# Bounded Attitude Control with Active Disturbance Rejection Capabilities for Multirotor UAVs
## 1 Introduction  
### Motivations and Background  
Research and development on unmanned aerial vehicles (UAVs) have shown enhancements in both the design and control of smaller and more economical aerial robots, which can be used in large-scale applications. Vertical take-off and landing (VTOL) multirotor vehicles have taken and consolidated their dominance in the market of small aircraft, also becoming a standard platform for aerial robotics research [1, 2, 3]. The abilities to evade obstacles, maneuver in confined spaces, hover in flight, collect data, and interact with different robots, make multirotors and mainly quadrotors able to solve endless problems, such as in search and rescue operations, temporary communication networks, aerial mapping, natural disaster monitoring, and kit delivery, to name a few [4]. Nowadays, the quadrotor's mathematical model is well known, and many control approaches have been proposed using different attitude representations, e.g., Euler angles, rotation matrices, or quaternions. An excellent overview of these approaches is shown in [5, 6] and references therein. However, most of the proposed control techniques are developed assuming slight attitude variations, knowledge of model parameters (to feedforward the nonlinearities), no bounds in the control signal, and the nonexistence of disturbances. In particular, PD, PID, and LQR controllers result in engaging solutions dueto their simplicity to real-time implementation [7], and have been applied to the attitude and position control of multirotor UAVs, for instance in [8; 9; 10; 11]. However, it is well known that proportional control cannot eliminate the impacts produced by disturbances (even constant ones), and a higher proportional control gain has to be designed to diminish the disturbance effects. In addition, when PID is used, the integral term could effectively reject the constant disturbance but achieves poor performance in the presence of time-varying disturbances. PID is also often implemented without the D part because of the noise sensitivity [12]. In recent years, the advances in sensing and onboard computing have driven the advancement of exceptionally small, innovative, and capable quadrotors, and so the variety of tasks and applications entrusted to these aircraft has increased. As a consequence, the before-mentioned assumptions are no longer valid. For instance, the disturbances in flight formation applications when quadrotors fly close to each other must be taken into account [13; 14; 15]. Other examples are the external forces and torques that a quadrotor might encounter within inspection applications, aerial manipulation, and load transportation, where the aircraft interacts physically with and flies near walls, surfaces, and objects in the environment [16; 17; 18; 19]. Furthermore, in many applications like agriculture and utility line inspection, the vehicles are subject to operating in a windy and complex environment, where aggressive attitude maneuvers are required to cope with external disturbances that affect their dynamic behavior [20; 21]. Two subsystems can be considered when dealing with mathematical models of under-actuated multirotors: rotational and translation dynamics [6]. These subsystems provide a cascade structure where translational motion is based on rotational dynamics [22]. Therefore, attitude control is the main part to fulfill trajectory-tracking in the space. This is not a simple task when considering both structural (parametric) and external disturbances. For these reasons, it is necessary to come back to the low-level control problem, i.e., the attitude control problem, and therefore to take into account explicitly in the control design model uncertainties, external disturbances, and signal control constraints. The disturbances-observed-based-control (DOBC) framework results are attractive in compensating for external disturbances and model uncertainties [23].