Persistently Excited Adaptive Relative Localization and Time-Varying Formation of Robot Swarms

In this article, we investigate the problem of controlling a multirobot team to follow a leader in formation, supported by a relative position estimate derived from distance and self-displacement measurements, thus waiving the need of external localization infrastructure. The main challenge of the problem, which is to simultaneously fulfill both relative localization and control tasks, is efficiently and novelly resolved by embedding a distance-displacement-based persistently excited adaptive relative localization technique into a time-varying formation with bounded control input (PEARL-TVF). By assuming that the leader is globally reachable and by selecting proper parameters, it is shown that the PEARL-TVF ensures exponentially convergent localization, which leads to exponentially convergent formation when the leader's behavior is deterministic, and bounded formation error for a nondeterministic leader. Numerical simulations and experiments on quadcopters are provided to verify the theoretical findings.