## 1 Introduction  
In recent years, wheeled mobile robots (WMRs) have been widely applied in industries such as industrial manufacturing, agriculture, and healthcare [1]. With the commercialization of robotics, the diversity of WMR types has expanded to meet the needs of different application scenarios. Based on their locomotion mechanisms, WMRs can be broadly categorized into two main types: wheeled robots and legged robots. Wheeled robots are faster and structurally simpler than legged robots. Furthermore, wheeled robots are characterized by their high technological maturity and broad applicability, making them highly favored in robotics. Typically, research on WMRs focuses on real-time environmental perception, decision-making, planning, and trajectory tracking. However, the accuracy and complexity of trajectory tracking for WMRs remain critical challenges. This paper aims to address these challenges by leveraging the high control accuracy and efficiency of 3 WID3 WIS mobile robots. By replacing MPC with DMPC, the computational complexity of MPC is reduced. Consequently, this study proposes a DMPC controller for the trajectory tracking of 3 WIDWIS mobile robots. Based on the arrangement of the robot's wheels, WMR can be classified into synchronous, Ackerman, differential, skid steer, car-like, and omnidirectional types. [PERSON] et al. studied synchronous mobile robots and proposed a cross-coupled controller for synchronous trajectory control of parallel manipulators in [2]; however, synchronous robots require high ground friction and are easily affected by external disturbances. A path tracking controller for the autonomous driving of Ackerman mobile robots was proposed in [3]; but in complex environments, these robots struggle with turning, negatively impacting path tracking accuracy. [PERSON], [PERSON] et al. proposed a tracking controller for differential drive-wheeled mobile robots with non-holonomic constraints, utilizing a backstepping feedback linearization approach in [4]; however, differential mobile robots have limited steering angles, and controlling speed during turns is challenging, leading to a potential slipping. An extended Kalman filter (EKF) for estimating the instantaneous center of rotation (ICR) in skid-steering robots was presented to enhance model-based motion prediction in [5]. However, slipping can still happen during turns [2]. In recent years, many control approaches have been proposed to solve the trajectory tracking problem of Omni-directional Mobile Robot (OMR) [6; 7; 8]. Most existing research utilizes models based on first principles. However, system modeling was carried out using the system identification technique [9], which takes into account more parameters that influence tracking accuracy, resulting in models that better fit real-world conditions. [PERSON] et al. [10] proposed an adaptive control law for longitudinal slip conditions, where they constructed an adaptive nonlinear feedback controller. An appropriate Lyapunov function was used to ensure system stability. Results show that this control algorithm effectively suppresses overshoots but does not address lateral and heading angle errors. In [11], a PID-based controller combined with odometry is presented for OMR trajectory tracking. Allowing the robot to monitor and maintain its direction along a planned path. However, traditional PID controllers have limited adaptability, requiring parameter adjustments for different trajectories. Later, an improved controller presented in [12] focuses on trajectory tracking using a fuzzy controller with visual feedback to minimize tracking errors. [PERSON] et al. established a kinematic model of OMR and designed an MPC controller with control and system constraints to achieve point stabilization and trajectory tracking in [13]. However, at high speeds, stability issues can arise, affecting tracking accuracy. To address these issues, MPC for 3 WID3 WIS mobile robots is a feasible solution. This type of robot can fully utilize the wheels' friction while offering higher acceleration.