## 1 Introduction
It can move in any direction and turn within the motion plane, providing excellent maneuverability. Consequently, the 3 WID3 WIS robot has become optimal for mobile robot decision-making, planning, and trajectory tracking. MPC is an online optimization technique utilizing present and past information to solve optimization problems and determine control values that meet constraint conditions. One of the advantages of MPC is that it does not require a highly accurate model, allowing it to perform effectively. This characteristic makes it one of the most effective methods for addressing constraint optimization problems. It is an advanced technique for control system development and has addressed remarkable successes in practical fields [14; 15]. In [16], [PERSON] et al. applied MPC to a 4 WID4 WIS robot. The MPC algorithm with dynamic constraints can significantly reduce the impacts of steering motor delays on trajectory tracking. However, the issue of slipping at high speeds was not addressed. Traditional MPC can determine optimal control actions by solving optimization problems online, which can enhance performance but requires complex computations. To address this challenge, many studies have been carried out in the last few years [17; 18; 19]. [PERSON] et al. [20] proposed a robust MPC strategy for trajectory tracking control of robots under various constraints. To improve the speed of Quadratic Programming (QP) solutions, they used a Delayed Neural Network (DNN). However, DNNs may struggle to find global optima and often only converge to local solutions. In [21], a modification of Nonlinear Model Predictive Control (NMPC), called Embedded Fast NMPC, was introduced; it ensures stable implementation of the position controller though at the expense of reduced tracking accuracy compared to traditional MPC. In [22], a method combining a novel robust MPC with function approximation using neural networks was proposed. This method allows for stability and compliance with constraints while significantly shortening the required computation time. This approach is capable of tracking dynamic set-points; however, further evaluation and validation of its real-time performance are necessary. [PERSON] et al. [23] proposed a straightforward and computationally efficient approach and designed a robust MPC specifically for uncertain, constrained linear systems. They utilized an approximate model to manage uncertainty, thereby improving the online solving speed of MPC for longer prediction horizons. This approach has been validated through numerical simulations, although potential errors from using an approximate model might affect practical applications. Although many methods have been proposed to reduce the computational complexity of MPC, their applicability is not strong, resulting in a large gap between theory and practical application. Inspired by those findings, a practical controller based on the dynamic model predictive control (DMPC) for trajectory tracking of the omnidirectional mobile robot is developed, which can maintain a good performance and lower the computational complexity. The proposed approach possesses the advantages below. A functional relationship between trajectory curvature and prediction horizon is constructed by adjusting the prediction horizon in traditional MPC. The length of the prediction horizon is dynamically adjusted during each control period based on the changes in trajectory curvature, which can eliminate a lot of unnecessary calculations in trajectory tracking that exist in traditional MPC. The new controller was applied to solve the trajectory tracking problem of OMRs, which was evaluated by experiments on an omnidirectional full-drive mobile robot and a comparative study of the errors in lateral and heading angles with traditional MPC. This study aims to develop a dynamic model predictive control (DMPC) to improve trajectory tracking accuracy and reduce computational complexity for 3 WID3 WIS mobile robots. The significant contributions of this paper are:  
1.