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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 ef´Čücient 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.

Alejandro Cornejo and Andrew J. Lynch and Elizabeth Fudge and Siegfried Bilstein and Majid Khabbazian and James McLurkin
The International Journal of Robotics Research (IJRR) (Accepted)