# Fast Lidar Inertial Odometry and Mapping for Mobile Robot SE(2) Navigation
## 3 Methodology
### Point-Cloud De-Skewing
It is believed that smoothness is an important attribute that can be further exploited for place recognition, similar to the intensity-based and geometric-based loop closure detection solutions [35; 36]. However, a Lidar scan is composed of tens of thousands of points, making the scan context computationally weak. Therefore, smoothness \(s\), consisting of only thousands of features, is introduced to construct the smoothness scan context as a global descriptor for place recognition. Some basic properties of the smoothness can be derived from (1), where the value is always non-negative, and the variance corresponding to the edge features is large. The planar features with a lower smoothness are less distinctive in the local frames, while the edge features are the opposite. To improve the place recognition accuracy, we first set the threshold \(\rho_{s}\) to filter features with a lower smoothness than \(\rho_{s}\), just like certain meaningless planar features. For the remaining available features, the logarithmic function is used to smooth the selected features:

\[s\Big{(}p_{k}^{i,j}\Big{)}=\log\Big{(}s\Big{(}p_{k}^{i,j}\Big{)}\Big{)}, \tag{22}\]

where the function \(s(\cdot)\) provides the smoothness value of a feature point \(p_{k}^{i,j}\). We rewrite the bin encoding function to construct the smoothness scan context as follows:

\[\phi\big{(}\mathcal{P}_{ij}\big{)}=\underset{p_{k}^{ij}\in\mathcal{P}_{ij}}{ \max}\Big{(}s\Big{(}p_{k}^{i,j}\Big{)}\Big{)}, \tag{23}\]

where \(p_{k}^{ij}\) is the set of points belonging to the bin with the \(i\)th ring and \(j\)th sector. Using the smoothness elements, the number of point clouds for the scan context is reduced by two orders of magnitude. The proposed algorithm only needs thousands of features to achieve the bin encoding function; in contrast, taking a 16-line Lidar as an example, the number of raw point clouds exceeds 30,000 in a frame scan. In the following scan context process, the search module is implemented by the two-phase search algorithm proposed in [36]. Building on this logic, the candidate loop closure frame \(\mathcal{P}_{c}\) can be calculated. Once \(\mathcal{P}_{c}\) is determined, the relative motion between the current frame \(\mathcal{P}_{k}\) and the candidate frame \(\mathcal{P}_{c}\) can be calculated using the ICP function \(h(\cdot)\), as follows:

\[\Delta\mathbf{T}_{k,c}=h(\mathbf{T}_{k},\mathbf{T}_{c}),\quad(k\
eq c+1) \tag{24}\]

where \(\mathbf{T}_{k}\) and \(\mathbf{T}_{c}\) are the poses corresponding to keyframes \(\mathcal{P}_{k}\) and \(\mathcal{P}_{c}\), respectively. The relative transformation \(\Delta\mathbf{T}_{k,c}\) between \(\mathcal{P}_{k}\) and \(\mathcal{P}_{k}\) is the loop closure factor linking these two keyframes. ## 4 Experimental Evaluation

To qualitatively and quantitatively analyze the proposed method, we conducted a series of experiments to evaluate F-LIOM and compare it with the state-of-the-art FLOAM [13], LIO-SAM [14], and LeGO-LOAM [12] methods. The physical experimental platform of this paper is shown in Figure 2a. A Leisen C-16 Lidar and a MicroStrain 3 DM-GX3-25 IMU were installed on the ground mobile robot TIABBOT TOM08Q2. TOM08Q2 is a four-wheel independently driven mobile robot with a maximum speed of 2 m/s and a drive wheel diameter of 152 mm. All the experiments were implemented in C++ and executed on an Intel NUC equipped with a Core i3 CPU and 4 Gib memory using the robot operating system (ROS) in the Ubuntu operation system. Different datasets were collected to validate the performance of F-LIOM in terms of rotating, moving, and loop closure. ### Outdoor Environment

This test aimed to evaluate the performance of F-LIOM in outdoor scenes when the system encountered aggressive perturbations in translation or rotation. We first drove the robot at a non-uniform speed in different outdoor scenes to validate the performance of the mapping. The reason for emphasizing non-uniform speed was to prove that GP contributed to eliminating point-cloud distortion under natural working conditions.