A Point Set Connection Problem for Autonomous Mobile Robots in a Grid

Consider an orthogonal grid of streets and avenues in a Manhattan-like city populated by stationary sensor modules at some intersections and mobile robots that can serve as relays of information that the modules exchange, where both module-module and module-robot communication is limited to a straight line of sight within the grid. The robots are oblivious and move asynchronously. We present a distributed algorithm that, given the sensor locations as input, moves the robots to suitable locations in the grid so that a connected network of all modules is established. The number of robots that the algorithm uses is worst case optimal

Plane Formation by Synchronous Mobile Robots in the Three Dimensional Euclidean Space

Creating a swarm of mobile computing entities frequently called robots, agents or sensor nodes, with self-organization ability is a contemporary challenge in distributed computing. Motivated by this, we investigate the plane formation problem that requires a swarm of robots moving in the three dimensional Euclidean space to land on a common plane. The robots are fully synchronous and endowed with visual perception. But they do not have identifiers, nor access to the global coordinate system, nor any means of explicit communication with each other. Though there are plenty of results on the agreement problem for robots in the two dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first result for robots in the three dimensional space. This paper presents a necessary and sufficient condition for fully-synchronous robots to solve the plane formation problem that does not depend on obliviousness i.e., the availability of local memory at robots. An implication of the result is somewhat counter-intuitive: The robots cannot form a plane from most of the semi-regular polyhedra, while they can form a plane from every regular polyhedron (except a regular icosahedron), whose symmetry is usually considered to be higher than any semi-regular polyhedrdon

Static and expanding grid coverage with ant robots: Complexity results

AbstractIn this paper we study the strengths and limitations of collaborative teams of simple agents. In particular, we discuss the efficient use of “ant robots” for covering a connected region on the Z2 grid, whose area is unknown in advance, and which expands at a given rate, where n is the initial size of the connected region. We show that regardless of the algorithm used, and the robots’ hardware and software specifications, the minimal number of robots required in order for such a coverage to be possible is Ω(n). In addition, we show that when the region expands at a sufficiently slow rate, a team of Θ(n) robots could cover it in at most O(n2lnn) time. This completion time can even be achieved by myopic robots, with no ability to directly communicate with each other, and where each robot is equipped with a memory of size O(1) bits w.r.t. the size of the region (therefore, the robots cannot maintain maps of the terrain, nor plan complete paths). Regarding the coverage of non-expanding regions in the grid, we improve the current best known result of O(n2) by demonstrating an algorithm that guarantees such a coverage with completion time of O(1kn1.5+n) in the worst case, and faster for shapes of perimeter length which is shorter than O(n)

Position Discovery for a System of Bouncing Robots

International audienceA collection of $n$ anonymous mobile robots is deployed on a unit-perimeter ring or a unit-length line segment. Every robot starts moving at constant speed, and bounces each time it meets any other robot or segment endpoint, changing its walk direction. We study the problem of {\em position discovery}, in which the task of each robot is to detect the presence and the initial positions of all other robots. The robots cannot communicate or perceive information about the environment in any way other than by bouncing. Each robot has a clock allowing it to observe the times of its bounces. The robots have no control on their walks, which are determined by their initial positions and the starting directions. Each robot executes the same \emph{position detection algorithm}, which receives input data in real-time about the times of the bounces, and terminates when the robot is assured about the existence and the positions of all the robots. Some initial configuration of robots are shown to be {\em infeasible} --- no position detection algorithm exists for them. We give complete characterizations of all infeasible initial configurations for both the ring and the segment, and we design optimal position detection algorithms for all feasible configurations. For the case of the ring, we show that all robot configurations in which not all the robots have the same initial direction are feasible. We give a position detection algorithm working for all feasible configurations. The cost of our algorithm depends on the number of robots starting their movement in each direction. If the less frequently used initial direction is given to $k \leq n/2$ robots, the time until completion of the algorithm by the last robot is $\frac{1}{2}\lceil \frac{n}{k} \rceil$. We prove that this time is optimal. By contrast to the case of the ring, for the unit segment we show that the family of infeasible configurations is exactly the set of so-called {\em symmetric configurations}. We give a position detection algorithm which works for all feasible configurations on the segment in time $2$, and this algorithm is also proven to be optimal

Terminating Exploration Of A Grid By An Optimal Number Of Asynchronous Oblivious Robots

International audienceWe consider swarms of asynchronous oblivious robots evolving into an anonymous grid-shaped network. In this context, we investigate optimal (w.r.t. the number of robots) deterministic solutions for the terminating exploration problem. We first show lower bounds in the semi-synchronous model. Precisely, we show that at least three robots are required to explore any grid of at least three nodes, even in the probabilistic case. Then, we show that at least four (resp. five) robots are necessary to deterministically explore a (2,2)-Grid (resp. a (3,3)-Grid). We then propose deterministic algorithms in the asynchronous model. This latter being strictly weakest than the semi-synchronous model, all the aforementioned bounds still hold in that context. Our algorithms actually exhibit the optimal number of robots that is necessary to explore a given grid. Overall, our results show that except in two particular cases, three robots are necessary and sufficient to deterministically explore a grid of at least three nodes and then terminate. The optimal number of robots for the two remaining cases is four for the (2,2)-Grid and five for the (3,3)-Grid, respectively