FSG-based divinable time-varying formation tracking of multiple Lagrangian agents with unknown disturbances and directed graphs

Abstract

In this paper, a flexible shape generator (FSG) is designed to achieve the divinable transformation process of the time-varying formation, and consider the FSG-based time-varying formation tracking (TVFT) problem of multiple Lagrangian agents with unknown disturbances and directed graphs. A hierarchical control algorithm is newly designed to achieve the control goal without using the prior information of the system model and bounded disturbances, and the specific implementation of the proposed hierarchical algorithms is also provided. By using the Hurwitz criterion and adaptive system theory, the sufficient conditions are derived and the stability analysis show that the formation tracking errors of the considered system are uniform ultimate bounded. Several simulation examples are performed on five two-degree-of-freedom mechanical arms to show the effectiveness of theoretical results.