# Research on Optimal Landing Trajectory Planning Method between an UAV and a Moving Vessel
## 5 Conclusions  
Since vessels are in a state of constant motion, the conventional UAV landing plans are obviously not efficient for such moving platform landings. In this paper, a method for calculating the optimal approach landing trajectory between an UAV and a small vessel is proposed. Simulation results demonstrate the ineffectiveness of conventional algorithms, since they present the following shortcomings: (1) At the point \(A_{3}\) of approaching the landing trajectory III, the error between the actual UAV landing trajectory and the calculated optimal landing trajectory is large, which seriously affects the autonomous guidance accuracy; (2) at the points \(\mathbf{A}_{1}\) and \(\mathbf{A}_{2}\) of the calculated optimal trajectory, a step change in the dip angle seriously affects the UAV's tracking planning path.  
In order to tackle the above two problems, the initial lead \(n\) is introduced in the calculation formula of the direction angle \(\gamma_{A}\) and dip angle \(\delta_{A}\) of the UAV flight speed vector. Based on the performed simulation results, the introduction of the initial lead can effectively solve the above two problems and provide the optimal value of the initial lead.  
In order to determine the initial error of the autonomous guidance segment, it is necessary to estimate the deviation of the calculated trajectory under the influence of the atmospheric random disturbance and the navigation system's error. At the end of the uniform landing of the UAV near the point \(\mathbf{A}_{3}\), the UAV needs to keep a lower flight height in order to achieve a connection to the landing device.  
Figure 9: Direction angle \(\gamma_{tr}\) and dip angle \(\delta_{tr}\) of the UAV flight speed vector.  
**Author Contributions:** Methodology, L.T.; validation, J.W.; investigation, J.W.; writing--original draft preparation, L.T.; writing--review and editing, X.Y. and S.S.  
**Funding:** This project is supported by National Natural Science Foundation of China (No. 61703126), the China Postdoctoral Science Foundation (No. 2018M631930), and the Research Innovation Fund of Harbin Institute of Technology (No. HIT.NSRIF.2019017).  
**Acknowledgments:** The authors would like to thank the anonymous reviewers for their constructive comments and suggestions.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
\(\gamma\): the track azimuth: rad \(\beta\): the track dip angle, rad \(L\): the length of the track, m \(C\): circle of center \(\varphi\): angular distance, deg \(R\): turning radius, m \(n_{z}\): lateral overload allowable value, m/s\({}^{2}\) \(\omega_{y}\): angular velocity of turn, rad/s \(\Delta t\): the error of time \(\varepsilon\): coordinate error of point \(A_{2}\), m \(M_{KP}\): fuel amount, kg \(m_{L}\): the amount of fuel consumed by the drone unit path, kg \(i\): the number of calculation points \(\Delta T\): the integration step \(A\): the distance between two adjacent points of the three-dimensional approach landing trajectory \(T\): the time constant of the steering gear system and the aircraft, s \(\xi\): the damping coefficients \(k\): loop transfer coefficient \(U\): auxiliary variable \(F\): the coordinate converter \(\Delta S\): the total deviation error, m \(n\): the initial lead steps \(\Delta X\): the coordinate deviation error, m Subscripts \(I\): physical quantity between \(A_{0}\) and \(A_{1}\): physical quantity between \(A_{1}\) and \(A_{2}\): physical quantity between \(A_{2}\) and \(A_{3}\): physical quantity between \(A_{3}\) and \(B_{T}\)