An MMB-MDS based approach to event-triggered affine formation control for multiples UUVs

This paper concentrates on the affine formation control problem for multiple unmanned underwater vehicles (UUVs) under mixed distance and bearing measurements. A distributed formation control strategy is developed to control all UUVs to a desired affine formation by integrating a mixed measurement based multi-dimensional scaling (MMB-MDS) algorithm and a discontinuous event-triggered mechanism. The control law design consists of two parts: one is a localization step using the MMB-MDS method to convert distance and bearing information into relative position information in a local coordinate frame, which reduces the complexity for stability analysis raised the mixture of distances and bearings; the other step is to control all UUVs under a distributed and discontinuous event-triggered based protocol to achieve a desired affine formation shape, which reduces the updating frequency of control inputs and communication. Simulation results are provided to illustrate the effectiveness of the proposed control schemes.