2018/03/26 by Seong‐Ho Kwon, Minh Hoang Trinh, Kwon, Seong-Ho +7 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #Mathematical Biology Tumor Growth #Micro and Nano Robotics #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1803.09545
openalex publication_date 2018/03/26 · openalex created_date 2018/04/06 · openalex updated_date 2026/08/01
In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak rigidity of a framework indirectly. An infinitesimal weak rigidity framework can be uniquely determined up to a translation and a rotation (and a scaling also when the framework does not include any edge) by its inter-neighbor distances and angles. We apply the new concepts to a three-agent formation control problem with a gradient control law, and prove instability of the control system at any incorrect equilibrium point and convergence to a desired target formation. Also, we propose a modified Henneberg construction, which is a technique to generate minimally rigid (or weakly rigid) graphs. Finally, we extend the concept of the weak rigidity in R2 to the concept in R3.