Problem of uniform deployment on a line segment for second-order agents

Consideration was given to a special problem of controlling a formation of mobile agents, that of uniform deployment of several identical agents on a segment of the straight line. For the case of agents obeying the first-order dynamic model, this problem seems to be first formulated in 1997 by I.A. Wagner and A.M. Bruckstein as "row straightening." In the present paper, the straightening algorithm was generalized to a more interesting case where the agent dynamics obeys second-order differential equations or, stated differently, it is the agent's acceleration (or the force applied to it) that is the control

Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with Holes

This article presents a distributed algorithm for a group of robotic agents with omnidirectional vision to deploy into nonconvex polygonal environments with holes. Agents begin deployment from a common point, possess no prior knowledge of the environment, and operate only under line-of-sight sensing and communication. The objective of the deployment is for the agents to achieve full visibility coverage of the environment while maintaining line-of-sight connectivity with each other. This is achieved by incrementally partitioning the environment into distinct regions, each completely visible from some agent. Proofs are given of (i) convergence, (ii) upper bounds on the time and number of agents required, and (iii) bounds on the memory and communication complexity. Simulation results and description of robust extensions are also included

Robots with Lights: Overcoming Obstructed Visibility Without Colliding

Robots with lights is a model of autonomous mobile computational entities operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation of computability in this model, initially suggested by Peleg, is under way, and several results have been recently established. In these investigations, however, an agent is assumed to be capable to see through another agent. In this paper we start the study of computing when visibility is obstructable, and investigate the most basic problem for this setting, Complete Visibility: The agents must reach within finite time a configuration where they can all see each other and terminate. We do not make any assumption on a-priori knowledge of the number of agents, on rigidity of movements nor on chirality. The local coordinate system of an agent may change at each activation. Also, by definition of lights, an agent can communicate and remember only a constant number of bits in each cycle. In spite of these weak conditions, we prove that Complete Visibility is always solvable, even in the asynchronous setting, without collisions and using a small constant number of colors. The proof is constructive. We also show how to extend our protocol for Complete Visibility so that, with the same number of colors, the agents solve the (non-uniform) Circle Formation problem with obstructed visibility

Second-Order Agents on Ring Digraphs

The paper addresses the problem of consensus seeking among second-order linear agents interconnected in a specific ring topology. Unlike the existing results in the field dealing with one-directional digraphs arising in various cyclic pursuit algorithms or two-directional graphs, we focus on the case where some arcs in a two-directional ring graph are dropped in a regular fashion. The derived condition for achieving consensus turns out to be independent of the number of agents in a network.Comment: 6 pages, 10 figure