# Target Tracking Based on a Nonsingular Fast Terminal Sliding Mode Guidance Law by Fixed-Wing UAV
## 1 Introduction  
With higher levels of autonomy, unmanned aerial vehicle (UAV) plays an important role in various complex tasks in civilian or military fields [1]. To increase the level of autonomy and reduce the dependencies on manual operators, various planning and control strategies have been developed regarding the problem of target tracking, target acquisition, disaster rescue and so on [2; 3; 4]. As one of the most complicated and important problems, the target tracking is regarded as a guidance law problem in this paper, assuming the target motion to be observed in the monitoring range. In addition, tracking a moving target by fixed-wing UAV is more challenging than following a predefined path because the target can vary its speed quickly over a large range while the UAV must keep moving forward to stay in the air. Meanwhile, the method for solving the problem of target tracking can be used in the path-following problem by considering the tracked target as a virtual target point on the desired path [5]. When executing the missions such as aerial search or aerial observation, the UAV is often required to orbit around a ground target at a desired distance [6] or maintain the target within a certain distance in front of UAV [7]. Based on the previous studies, the fight strategy for fixed-wing UAV can be divided into a loitering-pattern and following-pattern. Different from the vertical take-off and landing (VTOL) UAV (e.g., quadrotor), the fixed-wing UAV is constrained by the lower bound according to the stall condition. When the target's speed is lower than the minimum speed of the UAV, the circumnavigationis executed to circle around the target within monitoring range [8]. However, when the speed of the target is close to the UAV, the aircraft should be guided to follow the target by the following pattern. In previous works, various algorithms have been developed to the problem of target tracking for UAV. The differential geometry is adopted to solve the problem of rendezvous and target tracking guidance laws in [9]. The proposed method has the advantage of rigorous stability as well as less tuning parameters. By implementing Lyapunov vector fields, the guidance laws for unmanned aircraft applications are presented in [10; 11]. The vector fields have proven to be globally stable for circular loiter patterns. The concept of Hopf bifurcation is first applied to the standoff tracking problem [12]. It has been verified that the convergent speed of the proposed algorithm to desired distance is faster than the Lyapunov vector field approach. The target tracking problem is studied based on game theory [13]. The control strategy proposed in this study ignores the target's motion. In addition to the nonlinear control method, the model predictive control (MPC) [14; 15], backstepping-based controller [16; 17] and sliding mode control (SMC) [18] are presented to get good performance of target tracking. Due to the existence of the more maneuverable target, the problem of target tracking is more suitable to be solved by SMC so that the feature of sliding manifold can drive the UAV to maintain the desired distance. In order to reduce the effect of unmodelled dynamics and disturbances, the target tracking guidance algorithm is introduced by using SMC based on the tangent vector field [19]. The artificial potentials and SMC are combined to solve the problem of a maneuvering target tracking [20]. A class of the second-order sliding mode for the ground moving target tracking with special unknown bounded uncertainty has been proposed in [21]. In addition, the designed sliding manifold is linear in general SMC [18]. Although the tracking error can converge to zero and the convergence speed can be adjusted by selecting different parameters, it cannot converge to zero in finite-time [22]. The linear sliding manifold can only concern the exponential stability during the sliding phase; as a result, it is difficult for the tracking accuracy to ensure [23].