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This paper presents an open-loop control system for a new experimental vehicle, named the biorobotic autonomous underwater 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 redundancy. 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 experimental data to analyze the hydrodynamic forces and moments produced by a single foil as a function of its kinematic motion parameters. 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 effective, 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.