Gathering Anonymous, Oblivious Robots on a Grid

We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely simple robots is the following: The robots do not have a common compass, only have a constant viewing radius, are autonomous and indistinguishable, can move at most a constant distance in each step, cannot communicate, are oblivious and do not have flags or states. The only gathering algorithm under this robot model, with known runtime bounds, needs $\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On the other side, in the case of the 2-dimensional grid, the only known gathering algorithms for the same time and a similar local model additionally require a constant memory, states and "flags" to communicate these states to neighbors in viewing range. They gather in time $\mathcal{O}(n)$. In this paper we contribute the (to the best of our knowledge) first gathering algorithm on the grid that works under the same simple local model as the above mentioned Euclidean plane strategy, i.e., without memory (oblivious), "flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound matches the time bound of the best known algorithm for the Euclidean plane mentioned above. We say gathering is done if all robots are located within a $2\times 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be solved

Gathering on Rings for Myopic Asynchronous Robots With Lights

We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: M_{init}, which denotes the number of nodes between two border nodes, and O_{init}, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if M_{init} or O_{init} is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility

Asynchronous Gathering in a Torus

We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other but are endowed with visibility sensors that allow them to see the positions of the other robots. Most investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configurations. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robot unless it is their current node. Consequently, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network

Gathering over Meeting Nodes in Infinite Grid

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived

Gathering asynchronous and oblivious robots on basic graph topologies under the Look -Compute-Move model

Volume dedicated to the Workshop on Search and Rendezvous that took place in May 2012 in Lorentz CentreInternational audienceRecent and challenging models of robot-based computing systems consider identical, oblivious and mobile robots placed on the nodes of anonymous graphs. Robots operate asynchronously in order to reach a common node and remain with it. This task is known in the literature as the athering or rendezvous problem. The target node is neither chosen in advance nor marked differently compared to the other nodes. In fact, the graph is anonymous and robots have minimal capabilities. In the context of robot-based computing systems, resources are always limited and precious. Then, the research of the minimal set of assumptions and capabilities required to accomplish the gathering task as well as for other achievements is of main interest. Moreover, the minimality of the assumptions stimulates the investigation of new and challenging techniques that might reveal crucial peculiarities even for other tasks. The model considered in this chapter is known in the literature as the Look-Compute-Move model. Identical robots initially placed at different nodes of an anonymous input graph operate in asynchronous Look-Compute-Move cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. This means that the time between Look, Compute, and Move operations is finite but unbounded, and it is decided by the adversary for each robot. Hence, robots may move based on significantly outdated perceptions. The only constraint is that moves are instantaneous, and hence any robot performing a Look operation perceives all other robots at nodes of the ring and not on edges. Robots are all identical, anonymous, and execute the same deterministic algorithm. They cannot leave any marks at visited nodes, nor can they send messages to other robots. In this chapter, we aim to survey on recent results obtained for the gathering task over basic graph topologies, that are rings, grids, and trees. Recent achievements to this matter have attracted many researchers, and have provided interesting approaches that might be of main interest to the community that studies robot-based computing systems

Gathering of Mobile Robots with Defected Views

An autonomous mobile robot system consisting of many mobile computational entities (called robots) attracts much attention of researchers, and it is an emerging issue for a recent couple of decades to clarify the relation between the capabilities of robots and solvability of the problems. Generally, each robot can observe all other robots as long as there are no restrictions on visibility range or obstructions, regardless of the number of robots. In this paper, we provide a new perspective on the observation by robots; a robot cannot necessarily observe all other robots regardless of distances to them. We call this new computational model the defected view model. Under this model, in this paper, we consider the gathering problem that requires all the robots to gather at the same non-predetermined point and propose two algorithms to solve the gathering problem in the adversarial (N,N-2)-defected model for N ? 5 (where each robot observes at most N-2 robots chosen adversarially) and the distance-based (4,2)-defected model (where each robot observes at most two robots closest to itself), respectively, where N is the number of robots. Moreover, we present an impossibility result showing that there is no (deterministic) gathering algorithm in the adversarial or distance-based (3,1)-defected model, and we also show an impossibility result for the gathering in a relaxed (N, N-2)-defected model

Gathering of Mobile Robots in Anonymous Trees

Gathering problem of mobile robots is a class of graph problem that has a lot of relevance in everyday life. The problem requires a set of mobile robots, initially located at different nodes of a graph, to gather at the same location in the graph, which is not decided before. This report considers the gathering problem of mobile robots in anonymous trees. The robots considered here are identical, do not communicate directly with other robots and also, all the robots execute the same algorithm to achieve gathering. Robots are assumed to have minimal capabilities with respect to the memory associated with them as well as their visibility capability. In this report, three models have been proposed for solving gathering problem under three different scenarios. Possible solutions in each of these models have been described. The current work that has already happened and the future work that can be done in each model have also been mentioned

A unified approach for different tasks on rings in robot-based computing systems

International audienceA set of autonomous robots have to collaborate in order to accomplish a common task in a ring-topology where neither nodes nor edges are labeled. We present a unified approach to solve three important problems: the exclusive perpetual exploration, the exclusive perpetual search and the gathering problems. In the first problem, each robot aims at visiting each node infinitely often; in perpetual graph searching, the team of robots aims at clearing the whole network infinitely often; and in the gathering problem, all robots must eventually occupy the same node. We investigate these tasks in the Look-Compute- Move distributed computing model where the robots cannot communicate but can perceive the positions of other robots. Each robot is equipped with visibility sensors and motion actuators, and it operates in asynchronous cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it eventually moves to this neighbor (Move). Moreover, robots are endowed with very weak capabilities. Namely, they are anonymous, oblivious, uniform (execute the same algorithm) and have no common sense of orientation. In this setting, we devise algorithms that, starting from an exclusive rigid (i.e. aperiodic and asymmetric) configuration, solve the three above problems in anonymous ring-topologies