## 3 Methodology
### Motion Planning  
Prediction of dynamic obstacles is integrated with a sampling-based method to achieve path planning. **(1) Sample point generation:** The multi-sensor fusion method acquires environmental information within the complex space \(M\) for analysis. As the robot moves, the sensing range of the sensor at step \(i\) is denoted by \(f_{i}\). With continuous motion, the perception regions at consecutive steps overlap, represented by \(f_{i}\cap f_{i+1}\). According to the corresponding boundary information obtained, the occupied map \(M_{\infty}\), the free map \(M_{\text{fr}}\), and the corresponding unknown map \(M_{\text{unknown}}\) in the map are obtained. After obtaining the corresponding free map \(M_{\text{fr}}\), the corresponding observation viewpoint \(I\) is randomly generated in the free area, and in the corresponding observation viewpoint \(I\), the environmental information around the viewpoint is obtained. **(2) Node queries and connections** Given that this environment state needs to be continuously updated, new nodes do not directly establish a connection after they are generated. We use a judgment method similar to a time window to query the judgment points. As the motion of the obstacle is predicted, the potential for interference between the viewpoint and the obstacles can be calculated at a subsequent moment. If we predict that there will be an obstacle in the field at a viewpoint in the next moment, the viewpoint will not be added to our path map. As shown in Figure 3, we calculate the time it takes for each moving obstacle to approach the viewpoint, at which point in time it is not taken into account in planning. To better realize the planning of the robot, the planning time of the robot is considered to be:  
\[T_{p}=T_{1}\cap T_{2}\cap T_{3}\cap T_{p} \tag{14}\]  
where \(T_{p}\) is used to limit the robot's driving when the robot's planning time is at the intersection of three times. \(T_{1}\), \(T_{2}\), and \(T_{3}\) represent the time interval for the dynamic obstacle to reach viewpoint 1, viewpoint 2, and viewpoint 3, respectively, and \(T_{p}\) is the time for the robot to move to these three positions. The effective time is obtained by calculating the intersection of the robot's arrival time and the obstacle's arrival time \(T_{p}\). If the corresponding viewpoint selection is not completed within the intersection time, the selection will be made again within the time. Although the planning speed will be slower than other planning algorithms, dynamic obstacles can be avoided within the maximum fault tolerance. **(3) Path optimization:** When the mobile robot is driving, collisions with obstacles can be avoided to a great extent by selecting the viewpoint ahead. But, this will lead to a situation where the solution is not the optimal path. At this time, in order to better compensate for the path problem, the corresponding path optimization is adopted, in which the position of the next coordinate \(P_{i+1}\) performs the corresponding calculations:  
\[P_{i+1}=P_{i}+T_{p}\times v \tag{15}\]  
where \(v\) represents the current speed of the robot, and the corresponding speed is calculated as:  
\[v=\sum_{k=1}^{n}\frac{C_{k}}{n}v_{0} \tag{16}\]  
where \(n\) is all obstacles within the implementation, \(v_{0}\) represents the initial speed of the robot, and \(C_{k}\) is the corresponding predictor. The predictors are calculated as follows:  
\[C_{k}=\ln\frac{V_{i}}{\delta_{k}}\eta \tag{17}\]  
where \(\eta\) is the normalization factor, and \(V_{i}\) is the predicted speed information of the obstacle. \(\delta_{k}\) denotes the Euclidean distance between the mobile robot and the predicted position, corresponding to coordinates \((x_{s},y_{s})\) used to estimate the position of dynamic obstacle \(t\). Figure 3: (**a**) illustrates the generation of the robot’s viewpoint at the current position along with the predicted information of relevant obstacles, while (**b**) depicts the robot’s movement based on the generated viewpoint and the corresponding prediction data.