Consensus of Multi-Agent Systems With Nonholonomic Restrictions via Lyapunov’s Direct Method

Abstract

This letter presents a smooth time-varying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> -persistently exciting controller for full consensus of autonomous nonholonomic vehicles modeled as unicycles. This consists in the robots assuming a common prescribed Cartesian position relative to an unknown barycentre and an unknown common orientation. More significantly, for the first time in the literature, a strict Lyapunov function is provided and uniform global asymptotic stability for the closed-loop system is established. This is well beyond weaker convergence properties that are more commonly guaranteed in the literature.