise direction (i.e., chirality), a sequential activation schedule, and randomization (i.e., particles can flip coins to elect a leader).
In this paper we provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. The characterization is constructive: we provide a universal shape formation algorithm that, for each feasible pair of shapes (S_0,S_F), allows the particles to form the final shape SF (given in input) starting from the initial shape S_0, unknown to the particles. The final configuration will be an appropriate scaled-up copy of S_F depending on n.
If randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that there are enough particles.
Our algorithm works without chirality, proving that chirality is computationally irrelevant for shape formation. Furthermore, it works under a strong adversarial scheduler, not necessarily sequential.
We also consider the complexity of shape formation both in terms of the number of rounds and the total number of moves performed by the particles executing a universal shape formation algorithm. We prove that our solution has a complexity of O(n^2) rounds and moves: this number of moves is also asymptotically worst-case optimal
Shape formation by programmable particles
Shape formation (or pattern formation) is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter, where entities are assumed to be small and with severely limited capabilities. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessellation of the plane and have limited computational power (they have constant memory), strictly local interaction and communication capabilities (only with particles in neighboring nodes of the grid), and limited motorial capabilities (from a grid node to an empty neighboring node); their activation is controlled by an adversarial scheduler. Recent investigations have shown how, starting from a well-structured configuration in which the particles form a (not necessarily complete) triangle, the particles can form a large class of shapes. This result has been established under several assumptions: agreement on the clockwise direction (i.e., chirality), a sequential activation schedule, and randomization (i.e., particles can flip coins to elect a leader). In this paper we provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. The characterization is constructive: we provide a universal shape formation algorithm that, for each feasible pair of shapes (S0, SF), allows the particles to form the final shape SF (given in input) starting from the initial shape S0, unknown to the particles. The final configuration will be an appropriate scaled-up copy of SF depending on n. If randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that there are enough particles. Our algorithm works without chirality, proving that chirality is computationally irrelevant for shape formation. Furthermore, it works under a strong adversarial scheduler, not necessarily sequential. We also consider the complexity of shape formation both in terms of the number of rounds and the total number of moves performed by the particles executing a universal shape formation algorithm. We prove that our solution has a complexity of O(n2) rounds and moves: this number of moves is also asymptotically worst-case optimal
Brief Announcement: Shape Formation by Programmable Particles
Shape formation is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessellation of the plane, have constant memory, can only communicate with neighboring particles, and can only move from a grid node to an empty neighboring node; their activation is controlled by an adversarial scheduler. Recent investigations have shown how, starting from a well-structured configuration in which the particles form a (not necessarily complete) triangle, the particles can form a large class of shapes. This result has been established under several assumptions: agreement on the clockwise direction (i.e., chirality), a sequential activation schedule, and randomization.
In this paper we provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. As a byproduct, if randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that n is large enough. Our algorithm works without chirality, proving that chirality is computationally irrelevant for shape formation. Furthermore, it works under a strong adversarial scheduler, not necessarily sequential. We also consider the complexity of shape formation both in terms of the number of rounds and the total number of moves performed by the particles executing a universal shape formation algorithm. We prove that our solution has a complexity of O(n^2) rounds and moves: this number of moves is also asymptotically optimal
Line-Recovery by Programmable Particles
Shape formation has been recently studied in distributed systems of
programmable particles. In this paper we consider the shape recovery problem of
restoring the shape when of the particles have crashed. We focus on the
basic line shape, used as a tool for the construction of more complex
configurations.
We present a solution to the line recovery problem by the non-faulty
anonymous particles; the solution works regardless of the initial distribution
and number of faults, of the local orientations of the non-faulty
entities, and of the number of non-faulty entities activated in each round
(i.e., semi-synchronous adversarial scheduler)
Algorithmic Foundations of Self-Organizing Programmable Matter
abstract: 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.Dissertation/ThesisDoctoral Dissertation Computer Science 201
Convex Hull Formation for Programmable Matter
We envision programmable matter as a system of nano-scale agents (called
particles) with very limited computational capabilities that move and compute
collectively to achieve a desired goal. We use the geometric amoebot model as
our computational framework, which assumes particles move on the triangular
lattice. Motivated by the problem of sealing an object using minimal resources,
we show how a particle system can self-organize to form an object's convex
hull. We give a distributed, local algorithm for convex hull formation and
prove that it runs in asynchronous rounds, where is the
length of the object's boundary. Within the same asymptotic runtime, this
algorithm can be extended to also form the object's (weak) -hull,
which uses the same number of particles but minimizes the area enclosed by the
hull. Our algorithms are the first to compute convex hulls with distributed
entities that have strictly local sensing, constant-size memory, and no shared
sense of orientation or coordinates. Ours is also the first distributed
approach to computing restricted-orientation convex hulls. This approach
involves coordinating particles as distributed memory; thus, as a supporting
but independent result, we present and analyze an algorithm for organizing
particles with constant-size memory as distributed binary counters that
efficiently support increments, decrements, and zero-tests --- even as the
particles move
Collaborative Computation in Self-Organizing Particle Systems
Many forms of programmable matter have been proposed for various tasks. We
use an abstract model of self-organizing particle systems for programmable
matter which could be used for a variety of applications, including smart paint
and coating materials for engineering or programmable cells for medical uses.
Previous research using this model has focused on shape formation and other
spatial configuration problems (e.g., coating and compression). In this work we
study foundational computational tasks that exceed the capabilities of the
individual constant size memory of a particle, such as implementing a counter
and matrix-vector multiplication. These tasks represent new ways to use these
self-organizing systems, which, in conjunction with previous shape and
configuration work, make the systems useful for a wider variety of tasks. They
can also leverage the distributed and dynamic nature of the self-organizing
system to be more efficient and adaptable than on traditional linear computing
hardware. Finally, we demonstrate applications of similar types of computations
with self-organizing systems to image processing, with implementations of image
color transformation and edge detection algorithms
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