Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers

Akitaya, Hugo A.; Arkin, Esther M.; Damian, Mirela; Demaine, Erik D.; Dujmović, Vida; Flatland, Robin; Korman, Matias; Palop, Belén; Parada, Irene; Renssen, André van; Sacristán, Vera

doi:10.1007/s00453-020-00784-6

Cited by 18 publications

(7 citation statements)

References 18 publications

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“…However, the requirement that 3D configurations contain no non-convex holes requires global information to evaluate, which is undesirable. Follow-on work in [25] showed additionally that in 2D, if a configuration is not admissible, then as long as there are at least 5 free modules, reconfiguration is always possible.…”

Section: A Reconfiguration For Pivoting Cubesmentioning

confidence: 99%

Reconfiguring Non-Convex Holes in Pivoting Modular Cube Robots

Feshbach

Sung

2021

IEEE Robot. Autom. Lett.

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We present an algorithm for self-reconfiguration of admissible 3D configurations of pivoting modular cube robots with holes of arbitrary shape and number. Cube modules move across the surface of configurations by pivoting about shared edges, enabling configurations to reshape themselves. Previous work provides a reconfiguration algorithm for admissible 3D configurations containing no non-convex holes; we improve upon this by handling arbitrary admissible 3D configurations. The key insight specifies a point in the deconstruction of layers enclosing non-convex holes at which we can pause and move inner modules out of the hole. We prove this happens early enough to maintain connectivity, but late enough to open enough room in the enclosing layer for modules to escape the hole. Our algorithm gives reconfiguration plans with O n 2 moves for n modules.

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Section: A Reconfiguration For Pivoting Cubesmentioning

confidence: 99%

Reconfiguring Non-Convex Holes in Pivoting Modular Cube Robots

Feshbach

Sung

2021

IEEE Robot. Autom. Lett.

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“…Seeds allow shapes which are blocked or incapable of meaningful movement to perform otherwise impossible transformations. The use of seeds was established in a previous work [22], and more recently shown to enable universal reconfiguration in the context of connectivity preserving transformations [21], however to our knowledge there has been no attempt to investigate this problem using a seed which is a connected shape fully introduced before the transformation is initiated.…”

Section: Contributionmentioning

confidence: 99%

“…Such transformations are highly desirable due to the large numbers of programmable matter systems which rely on the preservation of connectivity. Progress in a very similar direction was made in another paper [21], which used a similar model but allowed for a greater range of movement, for example "leapfrog" and "monkey" movements. They accomplished universal transformation in O(n 2 ) movements using a "bridging" procedure which added up to 5 nodes during the procedure as necessary in a manner similar to the seed idea from the previous paper.…”

Section: Introductionmentioning

confidence: 96%

Centralised Connectivity-Preserving Transformations for Programmable Matter: A Minimal Seed Approach

Connor¹,

Michail²,

Потапов³

2021

Preprint

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We study a model of programmable matter systems consisting of n devices lying on a 2-dimensional square grid which are able to perform the minimal mechanical operation of rotating around each other. The goal is to transform an initial shape A into a target shape B. We investigate the class of shapes which can be constructed in such a scenario under the additional constraint of maintaining global connectivity at all times. We focus on the scenario of transforming nice shapes, a class of shapes consisting of a central line L where for all nodes u in S either u ∈ L or u is connected to L by a line of nodes perpendicular to L. We prove that by introducing a minimal 3-node seed it is possible for the canonical shape of a line of n nodes to be transformed into a nice shape of n − 1 nodes. We use this to show that a 4-node seed enables the transformation of nice shapes of size n into any other nice shape of size n in O(n 2 ) time. We leave as an open problem the expansion of the class of shapes which can be constructed using such a seed to include those derived from nice shapes.

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“…The assumed mechanisms in those models can significantly influence the efficiency and feasibility of shape transformations. For example, the authors of [2,17,18,19,27] consider mechanisms called sliding and rotation by which an agent can move and turn over neighbours through empty space. Under these models of individual movements, Dumitrescu and Pach [17] and Michail et al [27] present universal transformations for any pair of connected shapes (S I , S F ) of the same size to each other.…”

Section: Related Workmentioning

confidence: 99%

“…When l h sees 1 ○, it calls CollectArrows to draw one L-shaped route // Manhattan distance ∆ > i 8b. Otherwise, l h sees 2 ○ and calls CollectArrows to draw two L-shaped route…”

Section: Definition 1 (A Route) a Route Is A Rectangular Pathmentioning

confidence: 99%

Distributed Transformations of Hamiltonian Shapes based on Line Moves

Almethen¹,

Michail²,

Потапов³

2021

Preprint

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We consider a discrete system of n simple indistinguishable devices, called agents, forming a connected shape SI on a two-dimensional square grid. Agents are equipped with a linear-strength mechanism, called a line move, by which an agent can push a whole line of consecutive agents in one of the four directions in a single time-step. We study the problem of transforming an initial shape SI into a given target shape SF via a finite sequence of line moves in a distributed model, where each agent can observe the states of nearby agents in a Moore neighbourhood. Our main contribution is the first distributed connectivity-preserving transformation that exploits line moves within a total of O(n log 2 n) moves, which is asymptotically equivalent to that of the best-known centralised transformations. The algorithm solves the line formation problem that allows agents to form a final straight line SL, starting from any shape SI , whose associated graph contains a Hamiltonian path.

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Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers

Cited by 18 publications

References 18 publications

Reconfiguring Non-Convex Holes in Pivoting Modular Cube Robots

Reconfiguring Non-Convex Holes in Pivoting Modular Cube Robots

Centralised Connectivity-Preserving Transformations for Programmable Matter: A Minimal Seed Approach

Distributed Transformations of Hamiltonian Shapes based on Line Moves

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