Positioning Control of an Underactuated Surface Vessel An´ ıbal Matos and Nuno Cruz Faculdade de Engenharia da Universidade do Porto Instituto de Sistemas e Rob´ otica – Porto Rua Dr. Roberto Frias, 4200-465 Porto Portugal {anibal,nacruz}@fe.up.pt Abstract— This paper focuses on the positioning control of of a small size autonomous surface vessel (ASV) that can be used to carry a multitude of payload systems, including acoustic devices for underwater positioning and for communications with autonomous underwater vehicles. Its main motivation is the development of highly operational systems, by replacing typically moored support infrastructures with others that can dynamically position themselves. This work covers the design of feedback control laws that assure that the underactuated surface vessel Zarco can keep its position even in the presence of water currents and wind, and without special sensors to estimate such disturbances. Experi- mental results showing the performance of the designed control laws are also shown. I. I NTRODUCTION The last few years have witnessed the development of small autonomous boats, [1], [2], [3], as efficient tools for data collection missions, with an increasing number of applications. Some of these require the autonomous boat to hold its position at a given place. The problem of actively controlling large vessels to keep their position and orientation has already been addressed in an extensive number of works. Typically, the positioning control is assured by a sufficiently large (and even redundant) number of thrusters that allow for the direct rejection of detected disturbances. However, this approach is not appropriate to small size ASVs, since these vessels usually possess only two thrusters and the integration of additional ones would increase the size, weight and complexity of these platforms. The positioning control of underactuated vessels has already been addressed in several works, namely [4], [5]. In [4] it is shown that such vessels cannot be stabilized by a continuous state feedback of the state and a time-varying continuous feedback is proposed. Our work proposes a discontinuous feedback controller to assure the dynamic positioning of a small size vessel, without the need of extra thrusters, and presents experimental results obtained with the ASV Zarco (fig. 1). The feedback controller takes into account environmental disturbances on the vehicle motion caused by water currents and wind. The paper is organized as follows. Section II describes the ASV Zarco. Section III presents a dynamic model of the vehicle, while section IV addresses the kinematic and dynamic conditions that must be met when the vehicle is at rest. Section V discusses the proposed station keeping controller and, finally, in section VI, experimental results showing the behavior of the controller are presented. II. ZARCO ASV Zarco [6] is a small size craft designed to perform au- tonomous missions, mainly in rivers dams and estuarine en- vironments. It was built with the double purpose of carrying general payload systems for collecting data in those environ- ments, and of being a stationary or moving beacon for the navigation of underwater vehicles. Fig. 1. Zarco ASV. The vehicle is based on a catamaran type floating structure with 1.5 meters length and an overall width about 1 meter. In its basic configuration, Zarco weights a total of 50 kg, and has an additional payload capacity of more than 25 kg. The vehicle is powered by two electric motors capable of delivering a total thrust of 250 N, which allows for a maximum speed about 3 knots. The thrusters are located at the rear of the vehicle and their command allows the independent control of the vehicle forward and angular velocities. A set of easy replaceable rechargeable lead acid batteries provide energy for more than 4 hours of continuous operation. The vehicle also carries an on-board computer responsible for