In this paper, an optimal bounded robust control algorithm for secure autonomous navigation in quadcopter vehicles is proposed. The controller is developed combining two parts; one dedicated to stabilize the closed-loop system and the second one for dealing and estimating external disturbances as well unknown nonlinearities inherent to the real system's operations. For bounding the energy used by the system during a mission and, without losing its robustness properties, the quadratic problem formulation is used considering the actuators system constraints. The resulting optimal bounded control scheme improves considerably the stability and robustness of the closed-loop system and at the same time bounds the motor control inputs. The controller is validated in real-time flights and in unconventional conditions for high wind-gusts and LoE-Loss of Effectiveness-in two rotors. The experimental results demonstrate the good performance of the proposed controller in both scenarios.