A Distributed NSB Algorithm for Formation Path Following

This article presents a distributed null-space-based behavioral (NSB) algorithm for the formation path-following problem of vehicles moving in three dimensions. The algorithm is applied to fleets of underactuated autonomous underwater vehicles (AUVs). The algorithm combines null-space-based control with consensus methods. First, we present a continuous-time version of the algorithm and prove its stability using Lyapunov analysis. Then, we present a discrete-time event-triggered version that, compared to similar formation path-following methods, can achieve the same steady state-error performance with fewer inter-vehicle transmissions. The effectiveness of both the continuous-time and the discrete-time algorithm is verified in numerical simulations. Furthermore, the discrete-time version is tested in experiments.

I. Introduction

Autonomous underwater vehicles (AUVs) are being increasingly used in a number of applications such as transportation [1], oceanography [2], [3], and ocean energy industry-related tasks [4], [5]. In many applications, it is often advantageous to perform the tasks with a group of cooperating AUVs. Compared to a single vehicle, a group of AUVs can cover a larger area (e.g., in inspection and oceanographic tasks). A group is also more flexible, able to reconfigure if the mission parameters change, and able to complete the task even if one or more AUVs fail. In this article, we investigate the formation path-following problem, i.e., the problem of steering a group of AUVs along a predefined path in a given formation.