Stabilization and nonlinear control for a novel trirotor mini-aircraft
Introduction
An increasing interest for autonomous mini-aerial vehicles exists due to the growing number of civil and military applications of UAV (unmanned aerial vehicles) (Alderete, 1995, Castillo et al., 2004, Horn et al., 2005, Kendoul et al., 2007, Lozano et al., 2004, Muratet et al., 2005). The improvement of the capabilities of the existing flying vehicles requires contributions from different disciplines including aeronautics, electronics, signal processing, automatic control, computer science, sensors, etc. This is pointed out in international meetings like the UAV-MMNT03 in Sydney (UAV-MMNT03 Sydney, Australia, July 2003).
One of the current trends in UAV's is the development of small flying machines capable of performing hover as well as forward flight (Rahideh et al., 2008, Salazar-Cruz et al., 2007). Even though some efforts are devoted to improve the classical helicopter structure (Reid, 1996, Tanaka et al., 2004), there are some new aerodynamical configurations that present important features. The quadrotor is an interesting alternative to the classical helicopter. A quadrotor is mechanically simpler than a helicopter since it has propellers with constant pitch and does not require a swashplate. The quadrotor maintenance is therefore simpler than that of a classical helicopter.
In view of the interest for the development of micro-UAV's, several different aerodynamical configurations have been studied (Escareno et al., 2006, Kendoul et al., 2006). The paper focus on a multirotor rotorcraft having only three rotors with constant pitch propellers and no swashplate. It is clear that one of the advantages of trirotors with respect to quadrotors is that they require one motor less which can lead to a reduction in weight, volume and energy consumption. The challenge is to find a control strategy such that the trirotor configuration is able to perform as a classical helicopter. According to literature, few studies have been carried out for such configuration.
The work presented in this paper focuses on the trirotor helicopter depicted in Fig. 1 which was built using off-the-shelf components. The two main rotors in the forward part of the rotorcraft rotate in opposite directions and are fixed to the aircraft frame. Since the two front rotors rotate in opposite directions, the generated reaction torque is almost zero. The tail rotor can be tilted using a servomechanism in order to produce a yaw torque. The angular velocity of the two main rotors can be adjusted to produce the main thrust as well as the roll torque. The roll torque is obtained as a function of the angular speed difference of the two main rotors. Finally, the pitch torque is obtained by varying the angular speed of the tail rotor. There exist, however, several coupling phenomena which will be clarified in the paper. Three additional gyros have been added and some structural modification have done so that the trirotor can be manually controlled by a pilot. The pilot is not required to be highly skilled to be able to control the trirotor.
This paper presents a dynamical model of the trirotor rotorcraft using the Euler–Lagrange approach. The nonlinear model is then used to design a nonlinear controller. The control algorithm used to stabilize the aircraft takes into account the actuator's limitations (Khalil, 2002, Olfati-Saber, 2000). The controller proposed in this work is based on the technique of nested saturations (Teel, 1992). It is proved that the control algorithm is such that the state of the aircraft converges to the origin. The controller's performance has been tested in real-time experiments. The obtained results show that the controller performs satisfactorily in real-time applications.
Section snippets
Modeling of the trirotor
This section presents the model of a trirotor rotorcraft using the Euler–Lagrange approach (Fantoni & Lozano, 2002). The generalized coordinates describing the rotorcraft position and orientation arewhere denotes the position of the center of mass of the three-rotor aircraft relative to the inertial frame and , and are the three Euler angles yaw, pitch and roll and represent the orientation of the rotorcraft (see Fig. 2). Therefore, the model can be naturally separated
Nonlinear control law with nested saturations
This section presents a control strategy for stabilizing the trirotor when operating at hover. It will be shown that the closed-loop system is globally stable. Furthermore, the proposed controller design follows the ideas of Castillo et al. (2004) and is such that the resulting controller is relatively simple as compared to other controllers proposed in the literature (Marconi et al., 2002, Olfati-Saber, 2000).
The collective input in (17) is essentially used to make the altitude reach a
Experimental results
This section presents real-time experimental results obtained using the proposed controller when applied to the trirotor. A trirotor was built using spare parts of the commercial Draganfly quadrotor. A servo has been added to be able to tilt the tail rotor. Several other modifications were required to make it fly properly. The control inputs are transmitted to the rotorcraft using a commercial Futaba radio. The radio joystick potentiometers have been connected to a desk PC computer using the
Conclusions
A novel trirotor mini-rotorcraft which presents several advantages with respect to classical helicopters and quadrotors has been presented in this paper. The trirotor is mechanically simpler since it does not require a swashplate or variable pitch blades as classical helicopters. Contrary to quadrotors, the trirotor is not only suitable for hovering tasks but is also better adapted for forward flight. A trirotor is more compact than a quadrotor and has lower energy consumption. This paper has
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2013, Journal of the Franklin InstituteCitation Excerpt :The last decade has seen many successfully developed platforms of micro-UAVs, especially the quadrotor UAV, such as Australia National University's X-4 flyer aircraft prototype [1–4], the Stanford University's STARMAC quadrotor [5,6], the Swiss Federal Institute's OS4 aircraft prototype [7], and the University of Pennsylvania's Grasp micro-UAV test bed [8]. Many researchers have developed the control system of quadrotor UAV using kinds of method such as feedback linearization [9,10], back-stepping [10,11], sliding-mode [12], dynamic inversion [13], and Lyapunov function design method [14–17]. In recent years, one tendency in the research of UAV is to advance the function of the UAV beyond simple motion and observation.