# Hybrid Model-Based Analysis of Underground Articulated Vehicles Steering Characteristics
## 5 Conclusions  
In this paper, the steering characteristics of UAVs and the effects on trajectories were uncovered based on a validated hybrid dynamic model. Substantial results and contributions can be summarized as follows.  
(1) A hybrid dynamic model of a UAV incorporating a dynamic model of frames and a hydraulic power steering system was established.  
(2) A field test of a typical UAV, an LHD with 4 m\({}^{3}\) capacity, was carried out. The results of articulation angle, and dynamic responses of frames and hydraulic steering system, were used to verify the hybrid model in the time domain. The relatively small errors in the time domain proved the validity of the established model. In addition, owing to the poor handling stability of the UAV, oscillation was found in the dynamic responses of the frames and hydraulic steering system. The results were used to verify the dynamic model, and the accuracy of the involved parameters in the dynamic model was checked by the frequency domain results obtained with SFT. The test and simulation results showed the same dominant frequency of 3.9 Hz simultaneously, proving the accuracy of the model and involved parameters.  
(3) Based on the verified hybrid model, the steering characteristics of the UAV were uncovered, considering its load changes. The results showed that increasing the load of the front frame would lead to a decrease of the corresponding angular velocity, which would increase the 'oversteer'. The trajectories' deviation between empty and full load conditions in the lateral direction exceeded 0.3 m when the velocity was 2 m/s. Meanwhile, the effect of transient steering characteristics on the trajectories was investigated under different velocities. The maximum deviation of front and rear frame trajectories reached 0.21 m when the velocity was approximately 2 m/s.  
(4) This hybrid dynamic model can be used to analyze the dynamic characteristics of UAVs and the hydraulic steering system. Although the focus of this paper is LHD, the established dynamic model can also be applied to different articulated vehicles, such as articulated drill jumbos, charging vehicles, mining dump trucks, tractors, and even some agriculture and forestry machinery. The steering characteristics mentioned above should be considered for precise control, navigation and positioning of UAVs, which is crucial for the above-mentioned articulated vehicles.  
[PERSON] and [PERSON] developed the dynamic model of UAV, [PERSON], [PERSON], and [PERSON] processed the simulation and field test, [PERSON] wrote the article; [PERSON] and [PERSON] supervised the overall study and field test and revised the article.  
This research was funded the National Key Research and Development Program of China (Grant No. 2016 YFC0802900), the National Natural Science Foundation of China (grant number 51774019) for the financial support.  
Figure 17: Trajectory with constant steering radius at different velocity conditions. (**a**) Trajectories of frames at different velocities; (**b**) detailed information of trajectories under a transient steering process.  
**Acknowledgments:** The authors would like to acknowledge the Shandong Gold Group Co., Ltd. for the experimental UAV and sites.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.