Velocity regulation in 3D nonholonomic source seeking

We consider the three dimensional problem of steering a nonholonomic vehicle to seek the the source of an unknown, spatially distributed signal field without position measurement. In the literature, there exists an extremum seeking-based strategy keeping the forward velocity constant and tuning the pitch and yaw velocities. However, in this case the vehicle revolves around the source with a relatively large forward velocity when it converges near the source, which leads to complexities in the asymptotic behavior of the vehicle. In this paper, we tune the forward velocity along with the pitch and yaw velocities, with the intent of slowing down the vehicle around the source. Our control scheme also extends the two dimension case with both forward and angular velocities tunable. We present a theoretical analysis of the control scheme and simulations which illustrate the behavior of the vehicle under different scenarios.