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3D nonholonomic source seeking without position measurement

We consider the three dimensional problem of directing a nonholonomic vehicle to seek the source of a scalar signal without the use of position information. If we assume the signal strength decays with distance from the source then we achieve convergence to the source by making use of the extremum seeking method. In the kinematic vehicle model we employ, the forward velocity is constrained to a constant and the control inputs are the yaw and pitch velocities. We present a control scheme which tunes these angular velocities and prove the local exponential convergence of this scheme. We also provide simulations which illustrate the behavior of the vehicle under different scenarios, such as static and moving sources, signal fields with spherical and elliptical level sets and parameter regimes not covered by theory.