## 4 The Improved Self-Collision Detection Technology
### Approximate Improvement Via Multiple Sphere Elements  
Approximating the components is the first key step in self-collision detection, which mainly simplifies the description of the robot to make the component more suitable for self-collision detection than the actual physical structure. However, the objects used by researchers to approximate the structure shapes of various components mainly include the spherical element, the cylindrical element, and the elliptical element. When approximating the components of the robot, the standard approximate element needs to meet the following basic conditions: for the spherical element, the sphere's radius is regarded as the largest value to ensure that it surrounds the outer boundary of each component; for the cylindrical element, the length of the cylinder is equal to the maximum distance in the three directions, and the radius of the cylinder can envelop the lateral boundary of each component; finally, for the elliptical element, the longest axis of the ellipse needs to envelop the longest endpoint of the component, in addition to the shortest axis also being required to envelop the shortest cross-sectional length of the component, and the length of the other axis is selected as the minimum distance. The approximate results of the same components utilizing different approximate elements are shown in Figure 4. The basic conditions can completely distinguish the possible collisions between the surface points of different components. Currently, spherical elements are commonly selected to approximate each component. This is because other elements have many defects in approximating some components of the mobile manipulator robot. For example: first, collision detection is impossible to be determined by using the cylindrical element to approximate each component of the entire system, which is caused by different types of collisions in different positions of two cylindrical objects, including the arc surfaces of two cylindrical objects, the horizontal surface of two cylindrical objects, and the horizontal surface of one cylindrical object and the arc surface of another cylindrical object; second, collision deletion cannot be quickly determined using elliptical elements to describe each component, as the collisions of two elliptical objects can only be determined by the shortest distance between two surface points; third, collision detection of two spherical objects can be determined by the shortest distance between two surface points as well as by the shortest distance from the center of the radius of one sphere to that of another. Therefore, to accurately describe the various components and quickly determine the real-time self-collision detection, spherical elements were used to pre-process the self-collision detection of the mobile manipulator robot. As such, various suitable spherical objects were selected for the approximation of each component. One spherical element cannot simplify all components of the mobile manipulator robot, and we should simplify the special parts by using multiple sphere elements. In the mobile manipulator robot, self-collision detection requires different approximations of various components, including the mobile platform subsystem, the manipulator subsystem, and the carrying load. The mobile platform has a complete and closed structural feature, and the motors of the manipulator subsystem were also designed with a complete and closed structural feature. However, the connecting link between the adjacent joints of the manipulator subsystem are designed according to the actual requirements and appearance beautification. To quickly establish the approximation of the entire system for collision detection, each component needs to be rapidly approximated by selecting a simplified approximate object. For these motors in the manipulator subsystem, we can directly select a single sphere element to approximate, which can be seen in Figure 4a.