Dense r-robust formations on lattices

Abstract

Robot networks are susceptible to fail under the presence of malicious or defective robots. Resilient networks in the literature require high connectivity and large communication ranges, leading to high energy consumption in the communication network. This paper presents robot formations with guaranteed resiliency that use smaller communication ranges than previous results in the literature. The formations can be built on triangular and square lattices in the plane, and cubic lattices in the three-dimensional space. We support our theoretical framework with simulations.