Newton Nonholonomic Source Seeking for Distance-Dependent Maps

The topics of source seeking and Newton-based extremum seeking have flourished, independently, but never combined. We present the first Newton-based source seeking algorithm for a unicycle vehicle model. The algorithm employs forward velocity tuning, as in the very first source seeker for the unicycle, and incorporates an additional Riccati filter for inverting the Hessian and feeding it into the demodulation signal. Using second-order Lie bracket averaging, we prove convergence to the source at a rate that is independent of the unknown Hessian of the map. The result is semiglobal and practical for a map that is quadratic in the distance from the source. This article presents a theory and simulations that show the advantage of Newton-based over the gradient-based source seeking.