Servos for Local Map Exploration Onboard Nonholonomic Vehicles for Extremum Seeking

Extremum seeking control (ESC) often employs perturbation-based estimates of derivatives for some sensor field or cost function. These estimates are generally obtained by simply multiplying the output of a single-unit sensor by some time-varying function. Previous work has focused on sinusoidal perturbations to generate derivative estimates with results for arbitrary order derivatives of scalar maps or higher up to third-order derivatives of multivariable maps. This work extends the perturbations from sinusoidal to bounded periodic or almost periodic functions and considers multivariable maps. A necessary and sufficient condition is given for determining if time-varying functions exist for estimating arbitrary order derivatives of multivariable maps for any given bounded periodic or almost periodic dither signal. These results are then used in a source seeking controller for a nonholonomic vehicle with a sensor actuated by servo. The conducted simulation and real-world experiments demonstrate that by distributing the local map exploration to a servo, the nonholonomic vehicle was able to achieve a faster convergence to the source.