Biconnecting a network of mobile robots using virtual angular forces

This paper proposes a new solution to the problem of self-deploying a network of wireless mobile robots with simultaneous consideration to several criteria, that are, the fault-tolerance (biconnectivity) of the resulting network, its coverage, its diameter, and the quantity of movement required to complete the deployment. These criteria have already been addressed individually in previous works, but we propose here an elegant solution to address all of them at once. Our approach is based on combining two complementary sets of virtual forces: spring forces, whose properties are well known to provide optimal coverage at reasonable movement cost, and angular forces, a new type of force proposed here whose effect is to rotate two angularly consecutive neighbors of a node toward one another when the corresponding angle is larger than 60° (even if these two nodes are not themselves neighbors). Angular forces have the global effect of biconnecting the network and reducing its diameter, while not affecting the benefits obtained by spring forces on coverage. In this paper we give a detailed description of both types of forces, whose combination poses a number of technical challenges. We also provide an implementation that relies only on position exchanges within two hops. Extensive simulations are finally presented to evaluate the solution against all criteria (coverage, biconnectivity, quantity of movements, and diameter), and show its advantages over prior solutions.