Nonlinear model predictive control for improving range-based relative localization by maximizing observability

Wireless ranging measurements have been proposed for enabling multiple Micro Air Vehicles (MAVs) to localize with respect to each other. However, the high-dimensional relative states are weakly observable due to the scalar distance measurement. Hence, the MAVs have degraded relative localization and control performance under unobservable conditions as can be deduced by the Lie derivatives. This paper presents a nonlinear model predictive control (NMPC) by maximizing the determinant of the observability matrix to generate optimal control inputs, which also satisfy constraints including multi-robot tasks, input limitation, and state bounds. Simulation results validate the localization and control efficacy of the proposed MPC method for range-based multi-MAV systems with weak observability, which has faster convergence time and more accurate localization compared to previously proposed random motions. A real-world experiment on two Crazyflies indicates the optimal states and control behaviours generated by the proposed NMPC.