Relative Localization With Non-Persistent Excitation Using UWB-IMU Measurements

In multi-robot systems, accurate relative localization is indispensable for executing collaborative tasks in GPS-denied environments. This paper focuses on the relative localization problem relying on onboard UWB and IMU sensors. First, we propose a nominal adaptive gradient-based relative position observer for each robot. The estimation of time-varying relative position is transformed into the online constant parameter identification problem using only relative distance and velocity information. Furthermore, in order to relax the standard assumptions of persistently excited relative motions, a finite-time adaptive relative localization scheme is developed using the dynamic regression extension and mixing (DREM) technique. This scheme merely requires filtered relative velocity satisfying interval excited condition, which is milder than the persistent one. Finally, simulations are presented to verify the effectiveness of our theoretical results, followed by flight experiments on a team of three quadcopters. It indicates that the relative localization accuracy can reach centimeter level. Note to Practitioners - This paper is motivated by the relative localization problem without relying on any external infrastructure under GPS-denied environments, especially for situations where the robots' trajectories cannot be persistently excited. Existing relative localization approaches generally assume that the robots' velocities or displacements satisfy the persistent excitation condition, which restricts the motion forms of robots. This paper presents a new method that only requires the filtered relative velocity between robots to satisfy the interval excitation condition, so that accurate relative position estimations can be achieved within a finite time. In this paper, we provide a linear regressor equation generation method using the linear filter techniques, which mathematically characterizes the relationship between measurable signals (distance, velocity) and relative position. Then, we design a relative localization scheme based on the DREM method and give the convergence analysis. Both simulations and physical experiments suggest that the proposed method in this paper shows high localization accuracy about 10 cm and fast convergent speed. But it has not yet been applied to the specific control tasks. In future research, we will address the integration of relative localization and formation control in such scenarios.