IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 2, APRIL 2008 59 Open-Loop Control of a Multifin Biorobotic Rigid Underwater Vehicle Alberico Menozzi, Member, IEEE, Henry A. Leinhos, Member, IEEE, David N. Beal, and Promode R. Bandyopadhyay, Member, IEEE Abstract—This paper presents an open-loop control system for a new experimental vehicle, named the biorobotic autonomous un- derwater vehicle (BAUV). The rigid cylindrical hull of the vehicle is attached with six strategically located fins to produce forces and moments in all orthogonal directions and axes with minimal redun- dancy. The fins are penguin-wing inspired and they implement the unsteady high-lift principle found widely in swimming and flying animals. The goal has been to design an underwater vehicle that is highly maneuverable by taking the inspiration from nature where unsteady hydrodynamic principles of lift generation and the phase synchronization of fins are common. We use cycle-averaged experi- mental data to analyze the hydrodynamic forces and moments pro- duced by a single foil as a function of its kinematic motion parame- ters. Given this analysis, we describe a method for synthesizing and coordinating the sinusoidal motion of all six foils to produce any desired resultant mean force and moment vectors on the vehicle. The mathematics behind the resulting algorithm is elegant and ef- fective, yielding compact and efficient implementation code. The solution method also considers and accommodates the inherent physical constraints of the foil actuators. We present laboratory experimental results that demonstrate the solution method and the vehicle’s resulting high maneuverability. Index Terms—Autonomous underwater vehicle (AUV), biorobotics, high lift, maneuverability, open-loop control. I. INTRODUCTION N ATURAL flyers and swimmers have evolved to skillfully utilize physical principles from unsteady hydrodynamics to achieve high maneuverability and efficiency [1]–[6]. Man- made autonomous underwater vehicles (AUVs), on the other hand, have been conceived and operated for decades to either re- main safely within the realm of steady hydrodynamics—where the design of vehicle body, actuation mechanisms, and control system is simpler to understand and implement—or to avoid the issue altogether by using a number of thrusters to push an arbi- trarily shaped body through the water. This has often resulted Manuscript received July 20, 2007; revised December 7, 2007; accepted Feb- ruary 4, 2008. First published September 12, 2008; current version published October 31, 2008. This work was carried out at the Naval Undersea Warfare Center, Newport, RI, with sponsorship of the Cognitive and Neurosciences Pro- gram of the U.S. Office of Naval Research (PI: P. R. Bandyopadhyay). Associate Editor: F. S. Hover. A. Menozzi was with the Naval Undersea Warfare Center Division, Newport, RI 02841 USA. He is now with the Applied Research Associates, Inc., Raleigh, NC 27615 USA (e-mail: amenozzi@ara.com). H. A. Leinhos, D. N. Beal, and P. R. Bandyopadhyay are with the Naval Undersea Warfare Center Division, Newport, RI 02841 USA (e-mail: leinhosha@npt.nuwc.navy.mil; bealdn@npt.nuwc.navy.mil; bandyopad- hyaypr@npt.nuwc.navy.mil). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JOE.2008.918687 Fig. 1. NUWC’s BAUV prototype maneuvers efficiently by making use of un- steady hydrodynamics. It swims by coordinating the motion of six high-lift foils attached to its hull. These foils have been shown to generate forces more effi- ciently than conventional thrusters [7]. Inset shows foil cross section. in efficient cruising, but not in efficient maneuvering and has led to inefficiencies in energy consumption. This paper presents an innovative open-loop control system approach for a new ve- hicle, resulting in efficient maneuvering through the exploita- tion of unsteady hydrodynamics. The vehicle swims by coor- dinating the motion of six biology-inspired high-lift foils that are attached to its rigid cylindrical hull (see Fig. 1). Because of this connection to biology, this vehicle has been named the biorobotic AUV (BAUV). Bandyopadhyay et al. [7], [8] have conducted unsteady hydrodynamics experiments in the low-speed towing tank at the Naval Undersea Warfare Center (NUWC, Newport, RI), showing that these oscillating foils produce steering forces more efficiently than thrusters do. We use a cycle-averaged subset of these experimental data to perform an engineering analysis of hydrodynamic forces and moments produced by a single foil as a function of its motion parameters. After establishing the relationships between the motion parameters and the magnitude and direction of the corresponding mean forces and moments, we discuss a method for combining the sinusoidal motion of all six foils to produce any desired resultant mean force and moment on the vehicle. The method is centered on solving a linear system , where contains our knowledge of each foil’s force production characteristics and placement on the vehicle, and is the solution that yields the right combination of individual foil force vectors, which is ultimately a combination of sinusoidal motions, to produce any desired mean force-moment resultant . The solution is optimal with respect to power consumption, is computationally efficient, and generalizes to any situation where multiple vec- tored thrusts act on a rigid body. In addition, we show how to 0364-9059/$25.00 © 2008 IEEE