3-D Source Seeking for Underactuated Vehicles Without Position Measurement

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.