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Our past work introduced source seeking methods for GPS-denied autonomous vehicles using only local signal measurement and operating in two dimensions. In this paper, we extend these results to three dimensions. The 3-D extensions introduce many interesting challenges, including the choice of vehicle models in 3-D, sensor placement to allow probing-based gradient estimation of an unknown signal field in 3-D, the question of what type of pattern of vehicle motion can be produced in an underactuated 3-D vehicle to allow tuning by single-loop or multiloop extremum seeking, and the shape of attractors, which become very complex in 3-D. We present two control schemes that address these questions. The first scheme focuses on vehicles with a constant forward velocity and the ability to actuate pitch and yaw velocities. The second scheme employs vehicles with constant forward and pitch velocities and actuate only the roll velocity. Our results include convergence analysis and simulation results.

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In this paper, we present a method of locomotion control for underwater vehicles that are propelled by a periodic deformation of the vehicle body, which is similar to the way a fish moves. We have developed control laws employing "extremum seeking" for two different "fish" models. The first model consists of three rigid body links and relies on a 2-degree-of-freedom (DOF) movement that propels the fish without relying on vortices. The second fish model uses a Joukowski airfoil that has only 1 DOF in its movement and, thus, relies on vortex shedding for propulsion. We achieve model-free and position-free "source seeking," and, if position is available, navigation along a predetermined path.