Stability on Adaptive NN Formation Control with Variant Formation Patterns and Interaction Topologies

Abstract

The formation task achieved by multiple robots is a tough issue in practice, because of the limitations of the sensing abilities and communicating functions among them. This paper investigates the decentralized formation control in case of parameter uncertainties, bounded disturbances, and variant interactions among robots. To design decentralized controller, a formation description is firstly proposed, which consists of two aspects in terms of formation pattern and interaction topology. Then the formation control using adaptive neural network (ANN) is proposed based on the relative error derived from formation description. From the analysis on stability of the formation control under invariant/variant formation pattern and interaction topology, it is concluded that if formation pattern is of class Ck, k ≥1, and interaction graph is connected and changed with finite times, the convergence of the formation control is guaranteed, so that robots must form the formation described by the formation pattern.