Realization of $r$ -Robust Formations in the Plane Using Control Barrier Functions

Abstract

This letter presents control laws to drive groups of robots into formations with communication graphs that satisfy the r-robustness property, which allows for consensus in the presence of malicious robots. Using results in r-robustness and control barrier functions, the presented control laws ensure such formations in finite time, using a reference adjacency matrix or only a desired number of neighboring robots. The results are illustrated through simulations.