# Robust Control for a Slung-Mass Quadcopter Under Abrupt Velocity Changes
## 1 Introduction  
Many important practical situations require rapid deployment of Unmanned Aerial Vehicles (UAVs) for delivery of cargo, for example immediately after a natural disaster or an industrial accident, since these emergency situations require faster delivery times compared to traditional methods [1; 2]. In [3] the authors set the stage for the delivery of first aid kits to people lost in a forest, which is an environment crowded with vertical obstacles, such as the tree trunks. The use of a quadrotor aircraft is proposed, which must make the delivery of the package by overcoming the obstacles. In this case, experimental tests were performed in a controlled environment using a Motion Capture (MoCap) system, obtaining good results. Despite the wide range of applications, the transport of loads with quadrotors still represents an important challenge, since these aerial vehicles are by themselves multivariable systems, subactuated, highly nonlinear, and when adding the load its dynamics becomes even more complex [4; 5; 6]. To deal with this problem different solutions have been proposed whose main objective is to reduce the slung-mass oscillations that negatively impact the quadrotor's flight stability. One of those solutions is the use of multi-agents for cooperative load transport proposed by the authors in [7; 8; 9; 10] using two quadrotors while in [11] the use of three or more aerial vehicles is proposed in [12]. Although it has been shown that the use of multiple robots in cooperative tasks increases robustness against external disturbances, it also results in a system too expensive for small loads. Therefore, the most popular solution is the use of a single quadrotor UAV for transporting loads [13; 14; 15; 16]. In [17] the authors present a set of several suspended load methods using a UAV or a swarm of UAVs. However, these strategies are only implemented in a numerical simulation without checking their performance in real-time to observe the possible effect that the suspended load could have in outdoor environments. There exist two main proposals for the fastening the load: cable transport and handling with robotic arms. These methods have advantages and disadvantages: the robotic arm is more practicalfor gripping and releasing cargo, yet it adds extra weight to the aircraft, is expensive, and consumes a considerable amount of energy. The use of the cable does not have these disadvantages, which is why in this work this method is used for the transport of load with a quadrotor aircraft. As mentioned above, many works use a cable to transport a suspended load with a quadrotor due to its low cost and weight. However, the oscillations produced by the load represent a problem because they affect the performance of the flight of the aircraft, compromising its stability and trajectory [18]. [PERSON] et al. [19] developed a controller using the backstepping approach and Lyapunov theory to solve the tracking problem of a cable-suspended mass. Although the results confirm the effectiveness of the controller, only simulation tests are presented. [PERSON] et al. [20] proposed an optimized sliding mode control through an intelligent fuzzy genetic algorithm; their simulation results corroborate the robustness of the proposed method. [PERSON] et al. [21] developed a robust Fractional-Order Sliding Mode Control (FOSMC) to control the altitude, position and attitude of the quadrotor. A delayed feedback based anti-swing controller was also installed to limit the swing angle of the suspended load. MATLAB SIMULINK software was used to test and simulate the suggested controller. [PERSON] et al. [22] designed a Finite-Time Neuro-Sliding Mode Controller (FTNSMC) for a quadrotor with a suspended payload that is subject to parametric uncertainties and external disturbances. Numerical simulations to demonstrate the effectiveness of the proposed controller were presented.