In this article, we present the design and experimental validation of source-seeking control algorithms for a unicycle mobile robot that is equipped with novel 3-D-printed flexible graphene-based piezoresistive airflow sensors. Based solely on a local gradient measurement from the airflow sensors, we propose and analyze a projected gradient ascent algorithm to solve the source-seeking problem. In the case of partial sensor failure, we propose a combination of extremum-seeking control with our projected gradient ascent algorithm. For both control laws, we prove the asymptotic convergence of the robot to the source. Numerical simulations were performed to validate the algorithms, and experimental validations are presented to demonstrate the efficacy of the proposed methods.