# A Comparative Study for Control of Quadrotor UAVs
## 1 Introduction
The Model Predictive Control (MPC) approach solves an optimization problem at each defined time step to compute the optimal control input, satisfying the system's dynamics, input and state constraints. A prediction model is exploited to predict the future states of the system. MPC is quite robust to disturbances but may be slow in tracking. The MPC-based position trajectory controller designed in [12], despite exploiting a linear model for prediction, shows the ability to ensure tracking of complex trajectories. Furthermore, other control laws can be effectively applied to quadrotors, such as H-infinity, Backstepping, Adaptive, Fuzzy and Neural Network control. A Backstepping controller for position control of a quadrotor helicopter is designed and validated in [13], with stability being proven by the Lyapunov method. Additionally, a Fuzzy Logic controller for attitude control has been proposed in [14]. An L\({}_{1}\) adaptive controller is designed and validated in [15] for the attitude controller of a mini-UAV. Adaptive control does not need a parameter tuning procedure and deals with parametric uncertainties and unmodelled dynamics. The Sliding Mode-based adaptive controller with Proportional-Integral-Derivative gains proposed in [16] controls a micro-UAV, the Parrot Mambo Minidrone, and is demonstrated on a model-based platform. In [17], an adaptive controller is proven to be able to deal with parametric uncertainties and external disturbances and performs well with unknown time delays inserted in the closed-loop dynamics. In this paper, a comparative study of 3D trajectory control of a quadrotor system is proposed. The control system is decoupled into an outer loop for trajectory control and an inner loop for attitude control; input saturation is also taken into account. Despite several reviews of control algorithms for quadrotors being proposed in the literature, such as [6; 7; 8; 9] to state a few, there is, to the best extent of our knowledge, poor availability of comparative studies where several approaches are implemented and discussed. The comparative study proposed in [18] implements PID, LQR, Fuzzy and Adaptive controllers for position trajectory tracking, while PID, LQR and MPC-based attitude stabilizers are implemented and discussed in [19]. In order to enlarge the available state of the art of quantitative comparative performance evaluation for quadrotors' control, we propose a broad comparative implementation of different control approaches (PID, LQR, MPC, FL and SMC) to the quadrotor attitude stabilization problem. Linearized or simplified attitude dynamical systems are exploited in the design phase, yet all the controllers are tested with the proposed full nonlinear model. According to the fast dynamic response, the robustness to the discrepancy between the control model and the full nonlinear model and an approximative L\({}_{2}\) norm-based trade-off evaluation of both the tracking performance and the command effort of the controller, the most suitable method is selected for the inner loop control part of the complete proposed control architecture. The outer loop is designed to track velocity references by exploiting PID control and a dynamics inversion from a simplified translational dynamical model. This paper is organized as follows. The system model derived with the Newton-Euler formalism is reported in Section 2, as well as the proposed control system architecture, the proposed control laws and the simulation parameters setting. Section 3 presents the simulation results in which a micro-UAV is demonstrated to be able to execute complex trajectories with the complete control system. Conclusions and future research directions are drawn in Section 4.