Geometric formation control for autonomous underwater vehicles

This paper presents a novel approach based on Jacobi shape theory and geometric reduction for formation control of autonomous underwater vehicles (AUVs). We consider a three degree-of-freedom (DOF) dynamic model for the horizontal motion of each AUV that has control inputs over surge force and yaw moment. By using the Jacobi transform, the horizontal dynamics of AUVs are expressed as dynamics for formation shape, formation motion and vehicle orientation. The system decouples when additional symmetries in vehicle design are presented. Hence formation shape controllers, formation motion controllers, and vehicle orientation controllers can be designed separately. This approach reduces the complexity of formation controllers. We use the model for ODIN as an example to demonstrate the controller design process. Simulation results show the effectiveness of the controllers.