# Fast Lidar Inertial Odometry and Mapping for Mobile Robot SE(2) Navigation
## 3 Methodology
### Point-Cloud De-Skewing
However, it should be pointed out that the optimization process of FLOAM was not synchronized with the dataset when it was played at normal speed; the play speed of the dataset was set to 0.3 to achieve synchronization. The whole running time of FLOAM was more than three times the duration of the dataset, and it did not achieve real-time performance. Throughout all tests, the scan-matching run-time of F-LIOM in the three scenarios was significantly shorter than that of LIO-SAM and LeGO-LOAM. In some highly challenging cases, such as the bumpy ground scene shown in Figure 2c, the average run-times of LIO-SAM and LeGO-LOAM reached 578.49 milliseconds and 421.54 milliseconds, respectively. This meant that some Lidar frames were rejected in the process when the Lidar rotation rate was 10 Hz. Lastly, let us analyze LIO-SAM_FixZ; its average run-time was the longest under the different datasets. The initial idea of setting the z axis to a fixed value was intended to eliminate the possible drift of the z axis, so the z axis was reset during each optimization process. Due to the lack of z-axis information, the model did not match the actual state, making it difficult to converge during optimization. Finally, the experiment showed quantitatively that the optimization process took longer, and the average time reached 970 milliseconds in extreme cases. As shown, F-LOIM still achieved a quite notable performance in real time, even in complex environments, making it more promising for deployment in limited-resource embedded systems. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & _Garden_ & _Bumpy_ & _Park_ & **Synchronized with Dataset?** \\ \hline FLOAM & 146.98 & 192.03 & 154.95 & No \\ LeGO-LOAM & 245.05 & 421.51 & 97.45 & Yes \\ LIO-SAM & 521.32 & 578.49 & 238.84 & Yes \\ LIO-SAM\_FixZ & 730.68 & 970.23 & 242.86 & Yes \\
**Our method** & **265.10** & **258.05** & **69.15** & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average run-times of scan-matching module processing (ms). ## 5 Conclusions

This paper developed F-LIOM, a robust smoothness-aided Lidar inertial odometry method for ground mobile robots equipped with 3D Lidar in complex environments with rough terrain. The F-LIOM is cost-effective in terms of model complexity and calculation units, as it employs the proposed out-SE(2) constraint method that assumes the mobile robot is still moving in SE(2) and integrates the out-SE(2) perturbations as weights in the noise term and covariance matrix to optimize the estimated state. The system follows a tightly coupled Lidar inertial odometry structure, including tracking, real-time state estimation, mapping, and loop closure functions. Inspired by the recent work on Lidar intensity and geometry, a new global descriptor, the smoothness scan context, was presented that exploits geometry and smoothness properties and only requires a few thousand features, instead of tens of thousands of point clouds like existing methods. Multiple sets of experiments were carried out to evaluate the performance of the proposed algorithm in various scenes, including indoor, road, building, garden, and public datasets. The results showed that

Figure 5: Run-times of the scan-matching modules. (**a**) Run-times for _Garden_. (**b**) Run-times for _Bumpy_. (**c**) Run-times for the public _Park_ dataset. (**d**) Run-times for the _small-scale_ dataset. We can see that the run-times of the scan-matching modules were different in different scenarios. The more complex the scene, the more time was consumed. the proposed method achieved a competitive performance in real-time pose estimation, making it more suitable for deployment in low-power embedded systems. [PERSON] contributed the central idea, analyzed most of the data, and wrote the initial draft of the paper; [PERSON] reviewed the paper. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest.