Extremum seeking control of a nonholonomic mobile robot with limited field of view

We present an extremum seeking control (ESC) scheme for mobile robots with nonholonomic constraints. Many sensors, such as cameras, have a limited field of view. If a target function is based on such sensors, correct robot orientation is critical for optimizing the target function. Our approach is novel in that it will maximize a target function that is a function of robot position and orientation, while overcoming the nonholonomic constraints that prevent simple motion along the gradient of all degrees of freedom. Stability analysis proves our ESC scheme is well behaved and the robot will settle in the neighborhood of a maximum of the target function. Simulation results elucidate performance for different tasks.