Adaptive synchronized tracking of heterogeneous spherical robots using distributed hierarchical sliding surfaces under a directed graph

Abstract

This paper addresses an adaptive synchronized tracking problem of multiple spherical robots with heterogeneous nonlinearities and uncertain rolling resistances under directed networks. A dynamic leader is considered, and its information has been accessed by only a small fraction of follower robots. The main contribution of this paper is to present distributed hierarchical sliding surfaces in consideration of underactuated characteristics of spherical robots so that all followers track a dynamic leader and the swing-up angle of each follower tracks its swing-up balance angle in a fully distributed fashion. Based on these surfaces, we design an adaptive synchronized tracking algorithm with distributed estimators for estimating the leader signal's velocity and the swing-up balance angular velocity, and the adaptive laws for estimating rolling resistances. The stability of the overall closed-loop system is analyzed in the Lyapunov sense. A simulation result is given to illustrate the effectiveness of the proposed methodology.