Position Discovery for a System of Bouncing Robots

Abstract

A 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 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 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 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 ≤ n/2 robots, the time until completion of the algorithm by the last robot is

Deterministic Symmetry Breaking in Ring Networks

“…If n is odd, this solution works also under the assumptions of the basic model. In [10], oblivious algorithms are studied, in which an agent is not allowed to change its direction at the beginning of a round. However, agents have access to positions of all their collisions during a round.…”

“…One of the most studied network topologies in the context of distributed computation, as well as coordination mechanisms for mobile agents, is the ring network [3], [21], [22]. Recently, studies of geometric ring networks were initiated in the context of terrain exploration by agents/robots with limited communication and navigation capabilities [10], [18]. This refers to the concept of swarms, i.e., large groups of limited but cost-effective entities (robots, agents) that can be deployed to perform an exploration in a hard-to-access hostile environment.…”

“…Following [18], [10] we consider a model where the agents operate in synchronised rounds, and they lack direct means of communication. The trajectory of an agent in a given round is represented as a continuous curve that connects the start and the end points of the route adopted by the agent.…”

“…Most of the models adopted in the literature on swarms assume that the agents are either almost or entirely oblivious, i.e., throughout the computation process the agents follow a very simple, rarely amendable, routine of actions. Such a scenario is studied in [10], [11], [9], where agents are entirely oblivious but can register all their collisions. (In [11], [9] agents might have different velocities, and in [9] they might have different masses.)…”

Fence patrolling by mobile agents with distinct speeds

“…For practical purposes, it is important to consider decentralized settings where agents need to cooperate with limited global knowledge or computational power [12]. The fact that the partition-based strategy is not always optimal may be bad news in this context, since it is one of the simplest strategies to be realized in a distributed way, using systems of self-stabilizing robots, e.g., in models of "bouncing robots" [6]. Thus a natural question to ask next is whether and how movements better than the partition-based strategy can be realized in various distributed settings.…”