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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

In this paper we study the Near-Gathering problem for a finite set of dimensionless, deterministic, asynchronous, anonymous, oblivious and autonomous mobile robots with limited visibility moving in the Euclidean plane in Look-Compute-Move…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-28 Linda Pagli , Giuseppe Prencipe , Giovanni Viglietta

Shape formation is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter. Namely, it has…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-12 Giuseppe A. Di Luna , Paola Flocchini , Nicola Santoro , Giovanni Viglietta , Yukiko Yamauchi

We study a generalized motion planning problem involving multiple autonomous robots navigating in a $d$-dimensional Euclidean space in the presence of a set of obstacles whose positions are unknown a priori. Each robot is required to visit…

Algebraic Topology · Mathematics 2025-10-13 Gopal Chandra Dutta , Amit Kumar Paul , Subhankar Sau

This paper presents decentralized algorithms for formation control of multiple robots in three dimensions. Specifically, we leverage the mathematical properties of cyclic pursuit along with results from contraction and partial contraction…

Systems and Control · Computer Science 2016-11-17 Sumeet Singh , Edward Schmerling , Marco Pavone

The problem of gathering multiple mobile robots to a single location, is one of the fundamental problems in distributed coordination between autonomous robots. The problem has been studied and solved even for robots that are anonymous,…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-07-03 Zohir Bouzid , Shantanu Das , Sébastien Tixeuil

Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…

Pattern Formation and Solitons · Physics 2026-02-05 Vinod Ramakrishnan , Michael J. Frazier

In this work, we explore emergent behaviors by swarms of anonymous, homogeneous, non-communicating, reactive robots that do not know their global position and have limited relative sensing. We introduce a novel method that enables such…

Robotics · Computer Science 2018-04-19 Mario Coppola , Jian Guo , Eberhard K. A. Gill , Guido C. H. E. de Croon

We consider a swarm of mobile robots evolving in a bidimensional Euclidean space. We study a variant of the crash-tolerant gathering problem: if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-02-08 Quentin Bramas , Anissa Lamani , Sébastien Tixeuil

A swarm of anonymous oblivious mobile robots, operating in deterministic Look-Compute-Move cycles, is confined within a circular track. All robots agree on the clockwise direction (chirality), they are activated by an adversarial…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-11-19 Giuseppe A. Di Luna , Ryuhei Uehara , Giovanni Viglietta , Yukiko Yamauchi

This paper develops an algorithm that guides a multi-robot system in an unknown environment in search of fixed targets. The area to be scanned contains an unknown number of convex obstacles of unknown size and shape. The algorithm covers…

Robotics · Computer Science 2012-02-13 Jonathan Rogge , Dirk Aeyels

We consider the configuration formation problem in modular robotic systems where a set of singleton modules that are spatially distributed in an environment are required to assume appropriate positions so that they can configure into a new,…

Robotics · Computer Science 2022-10-04 Ayan Dutta , Prithviraj Dasgupta

We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other, but are endowed with visibility sensors that allow them to see the positions of the other robots. Most of the…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-01-15 Sayaka Kamei , Anissa Lamani , Fukuhito Ooshita , Sebastien Tixeuil , Koichi Wada

A mobile robot system consists of anonymous mobile robots, each of which autonomously performs sensing, computation, and movement according to a common algorithm, so that the robots collectively achieve a given task. There are two main…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-04 Paola Flocchini , Nicola Santoro , Masafumi Yamashita , Yukiko Yamauchi

This paper presents a role-adaptive Leader-Follower-based formation planning and control framework for teams of quadruped robots operating in cluttered environments. Unlike conventional methods with fixed leaders or rigid formation roles,…

Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…

Statistical Mechanics · Physics 2021-06-03 Malte Schröder , Marc Timme

Consider a group of autonomous mobile computational entities called robots. The robots move in the Euclidean plane and operate according to synchronous $Look$-$Compute$-$Move$ cycles. The computational capabilities of the robots under the…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-10-04 Archak Das , Satakshi Ghosh , Avisek Sharma , Pritam Goswami , Buddhadeb Sau

In this paper we propose and prove correct a new self-stabilizing velocity agreement (flocking) algorithm for oblivious and asynchronous robot networks. Our algorithm allows a flock of uniform robots to follow a flock head emergent during…

Networking and Internet Architecture · Computer Science 2011-05-23 Davide Canepa , Xavier Défago , Taisuke Izumi , Maria Potop-Butucaru

In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior…

Systems and Control · Electrical Eng. & Systems 2020-06-09 Nelson P. K. Chan , Bayu Jayawardhana , Hector Garcia de Marina

In the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center…

Optimization and Control · Mathematics 2010-01-26 Florian Dorfler , Bruce Francis