This article presents a holistic framework for the design, implementation and experimental validation of Battery Management Systems (BMS) in rotatory-wing Unmanned Aerial Vehicles (UAVs) that allows to accurately (i) estimate the State of Charge (SOC), and (ii) predict the End of Discharge (EOD) time of lithium-polymer batteries in small-size multirotors by using a model-based prognosis architecture that is efficient and feasible to implement in low-cost hardware. The proposed framework includes a simplified battery model that incorporates the electric load dependence, temperature dependence and SOC dependence by using the concept of Artificial Evolution to estimate some of its parameters, along with a novel Outer Feedback Correction Loop (OFCL) during the estimation stage which adjusts the variance of the process noise to diminish bias in Bayesian state estimation and helps to compensate problems associated with incorrect initial conditions in a non-observable dynamic system. Also, it provides an aerodynamic-based characterization of future power consumption profiles. A quadrotor has been used as validation platform. The results of this work will allow making decisions about the flight plan and having enough confidence in those decisions so that the mission objectives can be optimally achieved.