## 1 Introduction
In the existing literature, most of the MPC-based controllers for mobile robots are designed for electric motor-driven robots. These controllers typically employ kinematic models and adopt the desired velocity as the control output [18; 24], which is then sent to the motors for execution. However, for the heavy-duty mobile robots driven by hydraulic systems studied in this research, controlling them is much more complex compared to electric motor-driven systems [25]. This increased difficulty stems from the fundamental nonlinearity of fluid dynamics, compounded by issues such as fluid leakage and friction [26]. When the hydraulic drive system fails to precisely follow the desired velocity, maintaining accurate trajectory tracking for the entire robot becomes a difficult task. Consequently, designing a velocity controller for a hydraulic-driven system is essential, and also a challenging problem. Directly applying nonlinear fluid dynamics for control often fails to meet real-time requirements; thus, some studies have used simplified linear models combined with adaptive mechanisms, such as sliding mode control [27] or backstepping control [9], to handle model uncertainties and improve tracking performance. Meanwhile, obtaining a simplified model of a hydraulic system is a difficult task. The process of parameter identification is often time-consuming and expensive [26]. Additionally, due to cost and installation constraints, there may not be enough sensors available on the actual system to collect the data required for parameter identification [16]. Therefore, there is a need for a control scheme that does not rely on an explicit mechanistic model. Recently, the nonlinear mapping method has been adopted in various fields, including control systems and machine learning. Instead of starting with equations that describe the physics of the hydraulic system, a nonlinear mapping approach would use data collected from the motor's operation. These data include input variables (current in this study) and output variables (rotational speed in this study). And, by fitting these data into a function, the system can learn the relationship between inputs and outputs. Motivated by the challenges mentioned above, the trajectory tracking of a hydraulic-driven skid-steer mobile robot requires simultaneous consideration of both the robot's position control and the velocity control of the hydraulic motors. Due to the complexity of these two control tasks, this research proposes a hierarchical control strategy. The upper-level controller utilizes a nonlinear model predictive control method to track the desired pose while taking into account the physical constraints of the system. And, the lower-level controller is based on the nonlinear velocity mapping of the hydraulic motor. It obtains the reference control value through lookup mappings and employs the PID control method to compensate for errors. The main contributions of this study can be summarized as follows:  
1. The hierarchical control strategy allows for the decoupling of position control and hydraulic control tasks, thereby simplifying the overall controller design and enhancing the system's robustness and performance. By separating the control objectives and utilizing different control algorithms at each level, the system effectively addresses the complex dynamics and nonlinearity of the hydraulic-driven skid-steer mobile robot. 2. We propose a hydraulic motor control method based on nonlinear current-velocity mapping. By establishing the mapping relationship between the input (control current) and output (motor velocity) of the hydraulic motor, the dynamics are obtained, thus avoiding the need for complex mechanism modeling and parameter identification processes. By adopting this data-driven approach, the requirement for detailed knowledge of system dynamics and precise parameter identification is reduced, making the controller easier to apply in practical robot systems. 3.