# Robust Control for a Slung-Mass Quadcopter Under Abrupt Velocity Changes
## 1 Introduction
In [23] the authors also developed a backstepping controller using Lyapunov theory for a quadrotor with a slung-mass system that drives the mass angular position to a desired trajectory. However, they check the controller's performance experimentally in a controlled environment using a VICON MoCap system. To ensure the stability of a quadrotor with suspended load, [PERSON] et al. [24] developed a Lyapunov-based control strategy to satisfy the restrictions on the load oscillation angles. Furthermore, the authors demonstrated in numerical results that the proposed control guarantees the restrictions on the rotation angle of the payload and also reduces energy consumption. [PERSON] et al. [25] considered the torque generated by the suspended load as a disturbance that directly affects the stability of the aircraft. Therefore, they proposed an algorithm based on an extended harmonic state observer to compensate the induced torque. Other works consider more challenging scenarios, [PERSON] et al. [26] present a nonlinear observer-based backstepping controller that can compensate the slung-load disturbances, partial rotor failures, and wind gusts. They validated their proposal through numerical simulation. [PERSON] et al. [27] present a simple control scheme based on the active compensation of sudden load changes, rejecting disturbances and preserving the controller characteristics and parameters. They validated their experimental scheme in a controlled environment using the Qualisys MoCap system. There are some cases in which the load mass is unknown such as in packages delivery, and to deal with this problem different solutions are proposed. [PERSON] et al. [28] propose nonlinear control algorithms for the thrust and the angular velocity of the quadrotor, and a mass estimation algorithm. These control laws are robust to variations of the load mass and ensure trajectory tracking convergence. They validated their results through numerical simulations and experimentally in a controlled environment using a MoCap system. [PERSON] et al. [29] propose an adaptive control law designed in the framework of backstepping to estimate the unknown load mass and compensate disturbances caused by the slung-loading subsystem. Many studies focus on controlling or reducing load oscillations during transportation by implementing various robust nonlinear and model-based controllers [30; 31; 32]. For example, in [33], the authors emphasize the importance of mitigating suspended load oscillations, as they affect quadrotor performance. The study analyzes the modeling and control of a quadrotor with a suspended load using sliding mode control, with simulations demonstrating the effectiveness of the proposed control strategy. [PERSON] et al. [34], develop an algorithm that reduces the swing angle of a person suspended under a helicopter by adjusting the cable length during movement. [PERSON] et al. [35] combine multiple surface sliding control (MSSC), radial basis function neural networks (RBFNN), and deep reinforcement learning (DQN) to stabilize trajectory tracking and suppress oscillations of the suspended load. The present work aims not only to reduce the oscillations of a suspended mass in a quadrotor but also to stabilize it in response to abrupt speed changes.