# Robots in Partially Known and Unknown Environments:
## 5 Experiments and Results
### OfflineRMP Analysis
#### 5.2.2 OfflineRMP Results  
From these results, it is clear that both the simulated annealing and post-processing phases contribute to improving the lengths of the paths found. The lowest improvement in simulated annealing was obtained for the back_and_forth instance (14%), and the highest improvement was obtained for the bugtrap1 instance (197.1%). Moreover, the post-processing step achieved its lowest improvement of 2.3% in instance var_density, while its largest improvement of 9.7% was obtained for the corridor_wavy instance. The simulated annealing and the full approach performance show small standard deviations, even in the cases where the initial solution had large standard deviations, like for the bugtrap1, complex, and var_density cases. The Wilcoxon paired ranked tests showed statistical differences with 95% confidence for all the problem instances due to the application of the simulated annealing step and the post-processing step. Last, Tables 6 and 7 show a comparison between OfflineRMP and three approaches to solving RMP from the literature. The approaches chosen were a hybrid approach [3], an approach based on an ant colony optimization algorithm [21], and an approach based on the probabilistic roadmap method [12]. These approaches place points on the free space in every instance; the distance between each point is fixed and varies from 20 to 100. This reduces the instance resolution significantly. The hybrid approach changes the resolution during its execution if a feasible path is not found. The hybrid approach has a success rate of 100%; if there is any feasible path between the starting and target points, it will be found. The two-phase ACO and PRM approaches have lower success rates; given their dependence on the positioned points, they might not find a solution. Further, OfflineRMP has a distance between cells of 1; it considers every detail of the instance using its largest resolution. If there exists a feasible path, it will be found. It also identifies if there is no possible solution path. For comparison, we use the results of the hybrid approach, ACO, and PRM using width 20, which has the best results on average for each experiment; this decreases the resolution of each instance from \(2000\times 2000\) to \(500\times 500\) for OfflineRMP, and we maintain the original resolution. For all these experiments, we compare the best and average lengths, the average smoothness, and the average time to find a solution from a total of thirty executions. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Instance** & **Initial Length** & **SA Length** & **SA + PP Length** & **SA + PP Smoothness** & **Iteration** \\ \hline back\_and\_forth & \(5910\pm 0\) & \(5186\pm 42\) & \(4806\pm 0\) & \(108\pm 0\) & \(690\pm 239\) \\ corridor\_wavy & \(3161\pm 0\) & \(2742\pm 27\) & \(2499\pm 9\) & \(105\pm 3\) & \(951\pm 48\) \\ bugtrap1 & \(2311\pm 995\) & \(778\pm 2\) & \(750\pm 2\) & \(132\pm 7\) & \(586\pm 235\) \\ claps & \(6921\pm 0\) & \(3764\pm 13\) & \(3599\pm 2\) & \(119\pm 1\) & \(746\pm 203\) \\ complex & \(7029\pm 1587\) & \(2890\pm 7\) & \(2789\pm 6\) & \(134\pm 4\) & \(754\pm 218\) \\ potholes & \(2893\pm 337\) & \(2156\pm 29\) & \(2033\pm 20\) & \(77\pm 23\) & \(894\pm 90\) \\ rockpile & \(3566\pm 639\) & \(2319\pm 30\) & \(2135\pm 24\) & \(87\pm 7\) & \(899\pm 77\) \\ var\_density & \(4392\pm 1022\) & \(1634\pm 11\) & \(1598\pm 8\) & \(117\pm 19\) & \(751\pm 139\) \\ square\_spiral & \(10520\pm 0\) & \(4257\pm 24\) & \(4120\pm 1\) & \(112\pm 0\) & \(671\pm 205\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Component analysis—parameter configuration: \(\alpha=0.95\); \(t_{0}=500\). Table 6 shows competitive results of OfflineRMP; the best result in each problem instance is highlighted in bold. In five of the nine problem instances, OfflineRMP found better average results. The best result found by OfflineRMP is also shown, obtaining the best results in six of the nine instances; this is because our approach aims to find direct paths with fewer turns.