<p>The disturbances of wind fields and collisions introduce additional uncertain disturbance during the collision deicing process of UAV suspended load. The UAV suspension system’s position and attitude models are established separately based on traditional method such as Newton–Euler. Consequently, the introduction of multiple algebraic methods, including position vector and Euler angle, increases computational complexity. Accordingly, the system response delays and the control accuracy cannot meet the mission requirements. Therefore, it is essential to find a method for integrated position–attitude modeling and control. To address this problem, this paper proposes a collision dynamic model for a quadrotor UAV suspension system based on twistor. This twistor provides a unified description of translational and rotational motion. In addition, the introduction of twistor avoids the normalization constraints and parameter redundancy in dual quaternion. The stability of the UAV cannot be ensured due to the uncertain disturbances introduced by the wind field and collisions. As a result, there is a need to design a strong disturbance rejection controller. To mitigate impacts of these disturbances, a fuzzy sliding mode controller within the twistor framework is presented. Lyapunov theory and LaSalle invariance principles are used to prove the stability of the system. The simulation demonstrates that the fuzzy sliding mode controller within the twistor framework effectively ensures the stability and adaptability of the quadrotor UAV suspended system under the disturbances of wind fields and collisions.</p>