Showing papers by "Giuseppe Prencipe published in 2003"

Solving the robots gathering problem

Abstract: Consider a set of n > 2 simple autonomous mobile robots (decentralized, asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, deterministic) moving freely in the plane and able to sense the positions of the other robots We study the primitive task of gathering them at a point not fixed in advance (GATHERING PROBLEM) In the literature, most contributions are simulation-validated heuristics The existing algorithmic contributions for such robots are limited to solutions for n ≤ 4 or for restricted sets of initial configurations of the robots In this paper, we present the first algorithm that solves the GATHERING PROBLEM for any initial configuration of the robots

Multiple Agents RendezVous in a Ring in Spite of a Black Hole

Abstract: The Rendezvous of anonymous mobile agents in a anonymous network is an intensively studied problem; it calls for k anonymous, mobile agents to gather in the same site We study this problem when in the network there is a black hole: a stationary process located at a node that destroys any incoming agent without leaving any trace The presence of the black hole makes it clearly impossible for all agents to rendezvous So, the research concern is to determine how many agents can gather and under what conditions

Robotic cops: the intruder problem

Abstract: In this paper we present a self-stabilizing algorithm for the intruder problem. The problem can be formulated as follows: an enemy unit, or intruder, is trying to sneak through a field patrolled by an arbitrary number of friendly autonomous (i.e. robotic) units. These units must reach the intruder and block it by surrounding it. Our solution to this problem, provided as an algorithm for the autonomous patrolling units, makes minimal assumptions on their capabilities. In particular, we assume they are completely asynchronous, and moreover that they have no observable identities, no memory, and no means to explicitly communicate with each other. Each unit needs only to be capable of observing the current position of its fellows and of the intruder. All these features, while making the task harder, give to the algorithm the nice property of self-stabilization, thus improving its robustness. For example, if any unit is knocked out, all the others automatically adjust their behavior, in order to still complete the task. By concentrating on extremely simple units, we are also able to investigate which capabilities are really needed to solve this problem, with obvious cost benefits (especially if the units are deployed in a hostile environment). In the paper, we first present a computational model for our robotic "cops", followed by the description of the algorithm we propose. We also show results of computer simulations, providing quantitative measures on the efficiency of the algorithm.

The Weber Point can be Found in Linear Time for Points in Biangular Configuration

Abstract: The Weber point of a given point set $P$ is a point in the plane that minimizes the sum of all distances to the points in $P$. In general, the Weber point cannot be computed. However, if the points are in specific geometric patterns, then finding the Weber point is possible. We investigate the case of {\em biangular configurations}, where there is a center and two angles $\alpha$ and $\beta$ such that the angles w.r.t. the center between each two adjacent points is either $\alpha$ or $\beta$, and these angles alternate. We show that in this case the center of biangularity is the Weber point of the points, and that it can be found in time linear in the number of points.