The performances of braking control systems for robotic platforms, e.g., assisted and autonomous vehicles, airplanes and drones, are deeply influenced by the road-tire friction experienced during the maneuver. Therefore, the availability of accurate estimation algorithms is of major importance in the development of advanced control schemes. The focus of this paper is on the estimation problem. In particular, a novel estimation algorithm is proposed, based on a multi-layer neural network. The training is based on a synthetic data set, derived from a widely used friction model. The open loop performances of the proposed algorithm are evaluated in a number of simulated scenarios. Moreover, different control schemes are used to test the closed loop scenario, where the estimated optimal slip is used as the set-point. The experimental results and the comparison with a model based baseline show that the proposed approach can provide an effective best slip estimation.