  The ability to predict, and thus react to, oncoming collisions among a set of
mobile agents is a fundamental requirement for safe autonomous movement, both
human and robotic. This paper addresses systems that use range measurements
between mobile agents for the purpose of collision prediction, which involves
prediction of the agents' future paths to know if they will collide at any
time. One straightforward system would use known-location static anchors to
estimate agent coordinates over time, and use the track to predict collision.
Fundamentally, no fixed coordinate system is required for collision prediction,
so using only the pairwise range between two agents can be used to predict
collision. We present lower bound analysis which shows the limitations of this
pairwise method. As an alternative anchor-free method, we propose the
friend-based autonomous collision prediction and tracking (FACT) method that
uses all measured ranges between nearby (unknown location mobile) agents, in a
distributed algorithm, to estimate their relative locations and velocities and
predict future collisions between agents. Using analysis and simulation, we
show the potential for FACT to achieve equal or better collision detection
performance compared to other methods, while avoiding the need for anchors. We
then build a network of $N$ ultra wideband (UWB) devices and an efficient
multi-node protocol which allows all ${\cal O}(N^2)$ pairwise ranges to be
measured in $N$ slots. We run experiments with up to six independent robot
agents moving and colliding in a 2D plane and up to four anchor nodes to
compare the performance of the collision prediction methods. We show that the
FACT method can perform better than either other method but without the need
for a fixed infrastructure of anchor nodes.
