Source Seeking With a Torque-Controlled Unicycle

We propose a novel source seeking method for a torque-controlled unicycle. Our control law leads to a positive constant forward velocity and an oscillatory rotational velocity with non-zero mean. Under suitable assumptions, we prove that the unicycle tends to a circular motion around the source. An implementation of the proposed method only requires real-time measurements of the unknown scalar signal. The feedback law for the torque involves a periodic large-amplitude high-frequency perturbation signal. A suitable averaging argument for mechanical systems under vibrational control reveals that the closed-loop system approximates the behavior of a certain averaged system. The motion of the averaged system is determined by a symmetric product of a vector field from the approximating closed-loop system. This symmetric product causes a torque which is given by the gradient of the unknown scalar signal. The gradient-based torque can lead to asymptotic stability for the averaged system, which in turn implies practical asymptotic stability for the approximating closed-loop system.