Control of Underwater Vehicles in Inviscid Fluids. I: Irrotational Flows

TL;DR

This paper studies the controllability of underwater vehicles in inviscid, irrotational fluids, demonstrating local controllability results using boundary flow controls and Coron's return method for various control configurations.

Contribution

It introduces a finite-dimensional control system for underwater vehicles in irrotational fluids and applies Coron's return method to establish local controllability results.

Findings

Controllability achieved with six, four, or three control inputs.

Finite-dimensional model similar to Kirchhoff laws.

Local controllability results for vehicle position and velocity.

Abstract

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron's return method, we establish some local controllability results for the position and velocities of the underwater vehicle. Examples with six, four, or only three controls inputs are given for a vehicule with an ellipsoidal shape.