# Target Tracking Based on a Nonsingular Fast Terminal Sliding Mode Guidance Law by Fixed-Wing UAV
## 4 Simulation Results
### Maneuvering Target  
In this section, two typical maneuvering actions are designed to verify the effectiveness of the proposed algorithm for the maneuvering target: accelerated motion and sharp turn movement. Figure 8(a) represents the motion profile of the ground target that includes its speed and heading angle. The motion of the target is described as follows. The ground target moves from the start point \((10,10)\) m in the free environment with the initial speed \(v_{t}(t_{0})=2\) m/s and the initial heading angle \(\psi_{t}(t_{0})=-45^{\circ}\). Suppose that there is a homogeneous change of the speed and heading angle of the target. As shown in Figure 8(a), the target accelerates from 2 m/s to 7 m/s during 300 s to 350 s and accelerates to 11 m/s during 460 s to 470 s. Meanwhile, the heading angle has three changes: \(-100^{\circ}\), \(30^{\circ}\) and \(20^{\circ}\), during 400 s to 410 s, 460 s to 470 s and 550 s to 570 s, respectively, assuming that the UAV's initial heading angle \(\psi_{a}=30^{\circ}\) and the simulation time is 900 s.  
As shown in Figure 8(b), the UAV can circle around the target which has a low speed during the start time. In addition, the UAV follows the target, which accelerates to a larger speed behind a distance during the ending time. It can be found that some adjustments are executed during the whole flight stage. The adjustments are particularly evident in the sharp turn process of the target.  
Figure 8: The result of tracking a moving target along the S-shape trajectory.  
Figure 7: Tracking a moving target along the S-shape trajectory.  
From Figure (a)a, with the changing of the target speed and heading angle, all three of the algorithms can make the state converge to the desired position. Before the target changes its motion state, the NFTSM algorithm can make the distance error \(r\) converge to less than 0.0001 m in 24.3 s, while NFTSM\({}_{1}\) takes 34.2 s with oscillatory convergence. However, the TSM algorithm converges to the desired distance error range in 113.6 s. This result confirms that the proposed algorithm can converge quickly to the desired position again.  
When the target starts to accelerate movement from 300 s to 350 s, only the TSM has a large distance error of about 17.4 m, while both NFTSM and NFTSM\({}_{1}\) are stable. The TSM algorithm converges close to zero gradually when the speed of the target is not changing after 350 s. The larger distance error for the TSM occurs at about 460 s where the target motion has high acceleration and sharp left turn. However, the distance error for the TSM is still close to zero at 550 s where the target has a left turn again. Therefore, it proved that the TSM algorithm is sensitive to speed change of the target and insensitive to angle changing. There is an opposite phenomenon for the NFTSM\({}_{1}\) algorithm as shown in Figure (a)a. It is easy to find that the proposed NFTSM guidance law can keep the distance error steady (only has a \(\pm\)0.1 m error range) whether the speeding or angle changing. Hence, robustness against the target's speed and heading angle disturbances can be demonstrated for the proposed NFTSM algorithm. It is more sensitive for angle changing than speed according to the analysis of NFTSM\({}_{1}\).  
Figure 10: The results of tracking a maneuvering target.  
Figure 9: The trajectory of the moving target and the UAV.  
The heading angle \(\psi_{a}\) and the angle rate \(\omega_{\psi}\) is given in Figure 10b. It can be found that the input limit is only executed by NFTSM\({}_{1}\) in order to verify the influence by the unlimited maximum command of NFTSM and TSM. This is the reason why there is too large of a change in distance error for NFTSM\({}_{1}\) in Figure 10a. From 350 s to 400 s, there is about a 10.3 s delay compared to NFTSM and NFTSM\({}_{1}\) TSM such that NFTSM can converge in a quick amount of time.