Since the quadrotor unmanned aerial vehicle (UAV) is one of the systems that has four (4) control inputs and six (6) degree of freedom (DOF) which makes it as an underactuated system. Such underactuated mechatronic systems are very difficult to stabilize but at the same time these systems are power efficient and cost-effective because of a lower number of actuators. Later, if someone tries to stabilize this underactuated quadrotor UAV under the impact of unmodelled dynamic factors, it will lead to huge instability, low convergence rate, chattering effect, trajectory deviation and may also encounter some of the serious transient and steady state issues as well. This paper presents one of the adaptive-robust control algorithms, called the fuzzy based backstepping control (FBSC) design, to address the quadrotor�s helical trajectory tracking issue under an influence of unmodelled dynamic factors and external disturbances. This manuscript proposes the synthesis of the proposed FBSC design using MATLAB and Simulink software whereas these results are correlated with the conventional backstepping control (BSC) algorithm to show the effectiveness of the proposed algorithm by computing the integral absolute error values with and without disturbances. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.