## 1 Introduction
For example, the structural parameters of the manipulator subsystem in Figure 1 are similar to that of the typical UR5 robot shown in Figure 2a, we mark these motors from the base to the end-effector as the joint \(i\) (\(i=1,2,.....,6\)), and define link 1 (link 2) as the connecting part between motor 2 and motor 3 (motor 3 and motor 4). The positions of joints 2 and 3 cannot be solved in the mathematical model established by the traditional method; the position of connecting link 1 cannot be accurately expressed in the mathematical model. Therefore, according to the mathematical model, the control of the mobile manipulator robot may not be able to meet the actual motion requirements. For example, the end tool of the robot cannot reach the specified position due to the limitation of the physical structure of the connecting link 2; the above-mentioned joints and connecting link may collide with the external environment. By comparing the kinematic model and the actual physical model, we found that researchers are mainly focused on the relationship between the rotation angle of the driving joints and the position and posture of the robot. In order to ensure that the mathematical model is more consistent with the physical model of the mobile manipulator with the UR-like arm, we should consider the actual physical structure of the manipulator system in the kinematic modeling process. Self-collision detection is another major problem in controlling the mobile manipulator, and it has been concerned and studied by various researchers for many years [28; 29; 30]. According to the literature on self-collision detection without external sensors, the self collision detection of mobile manipulators mainly includes three steps: approximating each component, describing the position of each approximate object, and determining self-collision judgment. The first step aims to simplify each component through standard geometry to facilitate the mathematical analysis of self-collision detection. Owing to the complex structure of the mobile manipulator, the standard geometry, also called an approximate element, mainly includes the ellipsoidal object [31], the cylindrical object [32] and the spherical object [33]. Furthermore, multiple approximate elements are utilized to simplify each component for improving the approximating performance [34]. The second step describes the actual position of each approximation in the three-dimensional space during the movement of the mobile manipulator robot. Currently, the basic principle of the second step is the spatial transformation method, which needs to consider the positional relationship of each component at different times [35]. After completing the above steps, various self-collision detection technologies are proposed according to the actual needs of a given task. The simplest collision detection method directly uses the shortest distance between the surface points of different components as the primary judgment [36]. However, this method takes a long time and cannot be used for real-time collision detection. To reduce the required time for collision detection, the researchers proposed to use the relationship between spatial geometric objects as the principle of determination [37]. Additionally, the researcher reduced self-collision detection of components that never collide for optimizing self-collision detection technology [38]. In this paper, we developed a kinematic modeling method to accurately describe the actual structure of the mobile manipulator robot with a UR-like arm. Meanwhile, we specifically improved the performance of the self-collision detection process by reasonably approximating the structure of the mobile manipulator robot and reducing the time required for position description. The main contributions of this study are as follows:  
1. This paper proposes a new type of kinematic modeling method for mobile manipulator robots. We optimized the difference between the kinematic model and the actual physical model by considering the structure of the manipulator subsystem.