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Neutral atom arrays have emerged as a promising platform for both analog and digital quantum processing. Recently, devices capable of reconfiguring arrays during quantum processes have enabled new applications for these systems. Atom…

In the modular robot reconfiguration problem, we are given $n$ cube-shaped modules (or robots) as well as two configurations, i.e., placements of the $n$ modules so that their union is face-connected. The goal is to find a sequence of moves…

Computational Geometry · Computer Science 2024-03-15 Zachary Abel , Hugo A. Akitaya , Scott Duke Kominers , Matias Korman , Frederick Stock

We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra "helper" modules ("musketeers")…

We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of…

Computational Geometry · Computer Science 2025-10-09 Hugo A. Akitaya , Sándor P. Fekete , Peter Kramer , Saba Molaei , Christian Rieck , Frederick Stock , Tobias Wallner

A metamorphic robotic system is an aggregate of homogeneous robot units which can individually and selectively locomote in such a way as to change the global shape of the system. We introduce a mathematical framework for defining and…

Robotics · Computer Science 2007-05-23 A. Abrams , R. Ghrist

A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that…

Computational Geometry · Computer Science 2025-07-08 Hugo Akitaya , Matias Korman , Frederick Stock

We study centralized reconfiguration problems for geometric amoebot structures. A set of $n$ amoebots occupy nodes on the triangular grid and can reconfigure via expansion and contraction operations. We focus on the joint movement…

Data Structures and Algorithms · Computer Science 2026-03-12 Manish Kumar , Othon Michail , Andreas Padalkin , Christian Scheideler

We implement and evaluate different methods for the reconfiguration of a connected arrangement of tiles into a desired target shape, using a single active robot that can move along the tile structure. This robot can pick up, carry, or drop…

Consider a set of $n$ simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-30 Paola Flocchini , Giuseppe Prencipe , Nicola Santoro , Giovanni Viglietta

This study presents a systematic enumeration of spherical ($SO(3)$) type parallel robots' variants using an analytical velocity-level approach. These robots are known for their ability to perform arbitrary rotations around a fixed point,…

Robotics · Computer Science 2024-03-07 Hassen Nigatu , Li Jihao , Gaokun Shi , Guodong Lu , Huixu Dong

We consider a distributed system of n identical mobile robots operating in the two dimensional Euclidian plane. As in the previous studies, we consider the robots to be anonymous, oblivious, dis-oriented, and without any communication…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-11-14 Shantanu Das , Giuseppe A. Di Luna , Paola Flocchini , Nicola Santoro , Giovanni Viglietta , Masafumi Yamashita

We consider a set of k autonomous robots that are endowed with visibility sensors (but that are otherwise unable to communicate) and motion actuators. Those robots must collaborate to reach a sin- gle vertex that is unknown beforehand, and…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-05-02 Sayaka Kamei , Anissa Lamani , Fukuhito Ooshita , Sébastien Tixeuil

A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity…

Robotics · Computer Science 2017-08-08 Damien Chablat , Xianwen Kong , Chengwei Zhang

We give both efficient algorithms and hardness results for reconfiguring between two connected configurations of modules in the hexagonal grid. The reconfiguration moves that we consider are "pivots", where a hexagonal module rotates around…

The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. The best algorithm currently known for the reconfiguration…

Computational Geometry · Computer Science 2023-12-27 Irina Kostitsyna , Tim Ophelders , Irene Parada , Tom Peters , Willem Sonke , Bettina Speckmann

We study an elementary problem of the topological robotics: collective motion of a set of $n$ distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in…

Algebraic Topology · Mathematics 2007-05-23 Michael Farber , Sergey Yuzvinsky

We consider a swarm of $n$ robots in \mathbb{R}^d. The robots are oblivious, disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task gathering…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-09-12 Jannik Castenow , Jonas Harbig , Daniel Jung , Peter Kling , Till Knollmann , Friedhelm Meyer auf der Heide

Legged machines are becoming increasingly agile and adaptive but they have so far lacked the morphological diversity of legged animals, which have been rearranged and reshaped to fill millions of niches. Unlike their biological…

Robotics · Computer Science 2026-03-02 Chen Yu , David Matthews , Jingxian Wang , Jing Gu , Douglas Blackiston , Michael Rubenstein , Sam Kriegman

We describe algorithmic results for two crucial aspects of allocating resources on computational hardware devices with partial reconfigurability. By using methods from the field of computational geometry, we derive a method that allows…

Data Structures and Algorithms · Computer Science 2016-11-15 Ali Ahmadinia , Christophe Bobda , Sandor Fekete , Juergen Teich , Jan van der Veen

When considering motion planning for a swarm of $n$ labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel, collision-free robot motions. The objective is to reach the…

Computational Geometry · Computer Science 2024-07-25 Sándor P. Fekete , Peter Kramer , Christian Rieck , Christian Scheffer , Arne Schmidt
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