Research articleA new robust adaptive mixing control for trajectory tracking with improved forward flight of a tilt-rotor UAV
Introduction
The development of Unmanned Aerial Vehicles (UAVs) has attracted enormous interest from the academic community and industry. Although UAVs have originally been known by their military usage, the technological and theoretical advances accomplished in the area of control and robotics with the cost reduction of electromechanical components have provided many civilian applications, such as search and rescue [1], remote inspection [2], load transportation [3], public security [4], mapping [5], and agriculture [6] to name a few.
The most common UAV configurations found in the literature are rotary-wing and fixed-wing aircraft. Rotary-wing aircraft have the advantages of hovering flight and Vertical Take-Off and Landing (VTOL) despite having less flight endurance [7], [8], while fixed-wing ones provide better range and endurance performances, thus allowing improved energy consumption, but require external means (runways or catapults) for take-off and landing, and cannot hover [9], [10]. A third kind of aircraft, still relatively uncommon, is the fixed-wing convertible aircraft with VTOL capabilities. It has the advantages of fixed and rotary wing aircraft without most of their shortcomings. The tilt-rotor is a special configuration of convertible UAVs, which can hover and perform VTOL maneuvers as helicopters and, by tilting the rotors to the horizontal position, improve cruise flight as a fixed-wing aircraft. This kind of vehicle is a hybrid copter-plane, multi-body, highly-coupled underactuated mechanical system [11], [12]. Consequently, the relative wind generated by the aircraft motion substantially changes the vehicle dynamic behavior between hovering and cruise flight modes. In helicopter-flight mode (VTOL and hovering), the deflections of aerodynamic surfaces (aileron, rudder, and elevator) do not produce significant dynamical effects, whereas in cruise-flight mode, small deflections produce significant aerodynamic forces that can be used to generate both the necessary aerodynamic forces to sustain forward flight, and the aerodynamic moments that allow control and guidance. These facts pose some challenges for the control design of convertible UAVs, which cannot usually be solved using classical linear controllers when it is required to achieve good performance throughout the full flight envelop trajectory tracking. Furthermore, control techniques designed for mechanical systems, such as [13], [14], [15], [16], cannot be applied for tilt-rotor UAVs, since in these vehicles the rank of the input coupling matrix varies in time according to the magnitude of the relative wind-speed.
Only few works dealing with control design for the full flight envelope of the tilt-rotor UAV are found in the literature. Ref. [17] performs feedback linearization through a Neural Network. In [18], the Particle Swarm Optimization algorithm is applied in order to obtain the optimal value of a Linear Quadratic Regulator (LQR) during flight time; and work [19] applies a Linear Model Predictive Control (LMPC) by splitting the range of the UAV forward velocity in many subsets. Although good experimental and numerical results have been obtained in these works, they do not present stability analysis of the proposed strategies. Besides, some works identify the ideal conditions to perform the transition from hover and cruise [20], [21]. In contrast, many works have proposed control strategies for tilt-rotor UAVs in the helicopter-flight mode, for instance backstepping technique [22], [23], Proportional-Integral-Derivative (PID) control [24], LMPC [25], [26], linear mixed control [27], and feedback linearization [28]. In general, these works rely on model simplifications, such as system decoupling and linearization. Accordingly, from the best knowledge of the authors and as commented in [9], [29], the control design to carry out the transition between both flight modes, fully exploring the nonlinear model, is still an open research field.
Therefore, this work aims to design a new robust adaptive controller to perform trajectory tracking and improve the forward flight performance of a tilt-rotor UAV. The aircraft used in this work is illustrated in Fig. 1, which is composed of the fuselage, two thrusters groups, one at each side of the aircraft, and tail-surfaces. The tail-surfaces improve the forward flight performance by providing better trim stability to the aircraft. Despite the advantages of having tail-surfaces, as mentioned before, the control design becomes challenging, since the relative wind substantially changes the vehicle dynamic behavior between hovering and transition/cruise flights. For the tilt-rotor UAV used in this work, the thrusters groups provide an important contribution for both longitudinal and directional control, even in cruise flight, since there is no fixed-wing and, thereby, it is not possible to convert completely the rotors to the horizontal position. Accordingly, during the forward flight, the aircraft remains in transition/cruise flight. Therefore, the proposed control law is designed to accomplish the full flight envelope of this tilt-rotor UAV, which is composed of the following maneuvers: vertical take-off, axial flight, hovering, transition to cruise flight with constant altitude, longitudinal plane maneuvers (moving in the x–z plane), lateral-directional plane maneuvers (moving in the x–y plane), transition from cruise to hovering, and vertical landing.
In order to solve the mentioned trajectory tracking problem, this paper extends the Adaptive Mixing Control (AMC), introduced in [30], to deal with Linear Parameter-Varying (LPV) systems. Furthermore, we enhance our previous work [31] with a new adaptive mixing scheme capable of handling multiple varying parameters. A rigorous closed-loop stability analysis and a detailed description of the proposed control strategy are presented. The classic AMC technique, which was originally formulated through transfer functions, is also extended in [32] to deal with state-space systems that possess a single varying parameter. They handle actuator failure in a quadrotor UAV by exploring the gain margin property of LQR controllers in order to design the candidate controllers. Here, we deal with the general class of LPV systems with not known a priori but bounded large parameters, which are measured or estimated online. The LPV system is split into a set of convex polytopic systems accordingly to the large parameter intervals, for which candidate controllers are designed based on the linear mixed control theory, providing improved transient response as well as attenuation against unknown disturbances. The new robust AMC is designed to handle with the flight envelope of the considered tilt-rotor UAV. Therefore, multiple varying parameters, which are available online, are used by the adaptive mixing scheme in order to select or interpolate the appropriate candidate controllers that provide stability according to the current maneuver.
Furthermore, several works formulate the dynamics of tilt-rotor UAVs as a single body mechanical system [22], [23], [24], [25], [28], [33]. This is a questionable simplification, since it neglects the coupling between the thrusters groups and the main body, including the dynamics of servomotors, assuming that it can reach any inclination instantaneously. These simplified dynamics result in non-affine models with respect to the control inputs. This work overcomes such simplification by modeling the tilt-rotor UAV as a multi-body mechanical system, taking into account the dynamics of servos, resulting in a more accurate model.
The efficiency of the proposed control strategy is verified via numerical experiments that are conducted through a high fidelity simulator developed over the Gazebo [34] and Robot Operating System (ROS) [35] platforms based on the Computer-Aided Design (CAD) model.1
Therefore, the main contributions of this work are: (i) the whole-body dynamic model of a tilt-rotor UAV with tail-surfaces formulated through the Euler–Lagrange approach, considering it as a multi-body system with aerodynamic effects; (ii) a new Robust AMC (RAMC) to deal with convex polytopic systems in the state-space; and (iii) the synthesis of the new RAMC, with ensured stability, in order to cope with the full flight envelope trajectory tracking of the tilt-rotor UAV with tail-surfaces.
The remaining of the paper is structured as: Section 2 develops the tilt-rotor UAV equations of motion by using the Euler–Lagrange approach, in which the external forces and torques applied by the thrusters, servomotors, and aerodynamic surfaces are mapped to the generalized forces; Section 3 presents the design of the new robust adaptive mixing controller and the associated stability analysis; to corroborate the controller performance, Section 4 presents numerical results conducted on a high fidelity simulator developed over Gazebo and ROS platforms; and finally, Section 5 concludes the paper.
Section snippets
Tilt-rotor UAV modeling
This section develops the equations of motion of the tilt-rotor UAV using the Euler–Lagrange formulation. The aircraft is depicted in Fig. 2 and is composed of: (i) the fuselage, where electronic components are assembled, like battery, sensors, microprocessors and others; (ii) the thrusters groups, which include the propellers, DC brushless motors, and servomotors that tilt the propellers in order to generate motion along , and axes, and roll, pitch and yaw moments; and (iii) tail-surfaces
Robust adaptive mixing control strategy
In this section a novel robust adaptive mixing control strategy is proposed in order to solve the trajectory tracking problem of the tilt-rotor UAV with aerodynamic surfaces. The aim is to track a reference trajectory on , , and directions, maintaining stable the remaining variables. The trajectory tracking problem must be achieved taking into account the full flight envelope of the considered tilt-rotor UAV, that is: axial flight, hovering, transition/cruise, and turning flight level.
The
Numerical results
In this section, numerical experiments are conducted through the ProVANT simulator,9 which was developed using Gazebo and Robot Operating System (ROS) platforms. In the following, the simulation scenario and the aircraft physical features are described.
Conclusions
This work proposed a novel robust adaptive mixing controller in order to solve the full flight envelope trajectory tracking problem of a tilt-rotor UAV. This particular UAV is composed of two propellers, two tiltable mechanisms, fuselage, and tail-surfaces. The dynamic modeling of the tilt-rotor UAV was obtained through the Euler–Lagrange formulation considering it as a multi-body mechanical system. Since this model considers the dynamics of the tiltable mechanisms (servomotors), we could
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was in part supported by the project InSAC - National Institute of Science and Technology for Cooperative Autonomous Systems Applied to Security and Environment under the grant CNPq 465755/2014-3, FAPESP 2014/50851-0. This work was also supported in part by the Brazilian agencies CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior under the grant numbers 88887.136349/2017-00 and 001, CNPq under the grant numbers 313568/2017-0 and 426392/2016-7, and FAPEMIG under the
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