Scale-free coordinates for multi-robot systems with bearing-only sensors

We propose scale-free coordinates as an alternative coordinate system for multi-robot systems with large robot populations. Scale-free coordinates allow each robot to know, up to scaling, the relative position and orientation of other robots in the network. We consider a weak sensing model where each robot is only capable of measuring the angle, relative to its own heading, to each of its neighbors. Our contributions are three-fold. First, we derive a precise mathematical characterization of the computability of scale-free coordinates using only bearing measurements, and we describe an efficient algorithm to obtain them. Second, through simulations we show that even in graphs with low average vertex degree, most robots are able to compute the scale-free coordinates of their neighbors using only two-hop bearing measurements. Finally, we present an algorithm to compute scale-free coordinates that is tailored to low-cost systems with limited communication bandwidth and sensor resolution. Our algorithm mitigates the impact of sensing errors through a simple yet effective noise sensitivity model. We validate our implementation with real-world robot experiments using static accuracy measurements and a simple scale-free motion controller.