Search

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 four traditional models $\{ \mathcal{OBLOT},\ \mathcal{FSTA},\ \mathcal{FCOM},\ \mathcal{LUMI} \} $ have been extensively investigated both when the robots had unlimited amount of energy and when the robots were energy-constrained. In both the above cases, the robots had full visibility. In this paper, this assumption is removed, i.e., we assume that the robots can view up to a constant radius $V_r$ from their position (the $V_r$ is same for all the robots) and, investigates what impact it has on its computational capabilities. We first study whether the restriction imposed on the visibility has any impact at all, i.e., under a given model and scheduler does there exist any problem which cannot be solved by a robot having limited visibility but can be solved by a robot with full visibility. We find that the answer to the question in general turns out to be positive. Finally, we try to get an idea that under a given model, which of the two factors, $Visibility$ or $Synchronicity$ is more powerful and conclude that a definite conclusion cannot be drawn., Comment: arXiv admin note: text overlap with arXiv:2203.06546 by other authors

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.

In swarm robotics, a set of robots has to perform a given task with specified internal capabilities (model) and under a given adversarial scheduler. Relation between a model $M_1$ under scheduler $S_1$, and that of a model $M_2$ under scheduler $S_2$ can be of four different types: not less powerful, more powerful, equivalent and orthogonal. In literature there are four main models of robots with lights: $\mathcal{LUMI}$, where robots have the power of observing the lights of all the robots, $\mathcal{FSTA}$ , where each robot can see only its own light, $\mathcal{FCOM}$, where each robot can observe the light of all other robots except its own and $\mathcal{OBLOT}$, where the robots do not have any light. In this paper, we investigate the computational power of $\mathcal{FSTA}$ and $\mathcal{FCOM}$ model under asynchronous scheduler by comparing it with other model and scheduler combinations. Our main focus is to understand and compare the power of persistent memory and explicit communication in robots under asynchronous scheduler.

\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.

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 $\Omega(\log{\Delta})$ bits of memory to achieve dispersion, where $\Delta$ is the maximum degree of $G$. On the other hand, the best known memory upper bound is $min \{\Delta, max\{\log{\Delta}, \log{D}\}\}$ ($D$ = diameter of $G$), which can be $\omega(\log{\Delta})$, depending on the values of $\Delta$ and $D$. In this paper, we close this gap by presenting an optimal algorithm requiring $O(\log{\Delta})$ bits of memory., Comment: This is the full version of the paper, with the same title and authors, that was accepted in the 7th Annual International Conference on Algorithms and Discrete Applied Mathematics (CALDAM 2021), February 11-13, 2021, Ropar, India