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In the arbitrary pattern formation problem, $n$ autonomous, mobile robots must form an arbitrary pattern $P \subseteq \mathbb{R}^2$. The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to…

Robotics · Computer Science 2024-04-05 Christopher Hahn , Jonas Harbig , Peter Kling

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

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA)…

Emerging Technologies · Computer Science 2019-06-06 John Calvin Alumbaugh , Joshua J. Daymude , Erik D. Demaine , Matthew J. Patitz , Andrea W. Richa

Arbitrary Pattern Formation is a widely studied problem in autonomous robot systems. The problem asks to design a distributed algorithm that moves a team of autonomous, anonymous and identical mobile robots to form any arbitrary pattern…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-10-08 Kaustav Bose , Ranendu Adhikary , Manash Kumar Kundu , Buddhadeb Sau

Shape formation has been recently studied in distributed systems of programmable particles. In this paper we consider the shape recovery problem of restoring the shape when $f$ of the $n$ particles have crashed. We focus on the basic line…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-07-18 Giuseppe Di Luna , Paola Flocchini , Giuseppe Prencipe , Nicola Santoro , Giovanni Viglietta

Object rearrangement is a widely-applicable and challenging task for robots. Geometric constraints must be carefully examined to avoid collisions and combinatorial issues arise as the number of objects increases. This work studies the…

Robotics · Computer Science 2022-03-21 Rui Wang , Kai Gao , Daniel Nakhimovich , Jingjin Yu , Kostas E. Bekris

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…

The idea behind universal coating is to have a thin layer of a specific substance covering an object of any shape so that one can measure a certain condition (like temperature or cracks) at any spot on the surface of the object without…

Emerging Technologies · Computer Science 2016-01-07 Zahra Derakhshandeh , Robert Gmyr , Andrea W. Richa , Christian Scheideler , Thim Strothmann

We are considering the geometric amoebot model where a set of $n$ amoebots is placed on the triangular grid. An amoebot is able to send information to its neighbors, and to move via expansions and contractions. Since amoebots and…

Robotics · Computer Science 2025-03-11 Andreas Padalkin , Manish Kumar , Christian Scheideler

Arbitrary Pattern Formation (APF) is a fundamental coordination problem in swarm robotics. It requires a set of autonomous robots (mobile computing units) to form an arbitrary pattern (given as input) starting from any initial pattern. This…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-28 Avisek Sharma , Satakshi Ghosh , Pritam Goswami , Buddhadeb Sau

Given a set of $n\geq 1$ autonomous, anonymous, indistinguishable, silent, and possibly disoriented mobile unit disk (i.e., fat) robots operating following Look-Compute-Move cycles in the Euclidean plane, we consider the Pattern Formation…

Computational Geometry · Computer Science 2025-03-20 Rusul J. Alsaedi , Joachim Gudmundsson , André van Renssen

We present local distributed, stochastic algorithms for \emph{alignment} in self-organizing particle systems (SOPS) on two-dimensional lattices, where particles occupy unique sites on the lattice, and particles can make spatial moves to…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-09-15 Hridesh Kedia , Shunhao Oh , Dana Randall

Shape-programmed sheets morph from one surface into another upon activation by stimuli such as illumination, and have attracted much interest for their potential engineering applications, especially in soft robotics. Complex shape changes…

Soft Condensed Matter · Physics 2024-10-17 Daniel Duffy , Itay Griniasty , John Biggins , Cyrus Mostajeran

This paper presents a method for constrained motion planning from vision, which enables a robot to move its end-effector over an observed surface, given start and destination points. The robot has no prior knowledge of the surface shape,…

Robotics · Computer Science 2020-06-23 T. Pardi , V. Ortenzi , C. Fairbairn , T. Pipe , A. M. Ghalamzan E. , R. Stolkin

Planning trajectories for nonholonomic systems is difficult and computationally expensive. When facing unexpected events, it may therefore be preferable to deform in some way the initially planned trajectory rather than to re-plan entirely…

Robotics · Computer Science 2011-05-31 Quang-Cuong Pham

We describe a phase space generator which is flat for massless particles, and approximately flat for massive particles of masses much smaller than the typical mometum scales involved in the process. The same goal is achieved by the RAMBO…

High Energy Physics - Phenomenology · Physics 2013-08-14 Simon Plätzer

We study computationally-hard fundamental motion planning problems where the goal is to translate $k$ axis-aligned rectangular robots from their initial positions to their final positions without collision, and with the minimum number of…

Computational Geometry · Computer Science 2024-03-05 Iyad Kanj , Salman Parsa

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-06-03 Fabien Dufoulon , Shay Kutten , William K. Moses

The local arrangement of atoms is one of the most important predictors of mechanical and functional properties of materials. However, algorithms for identifying the geometrical arrangements of atoms in complex materials systems are lacking.…

Materials Science · Physics 2019-04-15 Arash Dehghan Banadaki , Jason J. Maldonis , Paul M. Voyles , Srikanth Patala

The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce…

Robotics · Computer Science 2018-09-17 Andreas Orthey , Olivier Roussel , Olivier Stasse , Michel Taïx