International Journal of Aerospace Engineering

Volume 2017 (2017), Article ID 5402809, 12 pages

https://doi.org/10.1155/2017/5402809

## Learning Control of Fixed-Wing Unmanned Aerial Vehicles Using Fuzzy Neural Networks

^{1}School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798^{2}Faculty of Electrical and Computer Engineering, Semnan University, Semnan 35131, Iran^{3}Infinium Robotics Pte Ltd., Singapore 128381^{4}Physical Sciences Department, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USA

Correspondence should be addressed to Erdal Kayacan

Received 21 August 2016; Revised 25 December 2016; Accepted 26 December 2016; Published 9 February 2017

Academic Editor: Christopher J. Damaren

Copyright © 2017 Erdal Kayacan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A learning control strategy is preferred for the control and guidance of a fixed-wing unmanned aerial vehicle to deal with lack of modeling and flight uncertainties. For learning the plant model as well as changing working conditions online, a fuzzy neural network (FNN) is used in parallel with a conventional P (proportional) controller. Among the learning algorithms in the literature, a derivative-free one, sliding mode control (SMC) theory-based learning algorithm, is preferred as it has been proved to be computationally efficient in real-time applications. Its proven robustness and finite time converging nature make the learning algorithm appropriate for controlling an unmanned aerial vehicle as the computational power is always limited in unmanned aerial vehicles (UAVs). The parameter update rules and stability conditions of the learning are derived, and the proof of the stability of the learning algorithm is shown by using a candidate Lyapunov function. Intensive simulations are performed to illustrate the applicability of the proposed controller which includes the tracking of a three-dimensional trajectory by the UAV subject to time-varying wind conditions. The simulation results show the efficiency of the proposed control algorithm, especially in real-time control systems because of its computational efficiency.

#### 1. Introduction

Over the past several decades, unmanned aerial vehicles (UAVs) have proved their potential in several applications by using their several capabilities,* inter alia*, continuous and persistent surveillance, eliminating the need of aircrew, image processing capabilities by using relatively cheap sensors, and decreasing the size and weight of the aerial vehicle when compared to a conventional aircraft. UAVs have been used in a variety of civilian applications; some of which are disaster rescue [1], agricultural monitoring [2], wildlife protection [3], infrastructure inspection [4], 3D environment reconstruction [5], and person following [6].

UAVs can be classified into two groups: rotary wing and fixed wing. While the former has the capability of having aggressive maneuvers and being able to land and take off in small areas, the latter offers long flight endurance due to its flight characteristics about their gliding capabilities with no power. Among the gigantic number of fixed-wing UAVs applications, surveillance seems to be the most common application while benefitting from advanced computer vision techniques [7]. The most common path for a fixed-wing UAV is a combination of straight lines and circular orbits on a constant altitude [8].

For having a full autonomy of the aircraft, model-based controllers require a precise dynamic model of the aircraft. The controller must also be robust to wind and gust disturbances. However, under the time-varying parameters of an aircraft as well as time-varying working conditions and several stochastic disturbances, a learning control strategy is preferred in this paper. The proposed control algorithm does not need an accurate model of the aircraft. Instead, the intelligent structure of the controller learns the system dynamics online throughout the flight and optimizes its performance for any arbitrary trajectory including both straight lines and circular orbits. For this purpose, the fusion of fuzzy logic and artificial neural networks, namely, FNNs, is preferred [9–12].

To eliminate all uncertainties in a control system and design a sophisticated model-based controller based on an accurate model of the system seems to be convincing. The reason is that, in the absence of model uncertainty, nonlinearity, and computational constraints, it is a well-known fact that linear-quadratic regulator (LQR) and linear-quadratic-Gaussian (LQG) control laws give reasonably satisfactory performance. However, eliminating all the uncertainties seems to be neither realistic nor a novel idea. For instance, till the beginning of the 20th century, it had been a big dream to eliminate all the uncertainties and to be able to achieve a fully predictable world. In 1814, P.S. Laplace formulated the predictability of the universe as follows:

“Given, for one instant, an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it an intelligence sufficiently vast to submit these data to analysis it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom. For it, nothing would be uncertain and the future, as the past, would be present to its eyes.” [13].P. S. Laplace

On the other hand, quantum mechanics and the theory of relativity, which both appeared in the beginning of the 20th century, showed that our universe is quite random, and it is almost impossible to model or predict everything. In other words, our universe, at least on the level of subatomic particles, is not working like a “giant clock” which was claimed by P. S. Laplace. Even in a deterministic system, that is, a chaotic system, inevitable uncertainties in the initial conditions lead to huge differences in the future states of the system. In a similar manner, estimation and prediction of all changes during a fixed-wing UAV flight cannot be foreseen and considered in advance. All the aforementioned facts force us to propose some intelligent control algorithms which have learning capabilities throughout the operation.

Fuzzy logic theory and probability theory are the most widely used approaches to deal with the aforementioned inevitable phenomena: uncertainty. Although the concept of fuzzy logic and the concept of probability seem to be similar, they are quite different. While probability makes guesses about a certain reality, fuzzy logic does not make probability statements but represents membership in vaguely defined sets. For instance, if 0.5 is defined as a probability value for the oldness of a person, it can be said that there is a chance that he/she can be old. It is not known whether he/she is old or young. However in fuzzy logic, if 0.5 is defined as the degree of membership in the set of young and old people, we have some knowledge about his/him and he/she is positioned in the middle of young and old people. Since fuzzy logic contained vagueness, it was not appreciated by researchers when it was proposed for the first time in 1960s. However, since the 1970s, this approach to set theory has been widely applied to control systems.

While the most significant feature of a fuzzy logic controller is its capability to inject expert knowledge into the controller design, the well-known capability of an artificial neural network is to be able to learn from input-output data. The fusion of fuzzy logic controllers and artificial neural networks results in FNNs [14, 15]. In any FNN architecture, the use of a learning algorithm is a must. In literature, there are three types of learning algorithms: derivative-based ones (backpropagation [16], Levenberg-Marquardt [17, 18], and least square), derivative-free ones (genetic algorithm, particle swarm optimization [19], and sliding mode control (SMC) theory-based), and hybrid algorithms (Levenberg-Marquardt-particle swarm optimization [20], backpropagation-Kalman filter, gradient descent-Kalman filter, and genetic algorithm-Kalman filter). The main problem with the derivative-based learning algorithms is that they need the calculation of the partial derivatives of the outputs of the FNN with respect to the antecedent parameters. Another problem worth mentioning is that derivative-based algorithms have always a possibility of getting trapped in local minima. In order to eliminate the aforementioned disadvantages of the derivative-based methods, derivative-free methods are proposed. As a derivative-free method, the disadvantage of the genetic algorithms is that their update formula is entirely random, and there is no mathematical guarantee that the cost function will decrease over time. Moreover, these algorithms are computationally expensive. On the other hand, as a derivative-free method, SMC based algorithms are computationally efficient and they provide robustness to the control of the system [21]. A detailed survey on the optimal tuning of FNNs can be found in [22].

Despite the fact that UAVs are being more and more visible in our daily life, their control is still a challenging task as they are open loop unstable, multi-input multi-output, and highly nonlinear systems in which there are significant intercouplings. What is more, they are always subjected to noise and disturbances because of the uncertainties in their navigation systems as well as wind and gust conditions. One way of controlling them is to use model-based control techniques. However, they need an accurate model of both the system and disturbances which is a challenging task in real life. A requirement is the use of sophisticated system identification methods to obtain the model of the aerial vehicle which is time-consuming task. The detailed steps and several methods for system identification and parameter estimation of aerial vehicles are discussed in [23]. What is more, the working conditions are always changing resulting in a fact that adaptability is a must. Motivated by the aforementioned drawbacks of the model-based controllers, a model free controller, the combination of a P controller and an FNN, is preferred in this paper. In order to be able to design a practical controller in real time in which computational power is always limited, we prefer one of the fastest learning algorithms in literature which is an SMC theory-based algorithm.

This paper presents a novel SMC theory-based learning algorithm with an adaptive learning rate and the evaluation of the algorithm performance for a UAV flying in changing wind conditions. The paper is organized as follows: Section 2 introduces a fully nonlinear aircraft dynamic model in the presence of wind. In Section 3, the overall control scheme is described. In Section 4, a fuzzy neural control approach is introduced. Furthermore, the proposed training method, based on SMC theory, for the parameters of the FNN is proposed for the case of Gaussian membership functions. In Section 5, the proposed method is used to control a fixed-wing UAV. Finally, the concluding marks are presented in Section 6.

#### 2. Mathematical Description of the UAV

This section briefly introduces the translational and rotational equations of motion (EOMs) for a fixed-wing UAV in the presence of wind.

##### 2.1. Translational Dynamics

Let denote the inertial coordinates of the UAV’s center of mass and let be the drag, thrust, lift, and side forces, respectively. Denote by the aerodynamic bank, climb, and track angles, respectively, and let be the wind perturbation vector (full expressions for these perturbations can be found in [24]). The wind is characterized by the sum of a mean speed (acting in a horizontal plane along a heading angle ) and gust components . Then, for a fixed-wing UAV of mass , the translational EOMs are given by where is the gravitational acceleration, is the air velocity, and and denote the aerodynamic angle of attack and sideslip angle, respectively. A superscript refers to the frame used within the formulations, and the abbreviations , , and are used throughout the paper. Note that and are expressed as where is the vector of linear velocities which is given, in body frame, as where denotes the rotation matrix from the Earth-fixed inertial frame to the UAV-fixed body frame, which is given by

##### 2.2. Rotational Dynamics

Let denote the UAV-fixed longitudinal, lateral, and directional axes, respectively. Assume that are principal axes and - is the symmetry plane so that the inertia tensor is given by where denote the principal moments of inertia and is the product of inertia. Let denote the roll, pitch, and yaw angles, respectively, and let be the aerodynamic angular velocity vector. Then, the rotational equations of motion can be expressed as where is the moment vector (the vector of rolling, pitching, and yawing moments, resp.); is the wind angular velocity vector; is the distance between the point of application of the thrust and the UAV’s center of mass along the axis; is the angular momentum vector of all rotors about the UAV-fixed , , axes; and is the wind perturbation vector (see [24]). Throughout the paper, Euler angle sequence is used, so that .

##### 2.3. Forces and Moments Expressions

The following expressions of forces and moments are used in this paper: where is the dynamic pressure; denote the air density, the wing surface, the mean aerodynamic chord, and the wing span, respectively; is a constant; denote the aileron, elevator, and rudder deflections, respectively; and represents the throttle position.

#### 3. The Proposed Control Structure

##### 3.1. Kinematic Controller

The kinematic model is given by (1)–(3), from which an inverse kinematic model can be obtained which allows to calculate the reference air velocity, air-path and air-track angles. It is written as follows: Therefore, assuming the existence of a suitable state estimator scheme that estimates the mean wind vector, the kinematic control law to be applied to the UAV for trajectory tracking control is written as where and th is the hyperbolic tangent; , , and are the position errors in the inertial , , and axes, respectively; the parameters , , and are controller gains and , , and are saturation constants; and stands for the desired inertial coordinates. The parameters , and are the generated references for the controllers.

The following reference value is defined (i.e., coordinated turn conditions):

Defining the trim angle of attack asthe generated references for the roll, pitch, and yaw angles can be linearly approximated by

##### 3.2. Proportional Controller Design

The proportional (P) controller can be implemented as follows: where , , , and are the air velocity, roll, pitch, and yaw errors, respectively; and the parameters , , , and are the gains of the P controller.

#### 4. Fuzzy Neural Control Approach

Even if Mamdani-type fuzzy logic controllers were firstly proposed in the literature, a Takagi Sugeno Kang (TSK) fuzzy structure is preferred in this paper benefitting from its capability to be adapted over time. In the proposed method, as shown in Figure 1, P controllers work in parallel with FNNs. The task of the conventional P controllers is to provide some time for the FNN to learn the system dynamics online without going into the unstable working region. On the other hand, there is no need for the conventional P controllers to be tuned precisely.