A geometric approach to deploying robot swarms

Abstract

We discuss the fundamental problems and practical issues underlying the deployment of a swarm of autonomous mobile robots that can potentially be used to build mobile robotic sensor networks. For the purpose, a geometric approach is proposed that allows robots to configure themselves into a two-dimensional plane with uniform spatial density. Particular emphasis is paid to the hole repair capability for dynamic network reconfiguration. Specifically, each robot interacts selectively with two neighboring robots so that three robots can converge onto each vertex of the equilateral triangle configuration. Based on the local interaction, the selfconfiguration algorithm is presented to enable a swarm of robots to form a communication network arranged in equilateral triangular lattices by shuffling the neighbors. Convergence of the algorithms is mathematically proved using Lyapunov theory. Moreover, it is verified that the self-reparation algorithm enables robot swarms to reconfigure themselves when holes exist in the network or new robots are added to the network. Through extensive simulations, we validate the feasibility of applying the proposed algorithms to self-configuring a network of mobile robotic sensors. We describe in detail the features of the algorithm, including self-organization, self-stabilization, and robustness, with the results of the simulation.

Collective Movement Method for Swarm Robot based on a Thermodynamic Model

“…This shape can be easily changed to other lattice shapes (triangle, square, etc.) by adjusting the density of the network topology [14]. Furthermore, the hexagonal-lattice shape is stabilized during collective movements, which was also confirmed in the control models proposed by Shimizu et al [7] and Pimenta et al [9].…”

Tracking multiple moving targets with swarms of mobile robots

“…Therefore, x d is asymptotically stable, implying that r i reaches a vertex of E i . Regarding the scalability of the algorithm, see [14].…”

“…This approach can be further applied to robotic sensor networks for tracking and/or capturing multiple toxic and hazardous substances or automated wide area surveillance. We employ the relative degree of attraction from individual targets based on the universal law of gravitation [13] and local interactions [14]. Specifically, the proposed coordinated tracking is achieved without using any leader, identifiers, common coordinate frame, memory of previous states, or explicit communication.…”

“…Due to similar reason, robots are enabled to achieve faster formation without deadlocks [19]. Our local interaction approach [14] based on such partially connected topology is to construct uniformly spaced equilateral triangles that can reduce the number of interacting robots in a given location, yet establish an energy-efficient routing [26]. Importantly, compared with the computation of virtual spring forces to calculate an equilibrium of force balance, each robot utilizes only relative distance information of other robots.…”

Geometric Computations by Broadcasting Automata on the Integer Grid

“…The problem of swarm (or a set of mobile robots) configuration into regular grids is well known for exploration tasks and environmental or habitat monitoring [5]. However, arranging robots into a regular grid structure has a number of other benefits in terms of self organization and efficient communication.…”