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We consider a 3-D problem of steering a nonholonomic vehicle to seek an unknown source of a spatially distributed signal field without any position measurement. In the literature, there exists an extremum seeking-based strategy under a constant forward velocity and tunable pitch and yaw velocities. Obviously, the vehicle with a constant forward velocity may exhibit certain overshoots and cannot decelerate even it approaches the source. To resolve it, we propose a regulation strategy for the forward velocity along with the pitch and yaw velocities. Under such a strategy, the vehicle decelerates near the source and stays within a small area as if it comes to a full stop, and controllers for angular velocities become succinct. We prove the local exponential convergence via the averaging technique. Finally, the theoretical results are illustrated with simulations.

3-D Velocity Regulation for Nonholonomic Source Seeking Without Position Measurement