On Local/Global Constructibility for Mobile Robots Using Bounded Range Measurements

We propose a state-constructibility analysis for a nonholonomic vehicle moving across an environment instrumented with fixed-frame range sensors (anchors). We consider a sparse deployment in which anchors are in a small number, and have finite and non-overlapping sensing ranges. Under the most extreme conditions (i.e., the robot being in sight of two anchors at different times), we provide a sufficient condition on the manoeuvres that the robot is required to execute within the range of each of the anchors in order to achieve global constructibility. When the robot travels along straight lines, these conditions are not met, but we can still have “local” constructibility to a degree quantifiable through the smallest eigenvalue of the Constructibility Gramian (CG). Our second contribution is to show how this metric changes according to the geometric parameters of the linear trajectory with respect to the position of the anchors and their sensing range.