General Framework using Affine Transformations to Formation Control Design

This paper deals with the control of a fleet of non-linear systems representing AUVs (autonomous underwater vehicles). This paper proposes a novel framework which is able to express in a simple manner the control law for a larger class of formations, including time-varying formations. This has been produced by applying a sequence of affine transformations such as translations, rotations and scalings. A cooperative control law based on consensus algorithms is added to reach the same formation and to achieve the uniform distribution of all the agents along the formation. This is achieved taking into account the communication constraints using a cooperative control which includes the Laplacian matrix of the communication graph. Several simulations are provided to illustrate the convergence.