Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform, External Forces

Becker, Aaron T.; Fekete, Sándor P.; Huang, Li; Keldenich, Phillip; Kleist, Linda; Krupke, Dominik; Rieck, Christian; Schmidt, Arne

doi:10.1109/icra40945.2020.9196551

Cited by 9 publications

(7 citation statements)

References 15 publications

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“…Mahadev et al [35] show how to gather n particles within an obstacle environment in O(n 3 ) actuation steps. Becker et al [10] improve the runtime to only depend on the geometric complexity of the workspace, rather than on the number of particles.…”

Section: Tilt Problemsmentioning

confidence: 99%

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Particle-Based Assembly Using Precise Global Control

et al. 2022

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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 induced by a global signal. In this paper we consider the single step model, i.e., a model in which each particle moves one unit step into the given direction. We restrict the assembly process such that at each single time step actually one particle is added to and moved within the workspace. We prove that deciding constructibility is NP-complete 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 or not a tree-shape in 2D or 3D is constructible. Scaling a shape yields constructibility; in particular we show that the 2-scaled copy of every non-degenerate polyomino is constructible. In the three-dimensional setting we show that the 3-scaled copy of every non-degenerate polycube is constructible.

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Section: Tilt Problemsmentioning

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 [3], gathering all particles [10,35], or assembling patterned rectangles [15] are well studied problems.…”

Section: Introductionmentioning

confidence: 99%

Particle-Based Assembly Using Precise Global Control

et al. 2022

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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%

“…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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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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“…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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Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform, External Forces

Cited by 9 publications

References 15 publications

Particle-Based Assembly Using Precise Global Control

Particle-Based Assembly Using Precise Global Control

Particle-Based Assembly Using Precise Global Control

Coordinating Swarms of Objects at Extreme Dimensions

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