In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities. Specifically, we introduce three controlled variables that form an orthogonal space and uniquely characterize a tetrahedron formation in 3D. This orthogonal space incorporates constraints on the inter-agent distances and the signed volume of tetrahedron substructures. The formation is modeled using a directed graph with a leader-follower type configuration and single-integrator dynamics. We show that the proposed decentralized formation controller ensures the \textit{global} asymptotic stability and the local exponential stability of the desired formation for an \textit{n}-agent system with no ambiguities. Unlike previous work, this result is achieved without conditions on the tetrahedrons that form the desired formation or on the control gains.
@article{arxiv.2012.03064,
title = {An Orthogonal Basis Approach to Formation Shape Control (Extended Version)},
author = {Tairan Liu and Marcio de Queiroz},
journal= {arXiv preprint arXiv:2012.03064},
year = {2020}
}