Infinitesimal Weak Rigidity and Stability Analysis on Three-Agent Formations

摘要

In this paper, new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks are introduced. 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 propose applying the new concepts to a three-agent formation control problem with a gradient control law, and further we finally propose a modified Henneberg construction which is a technique to generate minimally rigid (or weakly rigid) graphs.