Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE（法国国家信息与自动化研究所）；VERIMAG UMR 5104（VERIMAG实验室（法国国家科研中心联合研究单位5104））；Université Joseph Fourier（约瑟夫·傅里叶大学）；INRIA（法国国家信息与自动化研究所）；LIP UMR 5668（LIP实验室（法国国家科研中心联合研究单位5668））；Université de Lyon（里昂大学）；ENS Lyon（里昂高等师范学院）；Université Pierre et Marie Curie - Paris 6（巴黎第六大学（皮埃尔和玛丽·居里大学））；LIP6（LIP6实验室）
We consider a team of $k$ identical, oblivious, asynchronous mobile robots that are able to sense (\emph{i.e.}, view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by \emph{deterministic} robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the \emph{exploration} problem of anonymous unoriented rings of any size. It is known that $Θ(\log n)$ robots are necessary and sufficient to solve the problem with $k$ deterministic robots, provided that $k$ and $n$ are coprime. By contrast, we show that \emph{four} identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.
Institut für Algebra, TU Dresden（德累斯顿工业大学代数研究所）；University of Ottawa（渥太华大学）
A fundamental problem in Distributed Computing is the Pattern Formation problem, where some independent mobile entities, called robots, have to rearrange themselves in such a way as to form a given figure from every possible (non-degenerate) initial configuration. In the present paper, we consider robots that operate in the Euclidean plane and are dimensionless, anonymous, oblivious, silent, asynchronous, disoriented, non-chiral, and non-rigid. For this very elementary type of robots, the feasibility of the Pattern Formation problem has been settled, either in the positive or in the negative, …
Nagoya Institute of Technology（名古屋工业大学）；Japan Advanced Institute of Science and Technology（日本北陆先端科学技术大学院大学）；Kyushu University（九州大学）
Anonymous mobile robots are often classified into synchronous, semi-synchronous and asynchronous robots when discussing the pattern formation problem. For semi-synchronous robots, all patterns formable with memory are also formable without memory, with the single exception of forming a point (i.e., the gathering) by two robots. However, the gathering problem for two semi-synchronous robots without memory is trivially solvable when their local coordinate systems are consistent, and the impossibility proof essentially uses the inconsistencies in their coordinate systems. Motivated by this, this …
IRIF - Univ Paris Diderot（巴黎狄德罗大学 IRIF）；Sorbonne Universités, UPMC Univ Paris 06（索邦大学 皮埃尔和玛丽·居里大学）
We study verification problems for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. In particular, we focus in this paper on the model proposed by Suzuki and Yamashita of anonymous robots evolving in a discrete space with a finite number of locations (here, a ring). A large number of algorithms have been proposed working for rings whose size is not a priori fixed and can be hence considered as a parameter. Handmade correctness proofs of these algorithms have been shown to be error-prone, and recent attention had been given to the application of fo…
Jadavpur University（贾达普大学）；University of Washington（华盛顿大学）；Indian Statistical Institute（印度统计研究所）
This paper presents a deterministic algorithm for forming a given asymmetric pattern in finite time by a set of autonomous, homogeneous, oblivious mobile robots under the CORDA model. The robots are represented as points on the 2D plane. There is no explicit communication between the robots. The robots coordinate among themselves by observing the positions of the other robots on the plane. Initially all the robots are assumed to be stationary. The robots have local coordinate systems defined by Sense of Direction (SoD), orientation or chirality and scale. Initially the robots are in asymmetric…
We propose a new probabilistic pattern formation algorithm for oblivious mobile robots that operates inthe ASYNC model. Unlike previous work, our algorithm makes no assumptions about the local coordinatesystems of robots (the robots do not share a common "North" nor a common "Right"), yet it preserves theability from any initial configuration that contains at least 5 robots to form any general pattern (and not justpatterns that satisfy symmetricity predicates). Our proposal also gets rid of the previous assumption (in thesame model) that robots do not pause while moving (so, our robots really …
We consider the problem of exploring an anonymous unoriented ring of size $n$ by $k$ identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that $k$ must not divide $n$ for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size $n$ is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are suffici…
Aix-Marseille University（艾克斯-马赛大学）；University of Ottawa（渥太华大学）；Carleton University（卡尔顿大学）；JAIST（北陆先端科学技术大学院大学）；Kyushu University（九州大学）
The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of $P$, we minimize the number of searchers $k$ for which the Meeting problem is solvable. Specifically, if $P$ has a rotational symmetry of order $σ$ (where $σ=1$ corresponds to no rotational…
\textsc{Arbitrary Pattern Formation} is a fundamental problem in autonomous mobile 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 $F$ given as input. In this paper, we study the problem for robots whose movements can be inaccurate. Our movement model assumes errors in both direction and extent of the intended movement. Forming the given pattern exactly is not possible in this setting. So we require that the robots must form a configuration which is close to the given pattern …
Aix-Marseille University（艾克斯-马赛大学）；University of Ottawa（渥太华大学）；Carleton University（卡尔顿大学）；JAIST（北陆先端科学技术大学院大学）
In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward its destination. Each robot is punctiform and memoryless, it operates in $\mathbb{R}^m$, it has a local reference system independent of the other robots' ones, and is activated asynchronously by an adversarial scheduler. Moreover, robots are non-rigid, in that they may be stopped by the scheduler at each move before reaching their destination (but are guarant…
Nagoya Institute of Technology（名古屋工业大学）；Université Pierre et Marie Curie - Paris 6（巴黎第六大学（皮埃尔和玛丽·居里大学））；CNRS（法国国家科学研究中心）
This paper investigates the task solvability of mobile robot systems subject to Byzantine faults. We first consider the gathering problem, which requires all robots to meet in finite time at a non-predefined location. It is known that the solvability of Byzantine gathering strongly depends on a number of system attributes, such as synchrony, the number of Byzantine robots, scheduling strategy, obliviousness, orientation of local coordinate systems and so on. However, the complete characterization of the attributes making Byzantine gathering solvable still remains open. In this paper, we show s…
Hong Kong University of Science and Technology（香港科技大学）
Although the use of multiple Unmanned Aerial Vehicles (UAVs) has great potential for fast autonomous exploration, it has received far too little attention. In this paper, we present RACER, a RApid Collaborative ExploRation approach using a fleet of decentralized UAVs. To effectively dispatch the UAVs, a pairwise interaction based on an online hgrid space decomposition is used. It ensures that all UAVs simultaneously explore distinct regions, using only asynchronous and limited communication. Further, we optimize the coverage paths of unknown space and balance the workloads partitioned to each …
Min-Sum Uniform Coverage Problem by Autonomous Mobile Robots
Department of Mathematics（数学系）；Birla Institute of Technology, Mesra（比拉理工学院，梅斯拉）；Advanced Computing and Microelectronics Unit, Indian Statistical Institute（印度统计研究所高级计算与微电子单位）
