Simulated Simultaneous Localization and Mapping

We test simultaneous localization and mapping with three OctoSLAM variants, i.e. 3D, 2D (A), and 2D (B), as well as Hector SLAM. Variant 2D (B) refers to using a 2D map for registration with constant map updates, and (A) refers to using threshold triggered map updates after 0.4m distance traveled or 20◦ yaw rotation. The same thresholds are used for Hector SLAM. The RMSEs for all SLAM experiments are listed in Appendix A.2.1, and bar graphs for SLAM with no sensor noise are provided in Appendix A.2.2.

The results for SLAM in the “Willow” environment are given in Figure 3.12. While both OctoSLAM 2D A and B perform better on average than Octo SLAM 3D and Hector SLAM, the difference is not significant. It is however interesting to note that the SLAM RMSE of OctoSLAM nearly doubled in comparison to the “localization only” experiments, while the RMSE for OctoSLAM 2D did not. This can be explained by the fact that using 3D maps in

this environment barely provides an advantage over using 3D maps, as the environment mostly consists of walls perpendicular to the ground. However, while the simulated 2D LiDAR sensor captures a consistent 2D map for the 5m long 240 deg wide cone in front of the robot, the 3D map consists of many such scans stitched together via the pose estimates. Thus, the pose error accumulates until sufficient parts of the environment have been inserted into the 3D map. That being said, as the RMSE is below 0.10m for all SLAM approaches, we consider them all adequate for the “Willow” world. The episode used to generate the 3D map has a RMSE of 0.08m. Unfortunately, there is quite some clutter along the walls. However, keep in mind that even using ground truth data for mapping (Figure 3.7) does not produce a completely clean map of this environment. This can be explained by the fact that the walls in this environment line up exactly with the map cell boarders.

FIGURE3.12: This figure shows the SLAM results for the “Willow” environment. On the top

the 3D map generated by the OctoSLAM 3D median episode can be seen. On the bottom a graph of the RMSEs for SLAM in this environment is shown.

Figure 3.13 visualizes the results for SLAM in the “corridor” environment. Similar to the localization results for this environment, 3D map Octo SLAM significantly outperforms the 2D map variants. It scores an average RMSE of 0.11m, while other approaches suffer from at least twice the RMSE. 3D map OctoSLAM also has the lowest standard deviation of 0.04m, while the 2D map approaches deviate at least thrice as much. The octomap shown is generated by an episode with a RMSE of 0.11m. The walls in this map are rather clean, and the pillars are clearly visible and distinguishable from the lower wall.

The results for SLAM in the “sphere” world are given in Figure 3.14. In this environment, no approach has a significant advantage over the others in terms of average RMSE. Though, the high RMSEs, e.g. 0.35m for 3D map OctoSLAM, stand out. In contrast, in the “localiza- tion only” experiments 3D map OctoSLAM did not perform significantly worse here than in

Octo 3D Octo 2D (A) Octo 2D (B) Hector 0 0.5 1 1.5 2 2.5 3 3.5 0.01m Gaussian noise RMSE in m

FIGURE3.13: This figure shows the SLAM results for the “corridor” environment. On the top

the 3D map generated by the OctoSLAM 3D median episode can be seen. On the bottom a graph of the RMSEs for SLAM in this environment is shown.

other environments. Also noteworthy is the high standard deviation of 0.33m, brought about by four episodes in which 3D map OctoSLAM has a RMSE over 0.5m. When investigating these episodes we found that ascending in the middle of the map can instantaneously change most of the sensor readings when facing the two small inner walls. If the outer elements are not mapped at that point, the lack of anchor points for the scan registration results in an increased localization error. This is exacerbated by the lack of space for maneuvering, making robot at- titudes from which both parts of the inner and outer elements are simultaneously picked up by the sensor less likely. This environment shows the fragility of using a 2D sensor for a 6 DOF motion performing robot. While the median OctoSLAM episode with a RMSE of 0.15m, used for generating the 3D map shown in Figure 3.14, results in an acceptable map, this is not the case for 40% of all episodes.

Octo 3D Octo 2D (A) Octo 2D (B) Hector 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.01m Gaussian noise RMSE in m

FIGURE 3.14: This figure shows the SLAM results for the “sphere” environment. On the top

the 3D map generated by the OctoSLAM 3D median episode can be seen. On the bottom a graph of the RMSEs for SLAM in this environment is shown.

Figure 3.15 shows the results for the “tilted wall” environment. OctoSLAM 3D significantly outperforms the other three SLAM approaches with an RMSE of 0.13m, compared to RMSEs ranging from 0.260m to 0.844m for the 2D map approaches. Hector SLAM scores the worst RMSE average and also has the highest standard deviation. The episode used for mapping has a RMSE of 0.15m.

In general, the results show the same trend as the previous experiments for localization on a given map: 3D map OctoSLAM significantly outperforms the 2D map approaches in the “corridor” and “tilted wall” environment. In the other environments neither approach performs significantly better than the others. It should however be noted that 2D map OctoSLAM does on average perform slightly better in the “Willow” environment, where a 3D map barely provides additional information over a 2D map. Thus, if one can expect such an environment there is no

Octo 3D Octo 2D (A) Octo 2D (B) Hector 0 0.5 1 1.5 2 2.5 3 0.01m Gaussian noise RMSE in m

FIGURE 3.15: This figure shows the SLAM results for the “tilted wall” environment. On the

top the 3D map generated by the OctoSLAM 3D median episode can be seen. On the bottom a graph of the RMSEs for SLAM in this environment is shown.

reason to use a 3D map SLAM approach. Concerning “constant” vs. “threshold” mapping, i.e. OctoSLAM (A) vs (B), we found that there is no significant difference in performance between the two.