In this paper we derive a new capability for robots to measure relative
direction, or Angle-of-Arrival (AOA), to other robots operating in
non-line-of-sight and unmapped environments with occlusions, without requiring
external infrastructure. We do so by capturing all of the paths that a WiFi
signal traverses as it travels from a transmitting to a receiving robot, which
we term an AOA profile. The key intuition is to "emulate antenna arrays in the
air" as the robots move in 3D space, a method akin to Synthetic Aperture Radar
(SAR). The main contributions include development of i) a framework to
accommodate arbitrary 3D trajectories, as well as continuous mobility all
robots, while computing AOA profiles and ii) an accompanying analysis that
provides a lower bound on variance of AOA estimation as a function of robot
trajectory geometry based on the Cramer Rao Bound. This is a critical
distinction with previous work on SAR that restricts robot mobility to
prescribed motion patterns, does not generalize to 3D space, and/or requires
transmitting robots to be static during data acquisition periods. Our method
results in more accurate AOA profiles and thus better AOA estimation, and
formally characterizes this observation as the informativeness of the
trajectory; a computable quantity for which we derive a closed form. All
theoretical developments are substantiated by extensive simulation and hardware
experiments. We also show that our formulation can be used with an
off-the-shelf trajectory estimation sensor. Finally, we demonstrate the
performance of our system on a multi-robot dynamic rendezvous task.Comment: 28 pages, 25 figures, *co-primary author