We aim to solve the mutual visibility problem using $N$ autonomous, indistinguishable, homogeneous, oblivious and opaque point robots in the presence of mobility failure. The faulty robot cannot move when it becomes faulty, but the light remains working. Initially, from any arbitrary configuration, the problem of mutual visibility using robots aims to reach a configuration where any two robots can see each other. The challenge is to reach to such a configuration in the presence of faulty robots along with obstructed visibility under which two robots see each other only if the line segment joining them does not have any robots. Every robot operates in the conventional Look-Compute-Move cycles. Robots neither have any agreement in their coordinate system nor have the knowledge of $N$. The problem is not solvable for a specific symmetric initial configuration of the robots. We propose an algorithm that tolerates $f~ (\leq N)$ number of faulty robots and uses a constant number of colors in the FSYNC setting. To be specific, the algorithm requires $21$ colors and runs in $O(N^2)$ synchronous rounds. We present another algorithm much simpler than the prior one but can tolerate a single faulty robot. This algorithm needs only $2$ colors in the SSYNC and $5$ colors in the ASYNC setting.

We initiate the study of the Mutual Visibility problem using $N$ opaque luminous point robots that have inaccurate movements. Each robot operates in Look-Compute-Move cycles and has a persistent light attached to it to have a weak form of communication between robots using a constant number of colors. The inaccuracy for a robot $r$ is an angular deviation from its target point $T$ to a point $T'$ such that the angle $\angle TrT' <90^\circ$. The problem becomes unsolvable if this angle is $\geq 90^\circ$. From any initial configuration of the robots on the Euclidean plane, the problem aims to arrange the robots in a configuration such that any two robots are visible to each other. We assume that the robots agree on one coordinate axis. We present two collision-free algorithms, a $2$ color algorithm (which is optimal in the number of colors used) for semi-synchronous setting and a $3$ color algorithm for asynchronous setting, both of which run in $\mathcal{O}(N)$ epochs. We also study the problem in the presence of mobile faulty robots. A robot can exhibit both mobility failure and angular inaccuracies in its movement. We present a fault-tolerant algorithm that aims to bring the robots in a configuration where no three non-faulty robots are collinear, and no faulty robot lies between two non-faulty robots. This algorithm uses 10 colors and takes $\mathcal{O}(N)$ epochs under asynchronous settings.

We present the problem of finding a maximal independent set (MIS) (named as MIS Filling problem) of an arbitrary connected graph having $n$ vertices with luminous myopic mobile robots. The robots enter the graph one after another from a particular vertex called the Door and move along the edges of the graph without collision to occupy vertices such that the set of occupied vertices form a maximal independent set. In this paper, we explore two versions of the MIS filling problem, where two separate algorithms are proposed. First version of the problem considers a Single Door where our IND algorithm forms an MIS of size $m$ in $O(m^2)$ epochs under an asynchronous scheduler, where an epoch is the smallest time interval in which each participating robot gets activated at least once and performs a Look-Compute-Move cycle. The robots have three hops of visibility range, $\Delta + 8$ number of colors, and $O(\log \Delta)$ bits of persistent storage, where $\Delta$ is the maximum degree of the graph. The second version of the problem has Multiple Doors for which we present our MULTIND algorithm that forms an MIS in $O(m^2)$ epochs under a semi-synchronous scheduler using robots with five hops of visibility range, $\Delta + k + 7$ number of colors, and $O(\log (\Delta + k))$ bits of persistent storage, where $k$ is the number of Doors. We also achieve a lower bound of $\Omega(n)$ for MIS filling problem with Single Door, where $n$ is the number of vertices of the graph.

In this paper, we study uniform partitioning of a given bounded region $\Re$ with $N$ asynchronous autonomous opaque mobile robots operating under the LCM cycles in a distributed setup. The robots are oblivious except for a persistent light that determines colors from a fixed color set. The robots do not have any agreement on the coordinate axes or orientation. The Uniform Partitioning problem requires the robots to partition the region into sub-regions of equal area, each of which contains exactly one robot. Due to application-oriented motivation, we consider the region to be well-known geometric shapes such as rectangle, square and circle. We propose three algorithms corresponding to three different regions: rectangle, square, and circle. The algorithms for rectangular and square regions run in $O(N)$ epochs. The algorithms for the rectangular, square and circular regions require 2 (which is optimal), 5 and 8 colors, respectively.

The mutual visibility problem requires a set of $N$ autonomous mobile robots to reach a configuration on the 2D plane where every pair of robots can see each other, i.e., no robot lies on the line segment connecting any two others. We study the fault-tolerant mutual visibility problem under the barebones luminous model (each robot has a light that can flash a color from a finite prefixed color set), where the objective is to reach a configuration in which every pair of non-faulty robots are mutually visible, despite the presence of at most $f (\le N)$ robots prone to mobility failures. Mobility fault is a fault model in the existing literature that makes a robot immobile. However, the faulty robot executes the algorithms and its light remains functional. Unlike existing studies that assume coordinate agreement or partial synchrony, we consider the asynchronous ASYNC setting and disoriented robots (do not share a coordinate system or orientation), with both $N$ and $f$ unknown. We propose a deterministic $O(N)$-time algorithm in terms of epochs that utilises $O(1)$ colors and ensures collision-free movements, where epoch is the smallest time interval in which every robot completes at least one full LCM cycle. In addition, our algorithm solves a useful subproblem of detecting the global innermost layer under asynchronous setting only with the help of local view of the robots. The layer structure of any robot configuration represented as a sequence of disjoint convex polygons, that offers a way to organize progress even without shared coordinate system.

In a connected graph with an autonomous robot swarm with limited visibility, it is natural to ask whether the robots can be deployed to certain vertices satisfying a given property using only local knowledge. This paper affirmatively answers the question with a set of myopic (finite visibility range) luminous robots with the aim of filling a minimal vertex cover (MVC) of a given graph $G = (V, E)$. The graph has special vertices, called doors, through which robots enter sequentially. Starting from the doors, the goal of the robots is to settle on a set of vertices that forms a minimal vertex cover of $G$ under the asynchronous ($\mathcal{ASYNC}$) scheduler. We are also interested in achieving the minimum vertex cover (MinVC, which is NP-hard for general graphs) for a specific graph class using the myopic robots. We establish lower bounds on the visibility range for the robots and on the time complexity (which is $\Omega(|E|)$). We present two algorithms for trees: one for single door, which is both time and memory-optimal, and the other for multiple doors, which is memory-optimal and achieves time-optimality when the number of doors is a constant. Interestingly, our technique achieves MinVC on trees with a single door. We then move to the general graph, where we present two algorithms, one for the single door and the other for the multiple doors with an extra memory of $O(\log \Delta)$ for the robots, where $\Delta$ is the maximum degree of $G$. All our algorithms run in $O(|E|)$ epochs.

We explore the power of luminous mobile robots on both discrete and continuous domains. For the discrete domain, we solve a problem named MIS (maximal independent set) Filling on a given connected graph. In the continuous domain, we solve the Mutual Visibility problem on the usual Euclidean plane. These problems are well motivated by real-world applications such as information dissemination in a network, pattern formation and many more. We first discuss the MIS filling problem and then move to the Mutual Visibility problem.

We are given $N$ autonomous mobile robots inside a bounded region. The robots are opaque which means that three collinear robots are unable to see each other as one of the robots acts as an obstruction for the other two. They operate in classical Look-Compute-Move (LCM) activation cycles. Moreover, the robots are oblivious except for a persistent light (which is why they are called Luminous robots) that can determine a color from a fixed color set. Obliviousness does not allow the robots to remember any information from past activation cycles. The Uniform Partitioning problem requires the robots to partition the whole region into sub-regions of equal area, each of which contains exactly one robot. Due to application-oriented motivation, we, in this paper consider the region to be well-known geometric shapes such as rectangle, square and circle. We investigate the problem in asynchronous setting where there is no notion of common time and any robot gets activated at any time with a fair assumption that every robot needs to get activated infinitely often. To the best of our knowledge, this is the first attempt to study the Uniform Partitioning problem using oblivious opaque robots working under asynchronous settings. We propose three algorithms considering three different regions: rectangle, square and circle. Robots partition the region in a distributed way and reach their respective positions in the partitions. The algorithms proposed for rectangular and square regions run in $O(N)$ epochs whereas the algorithm for circular regions runs in $O(N^2)$ epochs, where an epoch is the smallest unit of time in which all robots are activated at least once and execute their LCM cycles.

We initiate the study of the Mutual Visibility problem using $N$ opaque luminous point robots that have inaccurate movements. Each robot operates in Look-Compute-Move cycles and has a persistent light attached to it to have a weak form of communication between robots using a constant number of colors. The inaccuracy for a robot $r$ is an angular deviation from its target point $T$ to a point $T'$ such that the angle $\angle TrT' <90^\circ$. The problem becomes unsolvable if this angle is $\geq 90^\circ$. From any initial configuration of the robots on the Euclidean plane, the problem aims to arrange the robots in a configuration such that any two robots are visible to each other. We assume that the robots agree on one coordinate axis. We present two collision-free algorithms, a $2$ color algorithm (which is optimal in the number of colors used) for semi-synchronous setting and a $3$ color algorithm for asynchronous setting, both of which run in $\mathcal{O}(N)$ epochs. We also study the problem in the presence of mobile faulty robots. A robot can exhibit both mobility failure and angular inaccuracies in its movement. We present a fault-tolerant algorithm that aims to bring the robots in a configuration where no three non-faulty robots are collinear, and no faulty robot lies between two non-faulty robots. This algorithm uses $10$ colors and takes $\mathcal{O}(N)$ epochs under asynchronous settings.

We aim to solve the mutual visibility problem using $n$ autonomous, indistinguishable, homogeneous, oblivious and opaque point robots where the number of robots that can be faulty is at most one. The fault may occur anytime. The faulty robot cannot move from the time it becomes faulty. Initially from any arbitrary configuration, the problem of mutual visibility using robots aims to reach a configuration where any two robots can see each other. The challenge is to reach to such a configuration in presence of obstructed visibility where two robots see each other only if the line segment joining them does not have any robots. Every robot operates in the conventional Look-Compute-Move cycles. Robots have no agreement in their coordinate system. We, in this paper, propose a distributed asynchronous algorithm for mutual visibility in presence of at most one faulty robot where robots has no agreement on any global coordinate axes.

We present the problem of finding a maximal independent set (MIS) (named as MIS Filling problem) of an arbitrary connected graph with luminous myopic mobile robots. The robots enter the graph one after another from a particular vertex called the Door and move along the edges of the graph without collision to occupy vertices such that the set of occupied vertices forms a maximal independent set. This paper explores two versions of the MIS filling problem. For the MIS Filling with Single Door case, our IND algorithm forms an MIS of size $m$ in $O(m^2)$ epochs under an asynchronous scheduler, where an epoch is the smallest time interval in which each participating robot gets activated and executes the algorithm at least once. The robots have three hops of visibility range, $\Delta + 8$ number of colors, and $O(\log \Delta)$ bits of persistent storage, where $\Delta$ is the maximum degree of the graph. For the MIS Filling with Multiple Doors case, our MULTIND algorithm forms an MIS in $O(m^2)$ epochs under a semi-synchronous scheduler using robots with five hops of visibility range, $\Delta + k + 7$ number of colors, and $O(\log (\Delta + k))$ bits of persistent storage, where $k$ is the number of doors.

In this paper, we study the line formation problem using $n$ oblivious point mobile robots located on distinct positions on the Euclidean plane. We assume that the robots agree on one coordinate axis. Robots operate in Look-Compute-Move (LCM) cycles and any two robots can see each other only if there is no robot present on the line segment joining them. Our aim is to solve the line formation problem even if some robots become faulty before achieving the goal. The robots cannot move anymore once they become faulty. We present a fault-tolerant distributed algorithm for line formation under $y$-axis agreement which runs in $O(n)$ epochs in semi-synchronous setting. The same algorithm runs in $D/y_{min}$ epochs in asynchronous setting, where $D$ is the vertical distance between the farthest robots along the $y$-axis and $y_{min}$ is the minimum non-zero vertical distance traveled by a robot in each LCM cycle.