Robot Localisation and Uncertainty Control with Intermittent Range-only Measurements

In this paper, we address the mobile robot localisation problem by combining relative measurements with intermittent measurements collected from range sensors (e.g., Ultra-Wide Band transmitters) with measurements on the relative motion of the robot. We present some basic results on the possibility of reconstructing the state using a very small number of measurements from two different anchors by setting up a system of linear equations. Next, we study how the observability of a trajectory can be quantified by the condition number of the system matrix, and hence related to the manoeuvres executed by the robot and to sampling time used to collect the measurements. As discussed in this paper, this result can be used as a basis to define control strategies aimed to maximise observability.