Distance-coupling as an Approach to Position and Formation Control

Abstract

In this letter, we study the case of autonomous agents which are required to move to some new position based solely on the distance measured from predetermined reference points, or anchors. A novel approach, referred to as distance-coupling, is proposed for calculating the agent's position exclusively from differences between squared distance measurements. The key insight in our approach is that, in doing so, we cancel out the measurement's quadratic term and obtain a function of position which is linear. We apply this method to the homing problem and prove Lyapunov stability with and without anchor placement error; identifying bounds on the region of attraction when the anchors are linearly transformed from their desired positions. As an application of the method, we show how the policy can be implemented for distributed formation control on a set of autonomous agents, proving the existence of the set of equilibria.