Table of Contents
People often ask, how to make a point cloud with a rangefinder?
Let’s find out!
How to Make a Point Cloud With Rangefinder?
The first step is to find out what kind of point cloud you want to make. There are two main types of point clouds: 3D and 2D. A 3D point cloud is made from a series of points that define the shape of something. For example, if you wanted to make a 3D model of a house, you would take measurements at different points around it. These points could be taken using a laser scanner or by taking photos of the object and then measuring the distance between each photo.
2D point clouds are used to represent the surface of objects. They are usually created by scanning them with a laser rangefinder. This type of point cloud is often called a ‘point cloud’ because it represents a set of points (in this case, the laser beam hits the target).
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Calibration Approach
The basic principle of the extraneous calibration of parameters between multiple LRFs is to establish correspondence features between their observations and to estimate the transformation matrix among them.
After two LRFs scans a target with a known radius in 3D space, there are two scanning planes containing a circular arc. By using PCL processing capabilities and the RANSAC method, the radius and the center of the circle can model, and then the center coordinate of the sphere in the body frame of each LRF can be extrapolated.
Even though the scanning planes from the two LRFs are different at the same time stamp, their calculated spherical centers can still be common within the global reference system, and they become a set of CPs for the estimation of the transformation matrix between the body frames of the two LRFs.
While continuously moving the target in the common view, we can obtain hundreds or thousands of pairs of CPs for establishing the calibration equation, which can be solved by a least square problem based on SVD or a nonlinear optimization problem based on a least square bundle adjustment.
Point Cloud Filtering
The red box is the filtering range, and the white points are the original point cloud. The green points are filtered out.
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RANSAC Circle Model Fitting
RANSAC is an iterated and non-deterministic algorithm used to estimate the parameters of the mathematical model from a set containing outliers. Assuming that there is a circle within the observations from the two-dimensional laser rangefinder (LRF), we can detect the circle by using the RANSAC algorithm and obtain some reliable properties such as center coordinates and circle radius, etc.
In order to fit a circle model to a set of data, we first need to select a subset of data as our hypothesized inliers. We call this subset the hypothetical inlier set. Then, we fit a circle model to the selected subset using the least squares method.
Once we have found the circle parameters (center and radius), we test each remaining point against the circle model. Points whose distance to the center is smaller than the circle radius are considered to be inliers.
A greedy algorithm always selects the first element in the list. In this case, we use a greedy algorithm to select the first element in the array.
The circle model is used to estimate the center of a circle. In this case, we want to know what the center of a circle looks like. We need at least three samples to get an idea about the shape of the circle.
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Extrapolation of the Spherical Center
Spherical centers are calculated by finding the average of the x-y coordinates of the points on the circumference of the circle. This is done using the following formula:
(x1 + x2 +… + xn) / n
The distance between the two centers is then found by subtracting the center point from the spherical center.
CP Matching
At the same time, although the scanning planes are different, the spherical centers of the LRFs are still common within the reference frame, and they form a pair of CPs to be used as the basis for the rotation matrix between the two Lrf bodies.
As long as the target is moved continuously by the LRFs, multiple pairs of CPs can be matched from multiple observations aligned with a specific timestamp.
Spherical centers of two laser sensors are synchronized. The distance between them is about 2 cm. The difference in the timestamps of the collected data is less than 5 ms. The error caused by the sensor sample being out of sync and movement of the spherical center can be ignored.
The error in the X and Y positions is mostly due to the error in the circle center. The error in the Z position depends on the radius of the circle and the radius of the ball. Both radii are uncorrelated, so the total derivative equation of (2) can be written as follows:
$$\frac{d^3r}{dt^3}\frac{1}{4}\left(\frac{dr}{dt}\right)^2+\frac{1}{2}\frac{dr}{dt} \frac{dR}{dt}$$
A machine with a CP with a low error can be selected to provide a high-precision calibration. After the selection, the detailed analyses of which will be presented below.
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Calibration Model
Calibration is used to estimate the transformation matrix from sensor to camera coordinate system. This process is called absolute orientation. A set of matched CPs must exist for each camera. Each camera is calibrated using a single CP.
This is the basic calibration model used in this paper. The goal is to solve for the rotation matrix R that minimizes the error of the CP pairs. Since the precision of each coordinate observation is roughly equal, and the point-to point error minimization metric is the objective optimization function, we use the following equation as our basic calibration model:
$$\min_{R} \sum_{i1}^{n}\left\|\
Solution of Equations
For the convenience of taking the derivatives of (7), the lie algebra form of the transformation matrices can be introduced as follows: is a 6 dimensional vector corresponding to the 6 degrees of freedom of the transformations matrices T, the first dimension represents translation but does not equal, the last dimension represents the Lie algebra of rotation, and the other terms are intermediates variables described in detail in Lie algebras theory.
The correlation between the two parameters affects the behavior of the reduced norm equation. This causes the morbidity of the normal equations matrix.
We should use the technique of iteration by adjusting the characteristic value to solve this problem of morbidity.
Processing Procedure
Calibration is the process of determining the relationship between two coordinate systems. In this case, we use a mobile sphere as an object to calibrate our system.
The first step is to calculate the spherical center of the mobile sphere. Then, we match the coordinates of the mobile sphere using the two lasers’ positions.
Finally, we determine the transformation matrix between the two coordinate systems.
Data Introduction
The Hokuyo UMT-30LX is a passive sensor that measures distance using reflected near-infrared light. It is used to detect objects such as people, cars, or animals. It is also used to detect the position of vehicles, pedestrians, and other objects.
Circle Model Fitting and the Distribution of CPs
The laser scanning data was filtered by our proposed method. The result shows that the majority of noise was removed effectively.
How to Make a Point Cloud With Rangefinder?
Conclusion
New calibration method for a combination of two 2D laser rangefinders (LRFs) based on a mobile sphere is presented. The proposed method is automatic and accurate.
Furthermore, a CP matching machine with a restriction constraint of the scan radius is established.
Experimental results indicate that the method can match the CPs with a low RMSE and improve the orientation accuracy to about 0.01 m.
This result suggests that the calibration method in our paper is effective and meets practical measurement requirements.
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