IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 33, NO. 4, OCTOBER 2008 563 Synchronization of Animal-Inspired Multiple High-Lift Fins in an Underwater Vehicle Using Olivo–Cerebellar Dynamics Promode R. Bandyopadhyay, Member, IEEE, Sahjendra N. Singh, Senior Member, IEEE, Daniel P. Thivierge, Anuradha M. Annaswamy, Fellow, IEEE, Henry A. Leinhos, Albert R. Fredette, and David N. Beal Abstract—The development of neuroscience-based control methodologies and their integration with the high-lift unsteady hydrodynamics of control surfaces inspired by swimming and flying animals are the subjects of this paper. A biology-inspired rigid autonomous undersea vehicle called the biorobotic au- tonomous undersea vehicle (BAUV) has been developed at the Naval Undersea Warfare Center (NUWC), Newport, RI. The BAUV is equipped with six simultaneously rolling and pitching fins for generating large unsteady control forces for performing agile maneuvers. First, as an exploratory example, we introduce the van der Pol oscillator as an oscillatory controller for the BAUV and we describe experiments performed to examine the fin forces (thrust and lift) and electric power requirement, and to demon- strate the effectiveness of the oscillator’s limit cycle property for disturbance rejection effectiveness. We then describe a BAUV control system that includes six inferior-olive (IO) neuron models for control of the pitch and roll motion of the six foils. These IO neurons exhibit limit cycle oscillation (LCO). For control of the BAUV, these IO neurons must oscillate in synchronism with specific relative phases. We present here four feedback linearizing control systems of varying complexity for control of the relative phases of the IO neurons. It is shown that each of the IO control systems accomplishes asymptotic regulation of the phases and thus enables the foils to produce the required control forces. The first controller has a global synchronization property, but the remaining controllers accomplish local synchronization. We present simulation results for tracking piecewise, time-varying phase angle commands as well as experimental results for control of the BAUV by IO neurons. The results show that with appro- priate phasing of the fins, an optimal graceful gait of the BAUV is achieved where no untoward force or moment is present. An analog hardware version of the local controller with a cluster of six IO neurons has also been built, which allows five of the signals to rapidly synchronize to the reference, with or without prescribed phase shift, much like in the simulations. The designed controllers Manuscript received July 09, 2007; revised June 05, 2008; accepted August 21, 2008. Current version published February 06, 2009. This work was sup- ported by the Cognitive and Neurosciences Program of the U.S. Office of Naval Research, program officer Dr. T. McKenna. The research was carried out at the Naval Undersea Warfare Center, Newport, RI. Associate Editor: F. S. Hover. P. R. Bandyopadhyay, D. P. Thivierge, H. A. Leinhos, A. R. Fredette, and D. N. Beal are with the Autonomous Systems and Technology Depart- ment, Naval Undersea Warfare Center (NUWC), Newport, RI 02841-1708 USA (e-mail:promode.bandyopadhya@navy.mil; daniel.thivierge@navy.mil, henry.leinhos@navy.mil, albert.fredette@navy.mil, david.beal@navy.mil). S. N. Singh is with the University of Nevada, Las Vegas, NV 89154 USA (e-mail: sahaj@ee.unlv.edu). A. M. Annaswamy is with the Active-Adaptive Control Laboratory and the Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: aanna@mit.edu). 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.2008.2005356 can be used in any platform or multivariate BAUV-like system requiring fast, accurate phase control. Laboratory test results for the phase synchronization of two servomotors (roll and pitch) using the designed analog hardware controller are also shown. Index Terms—Biorobotic autonomous undersea vehicle (BAUV), feedback linearization, inferior olives (IOs), olivo–cerebellar con- trol, phase synchronization. I. INTRODUCTION W E marvel at the seeming grace with which swimming and flying animals maneuver. They have many control surfaces that seem perfectly synchronized, resulting in a motion that is free of undesired forces and moments. One assumes that this is efficient. We have been inspired by the works of Ellington [1] and Dickinson et al. [2], which show that the fins of flying insects undergo dynamic stall whereby a leading edge vortex is formed, resulting in high-lift that helps the insects stay aloft in a low-density-medium-like air. There is evidence that swimming animals also have pectoral fins undergoing dynamic stall. Due to the inviscid nature of dynamic stall, scaling has not been an issue. At the Naval Undersea Warfare Center (NUWC), New- port, RI, we have built a biorobotic underwater vehicle (BAUV) that has unprecedented maneuverability, is extremely quiet, and is energy efficient like animals of similar volumetric displace- ment [3]–[6]. This BAUV basically is a rigid cylinder to which six penguin-like fins are attached. We have succeeded in de- veloping open-loop and closed-loop engineering controllers for this vehicle. However, there are limitations of those controllers and the purpose of this paper is to report the development of a neuroscience-inspired fin phase synchronization controller that can act almost instantaneously and does not need any knowledge of the hydrodynamic characteristics of the fins because they will be optimized in real time, as needed. When a human steps on water or ice and becomes unbalanced, the neurons in the infe- rior-olive (IO) part of the brain are known to redistribute the mass promptly to bring balance to the gait [7]. Control of the BAUV, with multiple high-lift fins that produce high levels of instantaneous forces and moments, appears to be an analogous problem. Synchronized IO oscillations near 10 Hz have been observed in animals and they function as motor timing signal [8]. This ability originates from the properties of four nonlinear ordinary differential equations which describe the IO dynamics. We therefore took the IO neuron dynamics as the foundation for developing a fin phase synchronization controller. 0364-9059/$25.00 © 2008 IEEE