  Studies of coordinated motion in autonomous vehicle groups have become a
significant topic of interest in recent years. In this paper, we study the case
when the agents are limited to distance measurements from predetermined
reference points, or anchors. A novel approach, referred to as
distance-coupling, is proposed for approximating agent positions from anchor
distances. By taking the difference between squared distance functions, we
cancel out the quadratic term and obtain a linear function of the position for
the point of interest. We apply this method to the homing problem and prove
Lyapunov stability with and without anchor placement error; defining bounds on
the region of attraction when the anchors are linearly transformed from their
desired positions. To further increase complexity, we show how the policy can
be implemented on the formation control problem for a set of autonomous agents.
In this context, we prove the existence of the set of equilibria for the
distance-coupled formation controller and make preliminary claims on its
convergence. The performance for both controllers are subsequently validated
through simulation.
