Nonlinear Model Predictive Control (NMPC) is widely used for controlling high-speed robotic systems such as quadrotors. However, its significant computational demands often hinder real-time feasibility and reliability, particularly in environments requiring robust obstacle avoidance. This paper proposes a novel SDC-Based Model Predictive Control (MPC) framework, which preserves the high-precision performance of NMPC while substantially reducing computational complexity by over 30%. By reformulating the nonlinear quadrotor dynamics through the State-Dependent Coefficient (SDC) method, the original nonlinear program problem is transformed into a sequential quadratic optimization problem. The controller integrates an integral action to eliminate steady-state tracking errors and imposes constraints for safety-critical obstacle avoidance. Additionally, a disturbance estimator is incorporated to enhance robustness against external perturbations. Simulation results demonstrate that the SDC-Based MPC achieves comparable tracking accuracy to NMPC, with greater efficiency in terms of computation times, thereby improving its suitability for real-time applications. Theoretical analysis further establishes the stability and recursive feasibility of the proposed approach.