## 5 Conclusions  
This study presents a novel hierarchical control strategy for trajectory tracking of a hydraulic-driven skid-steer mobile robot. Firstly, a mapping relationship between the control current of the hydraulic motor and its output velocity is established, enabling the acquisition of the motor's dynamics through data modeling instead of complex mechanism modeling and parameter identification processes. Then, in the upper-level controller, the  
Figure 10: Tracking result of the circle-shaped trajectory: (**a**) trajectory; (**b**) errors; (**c**) left-side velocity; (**d**) right-side velocity.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Position Errors (m)**} & \multicolumn{1}{c}{**L-Shaped Trajectory**} & \multicolumn{1}{c}{**Circle-Shaped Trajectory**} \\ \hline \multirow{2}{*}{Proposed Controller} & Max & 3.07 & 1.80 \\  & RMSE & 0.72 & 1.02 \\ \multirow{2}{*}{LMPC + PID} & Max & 6.99 & 2.78 \\  & RMSE & 2.49 & 1.26 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Tracking errors of the trajectory tracking experiment.  
NMPC is employed to track the desired pose of the mobile robot, while considering the physical constraints of the system. The output of the upper-level controller is the desired velocity. Consequently, in the lower-level controller, the control signal for the hydraulic actuator is obtained directly from looking up the velocity mappings, and a PID controller is utilized to compensate for velocity tracking errors. This hierarchical control strategy effectively decouples the pose control of the robot from the velocity control of the hydraulic system, simplifying the overall controller design. Experimental validation was conducted on a heavy-duty skid-steer mobile robot, and the results demonstrate the superior trajectory tracking control performance achieved by the proposed control strategy.  
Our future research will aim to create a more sophisticated, intelligent, and robust control system for skid-steer mobile robots, enabling them to operate efficiently in complex unstructured environments. Firstly, considering the issue of skidding in skid-steer mobile robots, machine learning techniques may be applied to help predict slip before it occurs by analyzing patterns from historical sensor data. Neural networks or support vector machines could be trained to identify the precursors of skidding events. Then, enhancements to the robot's control algorithms will be crucial. This might involve the development of MPC schemes that can anticipate and adjust for slip, or adaptive control systems that can learn and compensate for the skidding behavior dynamically. Moreover, for SLAM to be effective in unstructured environments, a fusion of different types of sensors (e.g., LIDAR, RADAR, cameras) may be required to provide robust data under varying conditions, such as poor lighting or adverse weather. Meanwhile, developing or improving algorithms that can handle the uncertainty and variability in unstructured environments will be necessary.  
Conceptualization, J.W. and D.Z.; methodology, J.W. and Z.L.; formal analysis, Y.Z. and C.P.; data curation, H.C.; writing--original draft preparation, J.W.; writing--review and editing, D.Z. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data are not publicly available due to privacy.  
Authors [PERSON] and [PERSON] were employed by the company Sunward Intelligent Equipment Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.