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In this paper, techniques from geometric mechanics and geometric nonlinear control theory are applied to modeling and construction of trajectory tracking algorithms for a free-swimming underwater vehicle that locomotes and maneuvers using a two-link actuated ldquotailrdquo and independently actuated ldquopectoral finrdquo bow planes. Restricting consideration of fluid forces to the simple effects of added mass and quasi-steady lift and drag, the resulting system model can be expressed in a control-affine structure. With particular choices of oscillatory actuation of the four system joints, maneuvers such as swimming forward, in and out of plane turning, surfacing, and diving can be constructed. Further, the vehicle and model can generate agile maneuvers such as snap turns. Trajectory tracking can then be produced using state error feedback. The methods are demonstrated both in simulation and in experiment using the University of Washington prototype fin-actuated underwater vehicle.