Chattering-free and finite-time estimation of the time-varying geometrical center for the multi-targets enclosing control problem

Abstract

This paper investigates the finite-time estimation of the time-varying Geometrical Center of Targets (GCT) in Multi-Target Enclosing Control Problem (MTECP). Existing estimators exhibit a chattering phenomenon that is harmful to the mechanical components of the deployed robots when forming the enclosing formation. We thereby propose two chattering-free finite-time estimators, employing a fully distributed approach demanding only the local observation and neighboring communication. The first fractional-order estimator is formulated by replacing the discontinuous term in the existing finite-time estimator by a fractional-order term, which remains smooth when the consensus error approaches zero. Theoretical results show that the estimation error can be stabilized into a bounded region adjustable by tuning the parameters. Then, another novel estimator with double integral architecture is designed to further eliminate the bounded estimation error in the first-order estimator i.e. can achieve exact tracking of the GCT in finite-time. Its continuity of estimation arises from the integration of a discontinuous unit-vector term and three more internal states are introduced to realize the double integral architecture. Finally, simulation and comparison results validate the correctness and smoothness of the proposed estimators.