Acceleration-Actuated Source Seeking Without Position and Velocity Sensing

Abstract

We study the problem of source seeking for an acceleration-controlled unicycle. The objective is to asymptotically stabilize the unicycle around states where a smooth position-dependent signal (or cost) function attains a minimum value. An implementation of the proposed control strategy only requires measurements of the cost function value at the current position. We do not assume that the unicycle can measure its current positions or its current forward velocity. For this purpose, we extend a recently introduced approach to extremum seeking control, which is based on the approximation of symmetric products of vector fields. An additional high-gain observer is used to estimate the derivative of the sensed cost signal. The estimates provided by the observer compensate for the missing velocity measurements and allow a reduction of the kinetic energy without velocity-dependent damping. Under suitable assumptions on the cost function, the control law leads to semi-global practical asymptotic stability.