## 1 Introduction  
In the application of unmanned aerial vehicles (UAVs), one of the basic requirements is for the UAVs to autonomously follow a planned path. In most cases, the reference path given by planning algorithms [1] is a curve. This requires that the UAVs can accurately track the reference curve. In addition, obstacle avoidance is another problem that has to be considered during path following. Although preknown static obstacles can be considered in path planning [2, 3], unknown obstacles may be detected when the UAVs follow the planned path in a complex dynamic environment [4, 5]. It is required that the UAVs are able to avoid the newly discovered obstacles and come back to the planned path. In this paper, we focus on the problems of path following and obstacle avoidance in UAVs. Path following and obstacle avoidance have been hot topics in the field of UAVs for a few years. The following is a brief overview of the existing methods in the literature. A. Path following  
Various strategies have been proposed in the literature for path following. Two main categories are control-theory-based approaches and geometry-based approaches. Several types of control-theoretic techniques have been developed for path following. Some of the well-known techniques are proportional integral differential (PID) control [6], model predictive control (MPC) [7, 8, 9], adaptive control [10, 11, 12], sliding mode control [13, 14], and linear quadratic regulator (LQR) [15, 16]. Other novel techniques, such as iterative learning control [17], were developed for path following. The main advantage of these control-theory-based approaches is the guarantee of the stability and the convenience for performance analysis in theory. One drawback is the longer man-hours associated with the controller's implementation when compared with the geometric methods. Many control-theory-based methods rely on mathematical models of the UAVs, and it is time consuming to obtain an accurate model of a UAV, especially for a low-cost small fixed-wing UAV. If the model is not sufficiently accurate, more time may be required to adjust the parameters of the method in real applications. In addition, in terms of theoretical complexity, it takes more time for many engineers to understand and apply complex control theories than it does for geometric-based approaches. Many geometric-based guidance laws were proposed for UAV path following, they are the line-of-sight (LOS) [18] method, pure pursuit (PP) [19] method, nonlinear guidance law (NLGL) [20], vector field (VF)-based guidance laws [21, 22], and the combination of LOS and pure pursuit [23]. In PP, LOS, and NLGL, a virtual target point is defined on the reference path. The guidance laws direct the UAV to track the virtual target point, so that the UAV eventually converges to the reference path. All of the four kinds of guidance laws are applicable when the reference path is a straight-line or a circle. Although the NLGL can be used to follow a curved path, the optimal parameters are different when the radius of the reference circle changes [24], so the cross-track error is still considerable when the reference curvature varies [25]. Since all these techniques use the geometric approach, computing the desired heading angle (or rate) is quick, and they are easy to implement. The performance of these techniques was evaluated and compared in [24] using straight-line following and loitering. A reference path with varying curvature was not considered. Accurately tracking a curved trajectory with a time-varying curvature remains a challenge. B. Obstacle avoidance  
Another hot topic in this research area is obstacle avoidance during path following. One of the most popular techniques that combines path following and obstacle avoidance is the MPC-based approach [26], for convenience to tackle the constraints of the obstacles. A limitation of the MPC-based approaches is the problem of computation complexity.