Morphing quadcopters have recently gained unprecedented popularity due to their flight flexibility, geometric reformation, and self-controlled arm management and the diversity of their applications. It has been established that in morphing quadcopter control, morphing formations in flight introduce time-varying parameters into the dynamic models, thereby increasing the complexity of the control problems, in addition to the non-linearity, coupling dynamics, and external disturbances present in the model. Thus, to address these challenges, this research therefore developed a robust backstepping sliding mode controller for morphing quadcopter position and orientation control. In the first stage, a mathematical model of an active morphing quadcopter (a foldable drone) was presented considering five morphing formations (X, H, T, O, and Y). Following the development of the system model, the proposed control method was designed in two stages: a high-performance sliding mode controller (HSMC) for attitude control to ensure chattering-free and fast convergence of the angles of orientation and a backstepping controller applied to position control were developed. Then, Lyapunov stability was used for an analysis of the stability of the closed-loop system. Finally, the robustness and effectiveness of the controller were investigated and benchmarked against a backstepping control approach using the mean square error and the sum of tracking errors as the performance metrics. The simulation results obtained show the effectiveness of the developed controller for the backstepping approach in the presence of parameter variations and external disturbances.