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To check the accuracy of the distance measurements using LiDAR when a water puddle exists, we configured an experimental device as shown in Fig. 1. A reservoir filled with water was placed on a floor, a plate with a square hole was placed on top of the reservoir, and a LiDAR sensor was installed pointing towards the center of the water surface. At the center of the water, the angle of incidence of the laser beam was 0°, and the angle of incidence increased in the left and right directions. The change in the accuracy of the measurement value of the angle of incidence was confirmed by moving the position of the water tank

Fig. 1. 
Experimental setup; (a) LiDAR, plate and box with water. (b) Photo

Fig. 2 shows the surface coordinate x, y from LiDAR. The right and top directions are the +X and +Y, respectively. Although the distance from the center to the water was 0.6 m, inaccurate values were output in the water surface area. More importantly, many measurements had an output of 0 because of a failure to measure properly. In this study, the goal was not to accurately measure the distance to the water surface but to recognize the area with water.

Fig. 2. 
LiDAR measurement

3D LiDAR is designed to scan a certain range of vertical and omnidirectional horizontal surfaces. For Ouster OS1 LiDAR, which was used in the experiment, the horizontal plane is scanned with 2048 channels, and the vertical plane is scanned with 128 channels over a 45° range. As shown in Fig. 3, an index was used to distinguish each measurement point; the vertical surface had an output format in which the vertical index j increased from top to bottom, and the horizontal surface had an output format in which the horizontal index i increased clockwise when viewed from above.

Fig. 3. 
LiDAR outputs index

In this study, to increase the measurement range and resolution of the vertical plane, we rotated the LiDAR 90° and fixed it, as shown in Fig. 1, and the resolution of the vertical plane was used as 2048 channels. In this paper, the LiDAR index is denoted as i, as shown in Fig. 3. LiDAR measures the distance to the laser beam reflection point (R), and outputs the coordinates of the reflection point (x, y, z) with respect to the LiDAR origin calculated internally using Eq. (1).

The computation time is reduced and the sampling frequency is increased by storing the values of cosθcosψ, cosθsinψ, sinθ for each scan position in advance as constant values, and the coordinate values are output by multiplying them with the measured distance value R. If the distance value is 0 owing to a measurement error, all the coordinates of the reflection point are output as 0. Although such errors rarely occur during LiDAR scanning, we confirmed that many errors occur when scanning the water surface. Therefore, the coordinate values may include significant amounts of errors; therefore, the intensity information is expressed based on the index value of the LiDAR instead, as shown in Fig. 4. In the figure, when the index value is 1024, the laser ray hits the center of the water surface. The intensity is relatively small in the area with water, and differences are observed in the plate part above the water tank located on the left and right sides and in the floor part on both sides. This paper presents a method for differentiating laser reflection surfaces using intensity information.

Fig. 4. 
LiDAR intensity output

The basic principle of LiDAR, which measures the distance to a reflection point, involves calculating the distance from the time required for the laser light to reflect and return. LiDAR provides not only the coordinates for each measurement point but also information such as intensity and reflectivity.

Fig. 5 shows the parameters associated with LiDAR installed at a height of h above the ground.

Fig. 5. 
Parameters for LiDAR sensing

The index value increases from top to bottom when scanning the vertical plane, and this is the movement position of the LiDAR internal mechanism, which can be assumed to be accurate. The angle changes for each index are set as equal; therefore, the value of ∆θ in the figure is constant. The distance from the LiDAR origin corresponding to index i to the measurement point has the following relationship:

The intensity is affected by the ambient lighting, reflector material, angle of incidence, and distance. For a surface with the same reflectivity, the intensity of the light reflected by the laser beam is inversely proportional to the square of the distance.

For the main area of interest, which is the lower half of the front when the LiDAR is installed at the height h = 0.8m, the relationship between the index value and the inverse squared distance is shown in Fig. 6. We can reasonably assume that 1R2, shown in blue, has a linear relationship with index i. The red line in the figure represents a linear relationship with the index.

Fig. 6. 
Calculated 1R2 versus index, i and linear regression results

Because the intensity is proportional to 1R2, and 1R2 has a linear relationship with i, the intensity is assumed to have a linear relationship with i for the same reflector material, and the measured intensity is analyzed using the linear regression method.

In the linear regression method, the relationship between the input variable x_{i = 1,...,N} and output variable y_{i = 1,...,N} is expressed in the form of Eq. (4), where y^ is the output value obtained using the linearized equation.

The parameters a, b are obtained by the following minimization method.

Using the expressions defined in Eqs. (6)-(8),

where x- = 1N∑i = 1N xi and y- = 1N∑i = 1N yi,a,b, in Eq. (4) can be obtained using Eq. (9) and Eq. (10), respectively:

To explain the concept of group segmentation, if the distribution of x, y consisting of two groups with a linear relationship is shown in Fig. 7.

Fig. 7. 
Sample data for segmentation

The method of segmenting data into two groups involves finding values that classify one group of ranges i = 1, ⋯ , k-1 and the other group of ranges i = k, ..., N, which is an optimization that minimizes the objective function in Eq. (11).

where, y^1,i is the output calculated using the equation after linearizing the group consisting of i = 1, ⋯ ,k-1 and y^2.i corresponds to the group consisting of i = k, ⋯ , N. The expected optimization results are shown in Fig. 8. The dotted lines represent linear equations for each group.

Fig. 8. 
Data segmentation results for two groups.

To improve the speed of the optimization process, we use the relationship in Eq. (12) to calculate Eq. (11).

Because the number of groups cannot be specified in advance for the measured values of the area of interest, the number of groups is also determined in the optimization process. This method is based on the residual error (sum of squares error) of the entire dataset. For example, if the residual error divided into two groups is smaller than the residual error when expressed as a single group using a linear regression equation, it is divided into two groups. However, as the number of groups increases, the residual error naturally decreases. Thus, a penalty that increases linearly with the number of groups is used.

With this method, the experimental results shown in Fig. 3 were segmented into five groups, as shown in Fig. 9.

Fig. 9. 
Segmentation into five groups based on intensity

The intensity changed depending on the type of reflection surface. The results show the water surface in the center, the left and right sides of the center, which were the plates above the reservoir, and both ends of the floor.

Potholes or puddles in front of the driving direction must be detected using LiDAR when driving on rough outdoor terrain. Thus, three experimental environments, as shown in Fig. 10(a) were studied: a water puddle in which the reservoir was buried, a pothole after the reservoir was removed (Fig. 10(b)), and the pothole filled with soil to flatten it (Fig. 10(c)).

Fig. 10. 
Experimental environment: (a) puddle, (b) pothole, (c) flat surface

First, for the puddle, the coordinates of the reflection point among the LiDAR output values for one vertical plane are shown as circles in Fig. 11. The water puddle was located 1.37 to 1.73 m ahead, the water depth was 0.08 m, and the height of the LiDAR origin was 0.6 m above the ground. The measurements of the reflected portion of the water surface did not indicate the location or depth of the water, and many measurements repeatedly had values of 0, as shown in Fig. 11. This was a measurement error in which the measured distance was 0, thereby the coordinate value calculated from this was an output of 0.

Fig. 11. 
LiDAR output (x, y) for an environment with a puddle

The results of group segmentation using linear regression for the output intensity and index values are shown in Fig. 12. The environment was divided into three groups: ground, central water, and ground.

Fig. 12. 
Segmentation of the LiDAR intensity output for an environment with a puddle

Fig. 13 shows the location of the water puddle, with the coordinate values belonging to the central group highlighted in green.

Fig. 13. 
Identified puddle in the LiDAR output (x, y)

Second, after the reservoir was removed, the intensity of the LiDAR measurements for the pothole formed a single group, as shown in Fig. 14.

Fig. 14. 
LiDAR intensity output for an environment with a pothole

Finally, the intensity measured after filling the pothole with soil and flattening it formed a group, as shown in Fig. 15, similar to the case with the pothole. We confirmed that only the cases in which water was present could be segmented into groups based on intensity values.

Fig. 15. 
LiDAR intensity output for flat surface

A method of detecting a pothole using distance R was published in [8]. For the three cases above, R with respect to the index is shown in Fig. 16.

Fig. 16. 
Index versus distance outputs for the puddle, pothole, and flat surface

Flat ground and potholes can be recognized by detecting changes in [8]. For puddles, some of these values are 0 in the area reflected on the water, but by classifying groups based on intensity, the ground and existence of puddles can be confirmed.

Measurements of intensity were performed on various surfaces including the asphalt, the brick and the rubber mat. Fig. 17 shows the results. We verified that a uniform surface may be modeled as linear function, while the brick surface shows larger variance.

Fig. 17. 
Various surfaces: (a) asphalt, (b) brick, (c) rubber mat (d) intensity

The Lidar has an internal 3-axis accelerometer and the update rate is 100 Hz. By monitoring the vertical acceleration, we can detect any abnormal vertical shock. This may cause incorrect point cloud reading. However, the intensity reading may not be directly affected.