# A Comparative Study for Control of Quadrotor UAVs
## 1 Introduction  
The growth of the number of applications of Unmanned Aerial Vehicles (UAVs) in many different fields, from civilian to military applications, has experienced a big rise over the last decade. As highlighted in specific literature reviews [1, 2], the civilian applications of UAVs include activities such as parcel delivery, transportation of medical samples, mapping, surveillance, precision agriculture and greenhouses [3], population health monitoring, disaster recovery, personal use and photography, to name a few. The advantages due to the adoption of UAVs in each application domain have been widely reviewed. Just to give an example, considering the logistic domain discussed in [4], UAVs can contribute to optimizing the logistic process, reducing resources' usage, traffic and CO\({}_{2}\) emissions, inducing the diversification of transportation options as well as giving rise to new business models. Therefore, UAVs have gained significant interest from the engineering research world over the last two decades. In particular, quadrotors are the most researched and used type of UAVs because of their mechanical structure, which is relatively simple to model, their enhanced closed-loop stability with respect to other configurations and their high maneuverability in both indoor and outdoor spaces, as described in [5]. However, quadcopters aremechanic systems with nonlinear, multivariable, unstable, coupled and underactuated characteristics, which make the control not trivial. Literature reviews such as [6; 7; 8; 9] provide a comprehensive analysis of the main state-of-the-art control strategies for quadrotor UAVs. The well-known Proportional-Integral-Derivative (PID) control can effectively handle both linear and nonlinear systems. This is because it is model-independent and has a simple-to-understand tuning principle. Additionally, PID control can achieve zero steady-state error. On the other hand, PID control cannot handle constraints, is poorly robust with respect to disturbances and uncertainties and may require extensive tuning. The research in [10] implements a quadrotor attitude controller by means of a PID controller optimized with a genetic algorithm. The Linear-Quadratic Regulator (LQR) control approach is equivalent to solving an optimization problem, with the cost function weighted of the squared norms of tracking error and control input signals, under the constraint of satisfying the system's dynamics. It is designed with a linear approximation of the system and may not guarantee a zero steady-state error. LQR control can find an optimal feedback gain matrix considering both the tracking performances and the command input effort of the controller. The Feedback Linearization (FL) control approach consists of a systematic procedure to linearize the system with a model inversion and control it with a new control input term. The system is transformed into a linear system without any linearization assumption and can be controlled according to the linear control theory. FL performs well when the nonlinear plant is similar to the one used for control design, so it is not very robust to parametric uncertainties and cannot handle constraints. A feedback linearization attitude controller with proportional action is proposed in [11]. The Sliding Mode Control (SMC) approach aims at bringing the system state to the \"sliding surface\", which is a subset of the state space that corresponds to a desired dynamical behavior. The control law is the sum of a continuous function of the system's state and the reference, which guarantees that the \"sliding surface\" is invariant (once the state is on the sliding surface, it remains on it), and a discontinuous term for convergence to the \"sliding surface\". SMC shows, in general, good robustness to model uncertainties and disturbances, but a smooth approximation of the control law is necessary to avoid chattering, which may lead to instability.