## 1 Introduction  
Industrial automation is a prerequisite for intelligent manufacturing, and mobile robots represent a core component of industrial automation systems. In recent decades, due to the broad applications for mobile robots, the core issues in motion control of mobile robots, including point stabilization, path planning, trajectory tracking, and real-time avoidance, have attracted considerable attention from both academic scholars and practitioners [1; 2; 3; 4; 5]. Although large numbers of mobile robots have begun to enter homes, hospitals, and many other industrial areas, mobile robots with new structures (as opposed to the traditional dual-drive wheeled mobile robots), are required to meet continuously increasing demands with respect to high flexibility, efficiency, and safety of complex and diverse applications in reality. Omni-directional mobile robots (OMRs) with mecanum wheels provide an alternative and have drawn much attention from researchers. In [6; 7], two different omni-directional mobile structures with mecanum wheels were proposed. In [7; 8], the kinematics of OMRs were analyzed and the motion control of robots was achieved. In [9], a comprehensive omni-directional soccer player robot with no head direction was proposed and it was capable of more sophisticated behaviors, such as ball passing and goal keeping. Compared with the traditional nonholonomic dual-drive wheeled robot, the omni-directional mobile robot is able to synchronize steering and linear motion in any direction. This advantage not only improves the flexibility of the robot greatly in order to achieve fast target tracking and obstacle avoidance, but also provides more references for robot motion control methods. Motion control is a core issue in the mobile robot system and guarantees the smooth movement of the robot. Due to the diversity of motion and increasing performance requirements, motion control algorithms are becoming more and more complex. In [10], a receding horizon (RH) controller was developed for the tracking control of a nonholonomic mobile robot. In [11], a novel biologically inspired tracking control approach for real-time navigation of a nonholonomic mobile robot was proposed by integrating a backstepping technique and a neurodynamics model. In [12], an approach was proposed for complete characterization of the shortest paths to a goal position and it was used for path planning of the robot. A novel method referred to as the visibility binary tree algorithm for robot navigation with global information was introduced in [13]. The set of all complete paths between the robot and target in the global environment with some circle obstacles was obtained by using the tangent visibility graph. Then, an algorithm based on the visibility binary tree created for the shortest paths was run to obtain the optimal path for the robot. In [14], a real-time obstacle avoidance approach for mobile robots was presented based on the artificial potential field concept. The motion control of omni-directional mobile robot has also been investigated and many results have been reported [15; 16; 17; 18]. Among them, the model predictive control (MPC) algorithm is the most common control method used for trajectory tracking of the OMR. The MPC algorithm is an efficient predictive control technique and is composed of model prediction, rolling optimization, and feedback correction. The MPC algorithm has been widely used in industrial control applications and is able to take various constraints into consideration. The core of MPC control problem finding the optimal solution of a cost function constructed according to the error between system output at the sampling time and the predicted output of the established prediction system model. The optimal solution is taken as the optimal control input in the future prediction time domain and the first control vector of the optimal solution is used as the real control input.