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Kaustav Bose

Publications and source records attributed to Kaustav Bose.

12 recordsLinked to original sources
arXiv2022

Mutual Visibility by Fat Robots with Slim Omnidirectional Camera

In the existing literature of the Mutual Visibility problem for autonomous robot swarms, the adopted visibility models have some idealistic assumptions that are not consistent with practical sensing device implementations. This paper investigates the problem in the more realistic visibility model called opaque fat robots with slim omnidirectional camera. The robots are modeled as unit disks, each having an omnidirectional camera represented as a disk of smaller size. We assume that the robots have compasses that allow agreement in the direction and orientation of both axes of their local coordinate systems. The robots are equipped with visible lights which serve as a medium of communication and also as a form of memory. We present a distributed algorithm for the Mutual Visibility problem which is provably correct in the semi-synchronous setting. Our algorithm also provides a solution for Leader Election which we use as a subroutine in our main algorithm. Although Leader Election is trivial with two axis agreement in the full visibility model, it is challenging in our case and is of independent interest.

cs.RO↗
arXiv2021

Exploring a Dynamic Ring without Landmark

Consider a group of autonomous mobile computational entities, called agents, arbitrarily placed at some nodes of a dynamic but always connected ring. The agents neither have any knowledge about the size of the ring nor have a common notion of orientation. We consider the \textsc{Exploration} problem where the agents have to collaboratively to explore the graph and terminate, with the requirement that each node has to be visited by at least one agent. It has been shown by Di Luna et al. [Distrib. Comput. 2020] that the problem is solvable by two anonymous agents if there is a single observably different node in the ring called landmark node. The problem is unsolvable by any number of anonymous agents in absence of a landmark node. We consider the problem with non-anonymous agents (agents with distinct identifiers) in a ring with no landmark node. The assumption of agents with distinct identifiers is strictly weaker than having a landmark node as the problem is unsolvable by two agents with distinct identifiers in absence of a landmark node. This setting has been recently studied by Mandal et al. [ALGOSENSORS 2020]. There it is shown that the problem is solvable in this setting by three agents assuming that they have edge crossing detection capability. Edge crossing detection capability is a strong assumption which enables two agents moving in opposite directions through an edge in the same round to detect each other and also exchange information. In this paper we give an algorithm that solves the problem with three agents without the edge crossing detection capability.

cs.DC↗
arXiv2021

Pattern Formation by Robots with Inaccurate Movements

\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 $F$. We call this the \textsc{Approximate Arbitrary Pattern Formation} problem. We show that with no agreement in coordinate system, the problem is unsolvable, even by fully synchronous robots, if the initial configuration 1) has rotational symmetry and there is no robot at the center of rotation or 2) has reflectional symmetry and there is no robot on the reflection axis. From all other initial configurations, we solve the problem by 1) oblivious, silent and semi-synchronous robots and 2) oblivious, asynchronous robots that can communicate using externally visible lights.

cs.DC↗
arXiv2020

Memory Optimal Dispersion by Anonymous Mobile Robots

Consider a team of $k \leq n$ autonomous mobile robots initially placed at a node of an arbitrary graph $G$ with $n$ nodes. The dispersion problem asks for a distributed algorithm that allows the robots to reach a configuration in which each robot is at a distinct node of the graph. If the robots are anonymous, i.e., they do not have any unique identifiers, then the problem is not solvable by any deterministic algorithm. However, the problem can be solved even by anonymous robots if each robot is given access to a fair coin which they can use to generate random bits. In this setting, it is known that the robots require $Ω(\logΔ)$ bits of memory to achieve dispersion, where $Δ$ is the maximum degree of $G$. On the other hand, the best known memory upper bound is $min \{Δ, max\{\logΔ, \log{D}\}\}$ ($D$ = diameter of $G$), which can be $ω(\logΔ)$, depending on the values of $Δ$ and $D$. In this paper, we close this gap by presenting an optimal algorithm requiring $O(\logΔ)$ bits of memory.

cs.DC↗
arXiv2020

Arbitrary Pattern Formation by Asynchronous Opaque Robots with Lights

The Arbitrary Pattern Formation problem asks for a distributed algorithm that moves a set of autonomous mobile robots to form any arbitrary pattern given as input. The robots are assumed to be autonomous, anonymous and identical. They operate in Look-Compute-Move cycles under an asynchronous scheduler. The robots do not have access to any global coordinate system. The movement of the robots is assumed to be rigid, which means that each robot is able to reach its desired destination without interruption. The existing literature that investigates this problem, considers robots with unobstructed visibility. This work considers the problem in the more realistic obstructed visibility model, where the view of a robot can be obstructed by the presence of other robots. The robots are assumed to be punctiform and equipped with visible lights that can assume a constant number of predefined colors. We have studied the problem in two settings based on the level of consistency among the local coordinate systems of the robots: two axis agreement (they agree on the direction and orientation of both coordinate axes) and one axis agreement (they agree on the direction and orientation of only one coordinate axis). In both settings, we have provided a full characterization of initial configurations from where any arbitrary pattern can be formed.

cs.DC↗
arXiv2020

Distributed Localization of Wireless Sensor Network Using Communication Wheel

We study the network localization problem, i.e., the problem of determining node positions of a wireless sensor network modeled as a unit disk graph. In an arbitrarily deployed network, positions of all nodes of the network may not be uniquely determined. It is known that even if the network corresponds to a unique solution, no polynomial-time algorithm can solve this problem in the worst case, unless RP = NP. So we are interested in algorithms that efficiently localize the network partially. A widely used technique that can efficiently localize a uniquely localizable portion of the network is trilateration: starting from three anchors (nodes with known positions), nodes having at least three localized neighbors are sequentially localized. However, the performance of trilateration can substantially differ for different choices of the initial three anchors. In this paper, we propose a distributed localization scheme with a theoretical characterization of nodes that are guaranteed to be localized. In particular, our proposed distributed algorithm starts localization from a strongly interior node and provided that the subgraph induced by the strongly interior nodes is connected, it localizes all nodes of the network except some boundary nodes and isolated weakly interior nodes.

cs.DC↗
arXiv2019

Arbitrary Pattern Formation by Opaque Fat Robots with Lights

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 given as input. The majority of the existing literature investigates this problem for robots with unobstructed visibility. In a few recent works, the problem has been studied in the obstructed visibility model, where the view of a robot can be obstructed by the presence of other robots. However, in these works, the robots have been modelled as dimensionless points in the plane. In this paper, we have considered the problem in the more realistic setting where the robots have a physical extent. In particular, the robots are modelled as opaque disks. Furthermore, the robots operate under a fully asynchronous scheduler. They do not have access to any global coordinate system, but agree on the direction and orientation of one coordinate axis. Each robot is equipped with an externally visible light which can assume a constant number of predefined colors. In this setting, we have given a complete characterization of initial configurations from where any arbitrary pattern can be formed by a deterministic distributed algorithm.

cs.DC↗
arXiv2019

Positional Encoding by Robots with Non-Rigid Movements

Consider a set of autonomous computational entities, called \emph{robots}, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant $δ> 0$, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than $δ$ amount. This model is known in literature as \emph{non-rigid} movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having $O(1)$ bits of persistent memory and ability to make circular moves.

cs.DC↗
arXiv2018

Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots

The Arbitrary Pattern Formation problem asks to design a distributed algorithm that allows a set of autonomous mobile robots to form any specific but arbitrary geometric pattern given as input. The problem has been extensively studied in literature in continuous domains. This paper investigates a discrete version of the problem where the robots are operating on a two dimensional infinite grid. The robots are assumed to be autonomous, identical, anonymous and oblivious. They operate in Look-Compute-Move cycles under a fully asynchronous scheduler. The robots do not agree on any common global coordinate system or chirality. We have shown that a set of robots can form any arbitrary pattern, if their starting configuration is asymmetric.

cs.DC↗
arXiv2017

Crash tolerant gathering on grid by asynchronous oblivious robots

Consider a system of autonomous mobile robots initially randomly deployed on the nodes of an anonymous finite grid. A gathering algorithm is a sequence of moves to be executed independently by each robot so that all robots meet at a single node after finite time. The robots operate in Look-Compute-Move cycles. In each cycle, a robot takes a snapshot of the current configuration of the grid in terms of occupied nodes (\emph{Look}), then based on the perceived configuration, decides whether to stay put or to move to an adjacent node (\emph{Compute}), and in the later case makes an instantaneous move accordingly (\emph{Move}). The robots have \emph{weak multiplicity detection} capability, which enables them to detect if a node is empty or occupied by a single robot or by multiple robots. The robots are \emph{asynchronous}, \emph{oblivious}, \emph{anonymous}, can not communicate with each other and execute the same distributed algorithm. In a faulty system, however, any robot can \emph{crash}, which means that it becomes completely inactive and does not take part in the process any further. In that case a fault-tolerant gathering algorithm is an algorithm that gathers all the non-faulty robots at a single node. This paper considers a faulty system that can have at most one crash fault. With these assumptions deterministic fault-tolerant gathering algorithms are presented that gather all initial configurations that are gatherable in a non-faulty system, except for one specific configuration called the \emph{2S2 configuration}.

cs.DC↗
arXiv2016

Euclidean 1-center of a set of static and mobile points

In this paper, we consider the problem of computing the algebraic parametric equation of the Euclidean 1-center function in $\mathbb{R}^d$, $d \geq 2$, for a system of $n$ static points and $m$ mobile points having motion defined by rational parametric functions. We have shown that the corresponding Euclidean 1-center function is a piecewise differentiable function and have derived its exact parametric algebraic equation. If the positions of the static points and the rational parametric equations of the motion of the mobile points are given, we have proposed an algorithm that computes the parametric equation of the Euclidean 1-center function.

cs.CG↗