Luminous Robots Research Articles

Mutual visibility of luminous robots despite angular inaccuracy

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 ∠TrT′<90∘. The problem becomes unsolvable if this angle is ≥90∘. 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 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 O(N) epochs under asynchronous settings.

Circle formation by asynchronous opaque fat robots on an infinite grid

This study addresses the problem of ‘Circle Formation on an Infinite Grid by Fat Robots’ ( CF _FAT _GRID ). Unlike prior work focused solely on point robots in discrete domain, it introduces fat robots to circle formation on an infinite grid, aligning with practicality as even small robots inherently possess dimensions. The algorithm, named CIRCLE _FG , resolves the CF _FAT _GRID problem using a swarm of fat luminous robots. Operating under an asynchronous scheduler, it achieves this with five distinct colors and by leveraging one-axis agreement among the robots.

Distributed algorithms for filling MIS vertices of an arbitrary graph by myopic luminous robots

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(m2) 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, Δ+8 number of colors, and O(log⁡Δ) bits of persistent storage, where Δ 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(m2) epochs under a semi-synchronous scheduler using robots with five hops of visibility range, Δ+k+7 number of colors, and O(log⁡(Δ+k)) bits of persistent storage, where k is the number of Doors. We also achieve a lower bound of Ω(n) for MIS filling problem with Single Door, where n is the number of vertices of the graph.

Perpetual torus exploration by myopic luminous robots

We study perpetual torus exploration for swarms of autonomous, anonymous, uniform, and luminous robots. We consider robots with only few capabilities. They have a finite limited vision (myopic), they can only see robots at distance one or two. We show that the problem is impossible with only two luminous robots and also with three oblivious robots (without light). We then address the problem assuming luminous robots (resp. oblivious) with visibility range one (resp. two). We design optimal solutions with respect to both the number of robots and colors when robots share a common chirality and have, respectively, vision one and two. We also present an optimal solution with respect to the number of robots when they are endowed with vision one and share no common chirality. Finally, we propose a solution for the case in which robots are oblivious, have vision two, and no common chirality that uses one additional robot.

Ring exploration of myopic luminous robots with visibility more than one

We investigate ring exploration algorithms for autonomous myopic luminous robots. We consider the constraint that the visible distance is any constant of at least two and the number of colors of light devices is two. As a main contribution, in the fully synchronous, semi-synchronous, and asynchronous models, we prove that 1) two robots are necessary and sufficient to achieve perpetual exploration and 2) three robots are necessary and sufficient to achieve terminating exploration. These results show the power of large visibility for luminous robots because, when the visible distance is one and the number of colors is two, three and four robots are necessary to achieve perpetual and terminating exploration, respectively, in the semi-synchronous and asynchronous models. We also show that the proposed perpetual exploration algorithm is universal. On the other hand, we show that no universal algorithm exists for terminating exploration with three robots.

An Asynchronous Maximum Independent Set Algorithm By Myopic Luminous Robots On Grids

Abstract We consider the problem of constructing a maximum independent set with mobile myopic luminous robots on a grid network whose size is finite but unknown to the robots. In this setting, the robots enter the grid network one by one from a corner of the grid, and they eventually have to be disseminated on the grid nodes so that the occupied positions form a maximum independent set of the network. We assume that robots are asynchronous, anonymous, silent and they execute the same distributed algorithm. In this paper, we propose two algorithms: The first one assumes that the number of light colors of each robot is three and the visible range is two, but uses the additional assumption that a local edge-labeling exists for each node. To remove this assumption, the second one assumes that the number of light colors of each robot is seven, and that the visible range is three. In both algorithms, the number of movements is $O(n(L+l))$ steps, where $n$ is the number of nodes and $L$ and $l$ are the grid dimensions.

Gathering a Euclidean closed chain of robots in linear time and improved algorithms for chain-formation

We consider formation problems for chains of disoriented, mobile robots with limited visibility operating in asynchronous rounds (Async). More precisely, we study the Chain-Formation and the Gathering problem. Chain-Formation considers a chain of robots between two stationary outer robots: Each inner robot has two identifiable neighbors, and the goal is to arrange the robots on the line segment connecting the outer robots. The Gathering problem considers a closed chain (without outer robots) and demands all robots to gather on a single, not predefined point. The robots move in the Euclidean plane and are luminous, i.e., equipped with a light visible to the neighboring robots. At each point in time, the light can have one out of a constant number of colors.We introduce a family of algorithms inspired by the Hopper algorithm [1]. For the Chain-Formation problem, we modify the Hopper algorithm so that we can guarantee a (1+ε)-approximation to the optimal chain length (instead of a 2-approximation). Our main result is an asymptotically optimal algorithm for Gathering of a closed chain of disoriented, luminous robots with limited visibility in the Euclidean plane. All algorithms have a worst-case optimal runtime of O(n).

Mutual visibility on grid by asynchronous luminous robots

For a team of autonomous opaque point robots on the plane, the Mutual Visibility problem asks for a distributed algorithm that allows the robots to reposition themselves, without colliding, to a configuration where they all can see each other, i.e., no three of them are collinear. In this paper, we investigate the problem on a grid based terrain where the movements of the robots are restricted only along the grid lines and only to a neighboring grid point in each step. The robots operate in Look-Compute-Move cycles under an asynchronous scheduler. They have no agreement in coordinate system and do not know the total number of robots in the team. We assume the luminous robots model where each robot is equipped with an externally visible light which can assume a constant number of predefined colors. These colors serve both as memory and as a form of communication. We give an algorithm that solves the problem from any initial configuration using 9 colors.

Terminating Grid Exploration with Myopic Luminous Robots

Terminating Grid Exploration with Myopic Luminous Robots

Ring exploration with myopic luminous robots

We investigate exploration algorithms for autonomous mobile robots evolving in uniform ring-shaped networks. Unlike previous works, we consider myopia (each robot can only observe its neighboring nodes) and luminosity (each robot can use only two colors for its light) properties for the robots.As a main contribution, we prove that (i) in the FSYNC model, two (resp. three) myopic robots are necessary and sufficient to achieve perpetual (resp. terminating) exploration, and (ii) in the SSYNC and ASYNC models, three (resp. four) myopic robots are necessary and sufficient to achieve perpetual (resp. terminating) exploration.We also show that, in all execution models, our perpetual exploration algorithm is universal. That is, the algorithm solves perpetual exploration from any solvable initial configuration with two (resp. three) myopic robots and two colors in the FSYNC model (resp. the SSYNC and ASYNC models). On the other hand, we provide impossibility results for universal terminating exploration.

Forming Sequences of Patterns With Luminous Robots

The extensive studies on computing by a team of identical mobile robots operating in the plane in Look-Compute-Move cycles have been carried out mainly in the traditional OBLOT model, where the robots are silent (have no communication capabilities) and oblivious (in a cycle, they have no memory previous cycles). To partially overcome the limits of obliviousness and silence while maintaining some of their advantages, the stronger model of luminous robots, LUMI, has been introduced where the robots, otherwise oblivious and silent, carry a visible light that can take a number of different colors; a color can be seen by observing robots, and persists from a cycle to the next. In the study of the computational impact of lights, an immediate concern has been to understand and determine the additional computational strength of LUMI over OBLOT. Within this line of investigation, we examine the problem of forming a sequence of geometric patterns, PatternSequenceFormation. A complete characterization of the sequences of patterns formable from a given starting configuration has been determined in the OBLOT model. In this paper, we study the formation of sequences of patterns in the LUMI model and provide a complete characterization. The characterization is constructive: our universal protocol forms all formable sequences, and it does so asynchronously and without rigidity. This characterization explicitly and clearly identifies the computational strength of LUMI over OBLOT with respect to the PatternSequenceFormation problem.

The topology of look-compute-move robot wait-free algorithms with hard termination

Look-Compute-Move models for a set of autonomous robots have been thoroughly studied for over two decades. We consider the standard Asynchronous Luminous Robots (ALR) model, where robots are located in a graph G. Each robot, repeatedly Looks at its surroundings and obtains a snapshot containing the vertices of G, where all robots are located; based on this snapshot, each robot Computes a vertex (adjacent to its current position), and then Moves to it. Robots have visible lights, allowing them to communicate more information than only its actual position, and they move asynchronously, meaning that each one runs at its own arbitrary speed. We are also interested in a case which has been barely explored: the robots need not all be present initially, they might appear asynchronously. We call this the Extended Asynchronous Appearing Luminous Robots (EALR) model. A central problem in the mobile robots area is bringing the robots to the same vertex. We study several versions of this problem, where the robots move towards the same (or close to each other) vertices. And we concentrate on the requirement that each robot executes a finite number of Look-Compute-Move cycles, independently of the interleaving of other robot’s cycles, and then stops. Our main result is direct connections between the (ALR and) EALR model and the asynchronous wait-free multiprocess read/write shared memory (WFSM) model. General robot tasks in a graph are also provided, which include several version of gathering. Finally, using the connection between the EALR model and the WFSM model, a combinatorial topology characterization for the solvable robot tasks is presented.

Mutual visibility by luminous robots without collisions

We consider the Mutual Visibility problem for anonymous dimensionless robots with obstructed visibility moving in a plane: starting from distinct locations, the robots must reach, without colliding, a configuration where no three of them are collinear. We study this problem in the luminous robots model, in which each robot has a visible light that can assume colors from a fixed set.Among other results, we prove that Mutual Visibility can be solved in SSynch with 2 colors and in ASynch with 3 colors. If an adversary can interrupt and stop a robot moving to its computed destination, Mutual Visibility is still solvable in SSynch with 3 colors and, if the robots agree on the direction of one axis, also in ASynch.As a byproduct, we provide the first obstructed-visibility solutions to two classical problems for oblivious robots: collision-less convergence to a point (also known as near-gathering) and circle formation.

Autonomous mobile robots with lights

We consider the well known distributed setting of computational mobile entities, called robots, operating in the Euclidean plane in Look-Compute-Move (LCM) cycles. We investigate the computational impact of expanding the capabilities of the robots by endowing them with an externally visible memory register, called light, whose values, called colors, are persistent, that is they are not automatically reset at the end of each cycle. We refer to so endowed entities as luminous robots.We study the computational power of luminous robots with respect to the three main settings of activation and synchronization: fully-synchronous, semi-synchronous, and asynchronous. We establish several results. A main contribution is the constructive proof that asynchronous robots, illuminated with a constant number of colors, are strictly more powerful than traditional semi-synchronous robots.We also constructively prove that, for luminous robots, the difference between asynchrony and semi-synchrony disappears. This result must be contrasted with the strict dominance between the models without lights (even if the robots are enhanced with an unbounded amount of persistent internal memory).Additionally we show that there are problems that robots cannot solve without lights, even if they are fully-synchronous, but can be solved by asynchronous luminous robots with O(1) colors. It is still open whether or not asynchronous luminous robots with O(1) colors are more powerful than fully-synchronous robots without lights.We prove that this is indeed the case if the robots have the additional capability of remembering a single snapshot. This in turn shows that, for asynchronous robots, to have O(1) colors and a single snapshot renders them more powerful than to have an unlimited amount of persistent memory (including snapshots) but no lights.