## 2 Global Destination Arrival Sequence Planning  
For multi-destination path planning of mobile robots, it is necessary not only to plan the path between two destinations, but also to consider the order of arrival of each destination, consider the global shortest path and time efficiency. The constructed multi-destination path planning scheme is shown in Figure 2. In Figure 2, \(S\) is the starting point. \(T_{i}\) (\(i=1,\,2,\,3,\,4\)) represents multiple destination points. Plan 1 and Plan 2 are two plans for multiple global multi-destination sequential arrival sequence planning. According to the global optimal path, the mobile robot can move.  
Figure 1: Algorithm structure of multi-destination path planning.  
Figure 2: Multi-destination path planning schemes.  
Global destination arrival sequence planning refers to the global planning of the arrival sequence of the robot from the starting point to all destinations before moving. First, it is necessary to calculate the environmental obstacle values between each starting location and each destination. Then, according to the calculated environmental obstacle value between the two locations, this article optimizes the arrival sequence of multiple destinations. In the end, the global path was chosen. As shown in Figure 2, it has the smallest environmental obstacle value. Global destination arrival sequence planning reduces the amount of calculation. The planned global path passes through all destinations at once. The obstacles of passing through are reduced. The length of the path is greatly reduced.  
As shown in Figure 2, such as \(S\)\(\rightarrow\)\(T_{1}\)\(\rightarrow\)\(T_{2}\)\(\rightarrow\)\(T_{4}\)\(\rightarrow\)\(T_{3}\)\(\rightarrow\)\(S\), \(S\)\(\rightarrow\)\(T_{3}\)\(\rightarrow\)\(T_{2}\)\(\rightarrow\)\(T_{1}\)\(\rightarrow\)\(T_{4}\)\(\rightarrow\)\(S\),..., there are many situations in the movement sequence. Therefore, it is necessary to optimize the ordering of multiple destinations. The selected global path can pass through all destinations with the fewest obstacles. It has a short distance. Therefore, this article first adopts the rules of the Go chess game to reconstruct the environmental grid map, as shown in Figure 3. Secondly, the matrix of the reconstructed environmental grid map is used to obtain the obstacle value of the environment between all two locations. The obstacle values are sorted, and those with the same environmental obstacle value can be processed twice. Assuming that there are \(n\) destinations in the multi-destination path planning of a mobile robot, there are \((n^{2}+n)/2\) combinations of the path arrival sequence, and there are also \((n^{2}+n)/2\) environmental obstacle values. Aiming at meeting the shortest motion path requirements of the mobile robot, the robot needs to select an optimal path from \((n^{2}+n)/2\) combinations. This article follows the environmental obstacle value to choose the optimal path.  
As shown in Figure 4, global destination planning can be divided into several steps and the several concrete steps are shown in the following Sections 2.1 and 2.2.  
Figure 3: Reconstruction of environmental grid map. (**a**) Original environment raster map. (**b**) Environmental grid map with obstacle values.