Connectivity-preserving adaptive synchronized tracking of heterogeneous spherical robots with limited communication ranges

Abstract

A distributed connectivity-preserving problem is addressed for adaptive synchronized tracking of networked heterogeneous nonlinear spherical robots with a dynamic leader. We assume uncertain rolling resistances, limited communication ranges of robots, and that only a small fraction of follower robots have access to the time-varying leader information. Compared with the previous synchronized tracking scheme based on distributed hierarchical sliding surfaces (DHSSs) for multiple underactuated spherical robots, the main contribution of this paper is to present a new error transformation approach of DHSS for preserving the initial connectivity while achieving the synchronized tracking of longitudinal positions of all followers to the dynamic leader and the balance tracking of the swing-up angle of each follower to its swing-up balance angle under the limited communication ranges of robots. A local connectivity-preserving adaptive synchronized tracker is designed using the proposed DHSS with the estimate of the leader velocity and the swing-up balance angular velocity. In addition, we derive a technical lemma to analyze the asymptotic stability and the initial connectivity preservation of the overall closed-loop system in the Lyapunov sense.