In this paper, a robust Radial Basis Function (RBF) Backstepping Sliding Mode controller (BS-SMC) is successfully developed for the attitude stabilization and tracking the trajectory of two wheeled self-balancing mobile robot under the external disturbance and uncertainty. The design of BS control is derived based on Lyapunov function to ensure the stability of the robot system and the SMC is designed with a switching function in order to attenuate the effects of the disturbances, the auto-adjustable RBF inference system is suggested to estimate the equivalent component of the BS-SMC to treat the model dependency problem and robustness improvement. Also a cuckoo search (CS) optimization algorithm is used to determine the optimal values of the backsteeping sliding mode controller. Numerical simulations show the efficiency of the suggested controller in handling the balance and tracking problems of the two wheeled self-balancing mobile robot