Distributed Newton and Quasi-Newton methods for formation control of autonomous vehicles
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2019, 2019 Informa UK Limited, trading as Taylor & Francis Group. This paper presents a distributed approach based on a Newton-type method for solving the fast formation problems of a group of autonomous underwater vehicles (AUVs) in the plane. Each AUV of this group aims at minimising its own local alignment error function that formulates the difference between the desired relative formation of the AUV and its neighbours and their current positions. In addition, the group jointly minimises the total cost composed by local alignment error functions. The presented approach utilises a modified Jacobi algorithm based on local position data to approximate the Newton direction. It is shown that when combining the descent direction with distributed line search algorithms, the approach exhibits the performance of super-linear convergence within the neighbourhood of the desired position. Two numerical examples are considered here to illustrate that using the proposed approach, all AUVs rapidly achieve the desired formation from any initial configuration and initial position in both static and dynamic formation scenarios.
