*Article* **A Path-Following Controller for Marine Vehicles Using a Two-Scale Inner-Outer Loop Approach**

**Pramod Maurya 1,\*, Helio Mitio Morishita 2, Antonio Pascoal <sup>3</sup> and A. Pedro Aguiar <sup>4</sup>**


**Abstract:** This article addresses the problem of path following of marine vehicles along straight lines in the presence of currents by resorting to an inner-outer control loop strategy, with due account for the presence of currents. The inner-outer loop control structures exhibit a fast-slow temporal scale separation that yields simple "rules of thumb" for controller tuning. Stated intuitively, the inner-loop dynamics should be much faster than those of the outer loop. Conceptually, the procedure described has three key advantages: (i) it decouples the design of the inner and outer control loops, (ii) the structure of the outer-loop controller does not require exact knowledge of the vehicle dynamics, and (iii) it provides practitioners a very convenient method to effectively implement path-following controllers on a wide range of vehicles. The path-following controller discussed in this article is designed at the kinematic outer loop that commands the inner loop with the desired heading angles while the vehicle moves at an approximately constant speed. The key underlying idea is to provide a seamless implementation of path-following control algorithms on heterogeneous vehicles, which are often equipped with heading autopilots. To this end, we assume that the heading control system is characterized in terms of an IOS-like relationship without detailed knowledge of vehicle dynamics parameters. This paper quantitatively evaluates the combined inner-outer loop to obtain a relationship for assessing the combined system's stability. The methods used are based on nonlinear control theory, wherein the cascade and feedback systems of interest are characterized in terms of their IOS properties. We use the IOS small-gain theorem to obtain quantitative relationships for controller tuning that are applicable to a broad range of marine vehicles. Tests with AUVs and one ASV in real-life conditions have shown the efficacy of the path-following control structure developed.

**Keywords:** path following; inner-outer loop control; input-to-output stability; AUVs; ASVs
