# A Random Sampling-Based Method via Gaussian Process for Motion Planning in Dynamic Environments
## 3 Experiments
### Robot Experiments
Compared with AO methods based on random trees, such as FMT*, although the DGLP cannot give the optimal path, it can output high-quality collision-free paths more quickly, which is especially important in dynamic environments, since there is not enough time and computational resources to plan the optimal path. Regarding the success rate of local re-planning, the DGLP performs very well. Its overall success rate in the simulation and experiment is 90%. In dynamic environments, it is of the greatest importance for a motion planning method to provide a collide-free path as soon as possible. Then, it should ensure the local path quality and planning success rate. We use the weighted stacking method to comprehensively evaluate the performance of each method. The weighted stacking equation is  
\[Y=w_{1}\cdot z_{1}-w_{2}\cdot z_{2}-w_{3}\cdot z_{3}, \tag{5}\]  
where \(Y\) is the comprehensive evaluation score, the \(z_{1},\ z_{2}\), and \(z_{3}\) are the normalized values of the planning success rate, computing time, and path cost, respectively, and \(w_{1}\), \(w_{2}\), and \(w_{3}\) are the weighting factors. We set \(w_{1}=0.5\) due to the computing efficiency priority principle, and set \(w_{2}=w_{3}=0.25\). According to Table 2 and Equation (5), we calculate the comprehensive evaluation scores of the methods, as shown in Figure 8. In all groups of comprehensive evaluation scores, the DGLP scores the highest and its scores are at least 44.92% higher than RRT and FMT*, which demonstrates that the DGLP can well balance the efficiency and quality of the local path re-planning. The ability of the DGLP to provide high-quality local re-planning paths smoothly and efficiently in dynamic environments has been tested by the simulations and experiments. The proposed method can be applied to motion planning for indoor service robots and smart vehicles which are often faced with unexpected situations in dynamic environments, and need to temporarily alter the original planning paths. The DGLP is able to fast plan collision-free local paths with high-quality for the robots in unexpected situations. The proposed method should be used with an offline planning method, i.e., the offline planning method gives a global path, and if part of the global path is invalid, the DGLP outputs the local re-planning paths online to replace the invalid partial path. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiments** & **Method** & **Avg. Time (s)** & **Avg. Path Cost (m)** & **Success Rate** \\ \hline \multirow{3}{*}{Robot simulation} & RRT & 1.04 (1.00) & 1.0641 (1.00) & 9/10 (\(-\)1.00) \\  & FMT* & 0.43 (\(-\)0.21) & 0.6969 (\(-\)1.00) & 10/10 (1.00) \\  & DGLP & 0.03 (\(-\)1.00) & 0.7449 (\(-\)0.74) & 10/10 (1.00) \\ \hline \multirow{3}{*}{Robot experiment} & RRT & 0.90 (1.00) & 0.9778 (1.00) & 7/10 (1.00) \\  & FMT* & 0.52 (0.116) & 0.8008 (\(-\)1.00) & 9/10 (\(-\)1.00) \\ \cline{1-1}  & DGLP & 0.04 (\(-\)1.00) & 0.8396 (\(-\)0.56) & 8/10 (0.00) \\ \hline \hline \end{tabular}  
* Each column of data is normalized and displayed in brackets, where the range of the normalized values is \([-1,1]\).  
\end{table} 
Table 2: The experimental results for dynamic local path re-planning.