Controlling triangular formations of autonomous agents in finite time using coarse measurements

This paper studies the performances of the popular gradient-based formation-control strategies for teams of autonomous agents when the agents´ range measurements are coarse. Since the dynamics of the resulting closed-loop system are discontinuous, Filippov solutions to non-smooth dynamical systems are introduced. Similar to the existing stability results for triangular formations with precise range measurements, we prove that under coarse range measurements, the convergence to the desired formation is almost global except for initially collinearly positioned formations. More importantly, we are able to make stronger statements that the convergence takes place within finite time and that the settling time can be determined by the geometric information of the initial shape of the formation. Simulation and experimental results are provided to validate the theoretical analysis.