Generalized weak rigidity: Theory, and local and global convergence of formations

Abstract

This paper proposes a generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient descent flow law. The generalized weak rigidity theory is utilized in order to characterize desired rigid formations by a general set of pure inter-agent distances and subtended angles, where the rigid formation shape with distances and subtended angles is determined up to translations and rotations (if the formation shape is composed of only subtended angles, then it is determined up to translations, rotations and, additionally, scaling factors). As the first result of its applications, this paper provides analysis of local exponential stability for a formation control system with pure distance/angle or only angle constraints in 2- and 3-dimensional spaces. Then, as the second result, it is shown that if there are three agents in 2-dimensional space then almost global exponential stability is ensured for a formation control system with pure distance/angle or only angle constraints. © 2020 Elsevier B.V.