New Schemes for GPS-Denied Source Localization Using a Nonholonomic Unicycle

Inspired by the extremum seeking (ES) algorithm, new approaches for source localization in global positioning system denied environments are presented using a nonholonomic unicycle. Existing ES-based schemes apply an excitation signal that causes difficulties in the analysis and performance of the unicycle. The aim of this brief is to develop schemes without employing any excitation signal. To this end, two control schemes are developed for tuning the forward and angular velocities of the unicycle. The first scheme only tunes the forward velocity and is based on the conventional form of ES. In this form, a high-frequency excitation signal (dither) is employed to find the gradient of an unknown function that is optimized. The proposed scheme benefits from the fact that the dither part already exists in the unicycle model. The second scheme only tunes the angular velocity and is based on the recently developed form of ES. In this form, the function that is optimized appears as the argument of a sine/cosine function. The presented scheme takes the advantage from the fact that the sine/cosine function of this form of ES already exists in the vehicle model. Both schemes are structurally simple and significantly improve the unicycle motion. A stability analysis of the schemes is carried out using the averaging theory and their performances are illustrated through carefully studied simulation examples.