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arXiv · 2012.03064

An Orthogonal Basis Approach to Formation Shape Control (Extended Version)

Tairan Liu·Marcio de Queiroz
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Abstract

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.

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Tairan Liu, Marcio de Queiroz. 2020-12-05. An Orthogonal Basis Approach to Formation Shape Control (Extended Version). https://arxiv.org/abs/2012.03064

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