Finite-time path following control for small-scale fixed-wing UAVs under wind disturbances

Abstract

By integrating the finite time control technique and finite-time disturbance observers together, the finite-time three-dimensional path following control problem for small-scale fixed-wing UAVs subject to external wind disturbances is investigated in this paper. The external wind disturbances are estimated through finite-time disturbance observers and the estimates are then incorporated into the finite-time feedback controller such that a composite control scheme is proposed. Under the proposed control scheme, the closed-loop system possesses not only faster convergence rate but also stronger disturbance rejection ability and better robustness, which is the main contribution of the paper. The effectiveness and superiorities of the proposed composite control scheme are demonstrated by numerical simulations.

Introduction

Unmanned aerial vehicles (UAVs) have aroused an increasing attention and development for several decades [1], [2], [3], [4], [5]. Owing to the features of low costs, strong endurance, large flight radius and fast cruise speed, small-scale fixed-wing UAVs have been widely utilized in military and civilian fields, such as battlefield surveillance, military reconnaissance, target localization, and road traffic monitoring [1], [4], [5]. For most of these missions, fixed-wing UAVs are demanded to follow predefined locations or geometric paths with satisfied accuracy. The tasks are generally divided into trajectory tracking problem [2], [3] and path following problem [4], [5], [6]. Different from trajectory tracking problem where the UAV should arrive at a particular location in a certain time, the path following problem only requires the UAV to follow some geometric paths with any feasible speed profiles. In path following problem, the fixed-wing UAV could fly at a constant airspeed, thus providing advantages of reducing the difficulty of control, saving energy, and preventing stall in downwind flight [6].

Due to the advantages of path following and the superior capabilities of fixed-wing UAVs, many results have been proposed for the path following problem of fixed-wing UAVs. A survey and analysis of the path following algorithms for fixed-wing UAVs focusing on two-dimensional (2D) profile is reported in [7]. Among various geometric and control methods, a popularly used path following algorithm is the vector fields (VFs) guidance algorithm [8], [9], [10], [11], [12]. In VFs guidance algorithm, the heading angle is designed based on the vector field to make the UAV approach the desired path. For example, in [8], a VFs guidance algorithm is employed to make fixed-wing miniature aerial vehicles follow the desired 2D straight-line paths, circular arcs and orbits asymptotically. Nevertheless, the VFs guidance algorithm mainly focuses on 2D straight line and circular orbit path [8], [9], [10], [11] or three-dimensional (3D) straight line path [12]. Other geometric methods, such as pure pursuit [13], virtual target point (VTP) based algorithm [14], [15] and line-of-sight based algorithm [16], [17], [18], are effective to solve path following problem with curved paths. However, complex frame transformations are often involved therein, which imposes additional demands to the design and parameterization of the desired paths. Furthermore, for better path following performance, many advanced control algorithms have been applied to path following control, such as nested saturation theory [19], backstepping control [20], model predictive control [21], gain scheduling theory [22], dynamic surface control [23] and fuzzy-logic method [24].

In the context of path following, a common manner is to parameterize the desired path in terms of an independent variable other than time variable and then design auxiliary dynamics for the path parameter such that the desired path is followed [7]. This method has been extensively used in the path following problem of fixed-wing UAVs [5], [25], [26], AUVs [27], and rotorcrafts [28]. Particularly, in [26], an auxiliary dynamic is adjusted for the parameterizing variable l and thereafter the 3D path following problem is investigated by using the Special Orthogonal group SO(3).

Owing to the light-weight structure, the fixed-wing UAV is more likely to be affected by external wind disturbances. The wind speed will reach up to 60 percent of the airspeed in certain particular case [12], which will definitely bring significant adverse effects on path following performance. Thus, the disturbance rejection ability of the fixed-wing UAV system is one of the most crucial factor to be considered when designing the controller. A prevalent strategy to handel external wind disturbances is to ignore the airspeed of the UAV and to pay attention to its ground trajectory (see [8] for an example). Hence, the ground speed and course angle information obtained from the global positioning system (GPS) are used in the controller. Since the GPS module has deficiencies of vulnerability in a poor-visibility environment and low update rate [1], the obtained information may be inaccurate and thus the path following performance will be compromised. Another manner is to consider the influence of wind when designing the controller, either by assuming that the wind speed is known [29], or estimating it through particular methods, such as adaptive method [5], [30] and disturbance observer based control (DOBC) approach [31]. For instance, in [29], a predictive path following control scheme is designed with known wind velocity and orientation. Based on VTP approach, [5] employs the adaptive technique to deal with modeling uncertainties and environmental disturbances while [31] developes a nonlinear disturbance observer to estimate the effects of wind disturbances. Due to the benefits of fast, low conservative and separable in dealing with disturbance, the DOBC approach is used to deal with external wind disturbances in this paper.

It is worth pointing out that almost all the existing literature on the path following control of fixed-wing UAVs obtained asymptotically stable results, which means that the UAV converges to the desired path as time goes to infinity. For the sake of faster convergence rate, the finite time control technique is an effective method. The main advantages of finite time control technique lie in two aspects. First, under the finite-time controller, the system possesses finite-time convergence, i.e., it will converge to the equilibrium point within finite time. Second, compared with the asymptotically stable system, finite-time convergent system also has some other nice features, such as stronger disturbance rejection ability and better robustness against uncertainties. With such advantages, the path following performance will be improved if the finite-time feature is incorporated into the designed scheme for the fixed-wing UAV. In recent years, the finite time control technique has been widely researched theoretically, such as finite-time state feedback control [32], [33], [34], finite-time output feedback control [35], [36], finite-time output regulation control [37], finite-time convergent observer design [38], [39], etc, and applied in various fields, such as aircraft system [35], [40], multiagent system [41], mobile robot system [42], DC-DC system [43], etc.

In this paper, the finite-time 3D path following problem is investigated for small-scale fixed-wing UAVs subject to external wind disturbances. By combining the finite time control technique and finite-time disturbance observers (FTDOs) together, a composite finite-time path following control scheme is developed for the fixed-wing UAV such that the UAV converges to the desired path in finite time. The desired path is parameterized by parameter θ and an auxiliary dynamics is set for the path parameter such that the path following problem is transformed into a tracking control problem. The design of the path following controller includes two parts.

• In the first part, the feedback linearization approach is carried out for the fixed-wing UAV system to obtain a second-order system which is convenient for the controller design.

• In the second part, the path following controller is designed in two stages. Firstly, in order to obtain better disturbance rejection ability, FTDOs are designed to accurately estimate the external wind disturbances and the estimation error systems are finite-time stable. Secondly, to further enhance the disturbance rejection ability and acquire faster convergence rate, the finite time control technique is applied to the feedback controller design by adding power integrator approach. Disturbance estimates obtained from FTDOs are added to the feedback controller to compensate the effects of disturbances such that a composite finite-time path following controller is designed.

Under the proposed composite controller, the UAV converges to the desired path profile in finite time. Rigorous stability analysis indicates that the closed-loop system will be stabilized in finite time under the proposed finite-time controller.

The main contribution of this paper is to achieve finite-time 3D path following for small-scale fixed-wing UAVs subject to external wind disturbances. By combining the finite time control technique and FTDOs together, a composite finite-time controller with fractional powers is developed. If the fractional powers of the proposed finite-time controller are taken as 1, the controller reduces to the corresponding asymptotically stable controller. Compared with the results in [19], [31] where asymptotic path following is achieved, the closed-loop fixed-wing UAV system under the proposed finite-time controller possesses not only faster convergence rate but also stronger disturbance rejection performance and better robustness. By numerical simulations, the effectiveness and superiorities of the proposed composite control scheme are verified.

The remainder of this paper is organized as follows. The model of the fixed-wing UAV system and control objective of this paper are described in Section 2. The composite path following controller design process and stability analysis of the closed-loop system are presented in Section 3. In Section 4, some numerical simulations are given to show the effectiveness and advantages of the proposed composite controller. Finally, conclusions are drawn in Section 5.