Collecting a swarm in a grid environment using shared, global inputs

Mahadev, Arun; Krupke, Dominik; Reinhardt, Jan-Marc; Fekete, Sándor P.; Becker, Aaron T.

doi:10.1109/coase.2016.7743547

Cited by 14 publications

(6 citation statements)

References 17 publications

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“…Mahadev et al [31] show how to gather n particles within an obstacle environment in O(n 3 ) actuation steps. Becker et al [7] improve the runtime to only depend on the geometric complexity of the workspace, rather than on the number of particles.…”

Section: Self-assemblymentioning

confidence: 99%

See 1 more Smart Citation

Particle-Based Assembly Using Precise Global Control

Keller¹,

Rieck²,

Scheffer³

et al. 2021

Preprint

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In micro-and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. In the presence of adhesive particles that can attach to each other, the challenge is to decide whether a shape is constructible. Previous work provides a class of shapes for which constructibility can be decided efficiently, when particles move maximally into the same direction on actuation.In this paper, we consider a stronger model. On actuation, each particle moves one unit step into the given direction. We prove that deciding constructibility is NP-hard for three-dimensional shapes, and that a maximum constructible shape can be approximated. The same approximation algorithm applies for 2D. We further present linear-time algorithms to decide whether a tree-shape in 2D or 3D is constructible. If scaling is allowed, we show that the c-scaled copy of every non-degenerate polyomino is constructible, for every c ≥ 2.

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Section: Self-assemblymentioning

confidence: 99%

“…However, it is also reasonable to expose the particles to these forces just for a limited amount of time, such that more precise movements become possible. Reconfiguration of a set of particles [2], gathering all particles [7,31], or assembling patterned rectangles [13] are well studied problems.…”

Section: Introductionmentioning

confidence: 99%

Particle-Based Assembly Using Precise Global Control

Keller¹,

Rieck²,

Scheffer³

et al. 2021

Preprint

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show abstract

“…The results of this section highlight a broad spectrum of joint work with Victor Baez, Aaron Becker, Erik Demaine, Golnaz Habibi, Li Huang, Phillip Keldenich, Linda Kleist, Dominik Krupke, Jarrett Lonsford, Arun Mahadev, Sheryl Manzoor, James McLurkin, Rose Morris-Wright, Hamed Mohtasham Shad, Christian Rieck, Christian Scheffer, and Arne Schmidt; see [3,4,[6][7][8]10,20,23,24,26,27] for further details. The shown video [2] is available at https://www.…”

Section: Uniform Global Control For Particle Swarmsmentioning

confidence: 99%

Coordinating Swarms of Objects at Extreme Dimensions

Fekete

2020

Lecture Notes in Computer Science

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We describe a variety of algorithmic challenges arising from coordination and reconfiguration of swarms of potentially many objects, ranging in size from minuscule particles all the way to far-away satellite swarms. Particular results include methods for coordinating the motion of vehicles in traffic in order to avoid inefficient stop-and-go congestions; using uniform global forces for controlling particle swarms; online triangulation and structured exploration; cohesive control for swarms of robots with only local communication; coordinated motion planning for efficiently reconfiguring an arrangement of robots; and constructing and reconfiguring large-scale structures by finite automata. All presented work is based on collaborations with a variety of authors, who are named in the respective sections of this overview.

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“…Moreover, even complex computations become possible: If we allow additional particles of double size (i.e., two adjacent fields), full computational complexity is achieved, see Shad et al [16]. Further related work includes gathering a particle swarm at a single position [14] and using swarms of very simple robots (such as Kilobots) for moving objects [6]. For the case in which human controllers have to move objects by such a swarm, Becker et al [3] study different control options.…”

Section: Related Workmentioning

confidence: 99%

Tilt Assembly: Algorithms for Micro-factories That Build Objects with Uniform External Forces

et al. 2018

Self Cite

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We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield micro-factories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles can bond when being forced together with another appropriate particle.Due to the physical and geometric constraints, not all shapes can be built in this manner; this gives rise to the Tilt Assembly Problem (TAP) of deciding constructibility. For simply-connected polyominoes P in 2D consisting of N unit-squares ("tiles"), we prove that TAP can be decided in O(N log N ) time. For the optimization variant MaxTAP (in which the objective is to construct a subshape of maximum possible size), we show polyAPX-hardness: unless P=NP, MaxTAP cannot be approximated within a factor of Ω(N 1 3 ); for tree-shaped structures, we give an O(N 1 2 )-approximation algorithm. For the efficiency of the assembly process itself, we show that any constructible shape allows pipelined assembly, which produces copies of P in O(1) amortized time, i.e., N copies of P in O(N ) time steps. These considerations can be extended to three-dimensional objects: For the class of polycubes P we prove that it is NP-hard to decide whether it is possible to construct a path between two points of P ; it is also NP-hard to decide constructibility of a polycube P . Moreover, it is expAPX-hard to maximize a path from a given start point.

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Collecting a swarm in a grid environment using shared, global inputs

Cited by 14 publications

References 17 publications

Particle-Based Assembly Using Precise Global Control

Particle-Based Assembly Using Precise Global Control

Coordinating Swarms of Objects at Extreme Dimensions

Tilt Assembly: Algorithms for Micro-factories That Build Objects with Uniform External Forces

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