On the runtime of universal coating for programmable matter

Daymude, Joshua J.; Derakhshandeh, Zahra; Gmyr, Robert; Porter, Alexandra; Richa, Andréa W.; Scheideler, Christian; Strothmann, Thim

doi:10.1007/s11047-017-9658-6

Cited by 36 publications

(37 citation statements)

References 19 publications

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“…Finally, the problem of coating a 2D shape has been studied theoretically in the context of self-organizing particle systems (SOPS), more specifically under the Amoebot model. In this theoretical approach, it is shown in [4,2] that the coating of a 2D object can be done using only local information in linear time with high probability. To the best of our knowledge, our work is the first work on the coating of a modular robotic structure by other modular robotic units in 3D.…”

Section: Related Workmentioning

confidence: 99%

3D Coating Self-Assembly for Modular Robotic Scaffolds

Thalamy¹,

Piranda²,

Bourgeois³

2020

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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This paper addresses the self-reconfiguration problem in large-scale modular robots for the purpose of shape formation for object representation. It aims to show that this process can be accelerated without compromising on the visual aspect of the final object, by creating an internal skeleton of the shape using the previously introduced sandboxing and scaffolding techniques, and then coating this skeleton with a layer of modules for higher visual fidelity.We discuss the challenges of the coating problem, introduce a basic method for constructing the coating of a scaffold layer by layer, and show that even with a straightforward algorithm, our scaffolding and coating combo uses much fewer modules than dense shapes and offers attractive reconfiguration times. Finally, we show that it could be a strong alternative to the construction of dense shapes using traditional selfreconfiguration algorithms.

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Section: Related Workmentioning

confidence: 99%

3D Coating Self-Assembly for Modular Robotic Scaffolds

Thalamy¹,

Piranda²,

Bourgeois³

2020

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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“…In this model, each particle can move from one grid point of a triangular grid to a neighboring grid point in a way that resembles an amoeba. Many problems of interest were addressed, including coating of materials [7,16,17], bridge building [1], energy distribution [12], shape formation [5,8,14,15,20,21], and shape recovery [19]. Towards solving these problems, a dominant strategy has been to elect a unique leader among the particles, which then coordinates all the movements.…”

Section: Introductionmentioning

confidence: 99%

“…In the current paper, we present a linear time algorithm to elect a unique leader deterministically when assuming a strong scheduler, regardless of the initial shape. (We make the rather common assumption that the particles have the same chirality; see Section 2.2 and [3,7,9,15,18,26,28].) The runtime of all the previous deterministic algorithms that did not assume special shapes of the particle Session 2: Biological Algorithms, Contention Resolution, and Radio Networks PODC '21, July 26-30, 2021, Virtual Event, Italy system (shapes with no holes) was at least quadratic in , where is the number of particles in the system.…”

Section: Introductionmentioning

confidence: 99%

Efficient Deterministic Leader Election for Programmable Matter

Dufoulon

Kutten

Moses

2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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It was suggested that a programmable matter system (composed of multiple computationally weak mobile particles) should remain connected at all times since otherwise, reconnection is difficult and may be impossible. At the same time, it was not clear that allowing the system to disconnect carried a significant advantage in terms of time complexity. We demonstrate for a fundamental task, that of leader election, an algorithm where the system disconnects and then reconnects automatically in a non-trivial way (particles can move far away from their former neighbors and later reconnect to others). Moreover, the runtime of the temporarily disconnecting deterministic leader election algorithm is linear in the diameter. Hence, the disconnecting -reconnecting algorithm is as fast as previous randomized algorithms. When comparing to previous deterministic algorithms, we note that some of the previous work assumed weaker schedulers. Still, the runtime of all the previous deterministic algorithms that did not assume special shapes of the particle system (shapes with no holes) was at least quadratic in , where is the number of particles in the system. (Moreover, the new algorithm is even faster in some parameters than the deterministic algorithms that did assume special initial shapes.)Since leader election is an important module in algorithms for various other tasks, the presented algorithm can be useful for speeding up other algorithms under the assumption of a strong scheduler. This leaves open the question: "can a deterministic algorithm be as fast as the randomized ones also under weaker schedulers?" CCS CONCEPTS• Theory of computation → Self-organization; Distributed algorithms; • Computing methodologies → Mobile agents.

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“…Of particular interest, from the distributed computing viewpoint, is the geometric Amoebot model of programmable matter [3,6,7,9,10,11,12]. In this model, introduced in [12] and so called because inspired by the behavior of amoeba, programmable matter is viewed as a swarm of decentralized autonomous self-organizing entities, operating on a hexagonal tessellation of the plane.…”

Section: Introductionmentioning

confidence: 99%

Shape formation by programmable particles

et al. 2019

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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 obtain several results that, among other things, 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 S F (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 optimal.

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On the runtime of universal coating for programmable matter

Cited by 36 publications

References 19 publications

3D Coating Self-Assembly for Modular Robotic Scaffolds

3D Coating Self-Assembly for Modular Robotic Scaffolds

Efficient Deterministic Leader Election for Programmable Matter

Shape formation by programmable particles

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