Autonomous road vehicles are increasingly becoming more important and there are several techniques and sensors that are being applied for vehicle control. This paper presents an alternative system for maintaining the position of autonomous vehicles without adding additional elements to the standard sensor architecture, by using a 3D laser scanner for continuously detecting a reference element in situations in which the GNSS receiver fails or provides accuracy below the required level. Considering that the guidance variables are more accurately estimated when dealing with reference points in front of and behind the vehicle, an algorithm based on vehicle dynamics mathematical model is proposed to extend the detected points in cases where the sensor is placed at the front of the vehicle. The algorithm has been tested when driving along a lane delimited by New Jersey barriers at both sides and the results show a correct behaviour. The system is capable of estimating the reference element behind the vehicle with sufficient accuracy when the laser scanner is placed at the front of it, so the robustness of the control input variables (lateral and angular errors) estimation is improved making it unnecessary to place the sensor on the vehicle roof or to introduce additional sensors.
Autonomous road vehicles are increasingly becoming more important and all manufacturers are involved in research projects in order to develop semiautomated or fully automated solutions [
The three most common methods for detecting long-range obstacles are radar [
Several techniques have been implemented to develop autonomous vehicle control, including navigation methods such as waypoints using Global Navigation Satellite Systems (GNSS) [
Laser scanners are taking on a very important role in the problem of autonomous driving, especially since they have moved from 2D scanners to 3D. By using 3D data, the problems of using 2D laser scanners are avoided, for example, measurement errors by the partially hidden observation of an obstacle or greater detail of the information obtained. Also, with 3D data, the information obtained is considerably more complete and can be used for several purposes [
This paper presents an alternative system for maintaining the position of autonomous vehicles without adding other elements to the standard sensor architecture by using the 3D laser scanner for both obstacle detection and positioning the vehicle in situations in which the GNSS receiver fails or provides accuracy below the required level. To this end, a representation of a reference element, such as a barrier, a tunnel wall, or a lane line (Figure
Elements perceived by the laser scanner for autonomous vehicle guidance: (a) new Jersey barriers, (b) tunnel wall, and (c) lane lines.
For a reliable representation and in order to reduce the influence of possible erroneous points, it is recommended to acquire points in front of and behind the vehicle. However, this would involve placing the sensor on the top of the vehicle, which is not the most feasible solution for implementation in a vehicle, or using the information fusion from various sensors [
The variables estimation for autonomous vehicle driving is based on a laser scanner, a technology that has been widely used for these purposes. As a sensor for identifying obstacles and autonomous navigation, a VLP-16 Velodyne 3D LiDAR sensor has been used which measures distances in real time by measuring the Time of Flight (TOF). This kind of laser scanner is a sensor used in automotive environments to detect objects that may appear in the surroundings of a vehicle. It is possible to acquire data from 5 to 20 Hz, with amplitude of 360° horizontal view (FOV, Field of View) and 30° vertically distributed in 16 layers, which provides up to 300,000 points per second. These sensors were originally developed for the DARPA (Defense Advanced Research Projects Agency) autonomous vehicle competitions [
With this equipment, it is possible to detect clouds of tridimensional points that represent obstacles, vehicles, pedestrians, and other road elements. However, the information generated by this sensor can also be used to detect the road boundaries as well as the separation between the lanes of the road. In Figure
Raw information captured by a 3D laser scanner on a highway section.
Two possible locations for the laser scanner in the vehicle (at the front and on the top) have been considered (Figure
Possible sensor placements. (a) At the front of the vehicle. (b) On the vehicle roof.
Unlike [
As mentioned in [
Furthermore, to keep computational complexity low, and when the characteristics of the object and its detection make its height irrelevant, the problem can be tackled by building a 2D model from the information provided by the 3D point cloud, just as is performed by other detection algorithms [
The detection algorithm for vehicle guidance is defined in 7 steps.
This region is defined as a function of the look-ahead distance following the suggestions developed in [
Each 3 points are grouped into sets following a criterion of neighbourhood, using Delaunay triangulation. This first clustering allows the representation of the detected objects as a set of surfaces, whose features will allow further analysis and classification.
(a) Delaunay triangulation mesh. (b) Normal vectors. (c) Detected obstacle. (d) Interest zone and control parameters calculated.
Once the mesh has been triangulated, the equation and the normal vector of each triangle are calculated in order to consider the orientation of the surface. Then, for each triangle
With the information supplied by the normal vectors of each surface, a filtering operation is executed by removing the triangles whose normal vector direction is out of a prefix threshold based on the global vertical axis. In the case of the New Jersey vertical barriers, the boundaries of the threshold have been defined between 75° and 90° from the horizontal considering the barrier geometry [
The next step is the clustering of the different set of points which are detected as candidates to represent a lateral barrier or wall. The calculations to determine the clustering and the shape of the barrier are made using bidimensional points since the vertical coordinate is not relevant once the barrier has been detected. This clustering is based on the Euclidean distance between the points and their density, using the density-based spatial clustering of applications with noise (DBSCAN) method [
Finally, once the candidate set of points is selected, the mathematical function that defined the barriers structure is calculated using a quadratic regression. Consider
Then it is possible to calculate the two main variables necessary to perform the autonomous vehicle control: the lateral and angular errors. In order to calculate both errors, firstly the point
It should be noted that, in the case of an obstacle that is located near the barrier, such as a car or traffic signs, the clustering step may include their points as part of the selected cluster. In the event that the outsider element is far away from the car, the number of points might not be sufficiently representative compared to the whole barrier so the function calculation may not be affected. But, in the event of the element being near the vehicle, the number of points associated with this detection may be high and may affect the calculation of the reference element equation in a very significant way because of the high relative relevance of these points. This situation can be seen in Figure
Example of detected points’ density versus distance to the sensor and weighting function definition.
The road line detection is easier, since it is based on the identification of changes in the measurement of the reflectivity in those points detected on the surface of the road, as shown in Figure
Should the laser be placed at the front of the vehicle, there is no information about the points belonging to the barrier or the wall behind the vehicle. The proposed method to obtain the necessary variables for autonomous vehicle control is based on adding to the detected points of the reference element, the portion of the reference element that is behind the vehicle and is not detected by the laser scanner. Since the use of GNSS is not feasible due to the inaccuracy of the measurement if differential corrections are not available [
In order to extrapolate the reference element to the area without data for an accurate and stable quadratic regression calculation, the vehicle trajectory in the past should be reproduced to complete the SLAM problem. Different solutions could be proposed to estimate this trajectory: (
Considering the limitations of the first 2 methods discussed above and the fact that even techniques such as Kalman filtering could provide accurate results combining the first two approaches [
To estimate the vehicle’s trajectory by simulating the vehicle dynamics, very different degrees of complexity models could be used [
Dynamic equations of sprung mass movements have been written considering the Cartesian coordinates system fixed to the sprung mass in which
Linear movements are as follows:
Angular movements are as follows:
Tyre forces are calculated using the Dugoff model and traction forces are obtained from a propulsion system model that includes engine and transmission [
It should be noted that the implementation of this model does not have an excessively high computational cost, but it could be simplified to guarantee real time execution. In this regard, instead of using simpler models such as traditional 3 dof models (two-wheel vehicle model) [
The above mathematical model does not take into account the influence of road superelevation rate. However, this influence could be significant. In order not to increase the complexity of the 2 input variables’ look-up table, it is proposed to correct the input of the steering wheel angle depending on the road superelevation rate. Thus, Figure
Two-wheel vehicle model moving along a road section with nonzero superelevation rate.
This force generates the tyre efforts in order to achieve a force balance and they are given by the following:
Assuming a linear relationship between the lateral forces in the tyres and their slip angles and constant transversal tyre stiffness
In order to maintain a straight trajectory, the vehicle slip angle
The mathematical model of vehicle dynamics has already been validated [
Estimation of the trajectory using vehicle dynamics simulation.
Moreover, it should be noted that the estimates of the path are subject to cumulative errors, similarly to those presented in [
Errors in trajectory estimation on 20-metre-long road stretches.
Points number | 64 |
Average value | 0.2314 |
Standard deviation | 0.1741 |
The algorithm has been tested using New Jersey barriers as reference element for autonomous driving. Although the algorithm has been developed to place the sensor at the front of the vehicle, in order to perform the results validation, in these tests the laser scanner has been placed on top of the vehicle, retrieving 360° measurements. The test site was the BUS-VAO independent-lane along the A6 highway (Madrid, Spain), which has a length of 12 km and 2 lanes except in specific sections that only have 1. The lane is limited by New Jersey barriers on both sides that are interrupted only by the incorporations which are made only on one side. These barriers were used as a reference for guiding the autonomous vehicle. The speed was set between 45 and 60 km/h and the acquisition rate was 20 Hz.
Firstly, the desirability of using the weighting factor for outsider filtering elements was analyzed. Figure
Algorithm response (a) without weighting function and (b) with weighting function.
Furthermore, Figure
Algorithm response for same frame number in two different configurations: (a) use of points detected in front of the vehicle and (b) use of points detected in front of and behind the vehicle.
The previous results justify the need to apply the method that extrapolates the detected reference element behind the vehicle where the sensor is unable to perceive it. In order to check the reliability of this proposed method, Figure Estimation of the geometric characteristics of the reference element using only the points detected in front of the vehicle (the case in which the laser scanner is at the front of the vehicle). Estimation of the geometric characteristics of the reference element using points detected in front of and behind the vehicle (in which case the laser scanner is on the top of the vehicle). Estimation of the geometric characteristics of the reference element using the points detected in front of the vehicle and estimating the location of the points behind it.
As can be seen, the adjustment determined in case (a) is far from the real solution compared to that provided by case (b), since the information is lost behind the vehicle. However, the adjustment in case (c) achieves good results. Table
Deviations between estimates of parameters for guiding the autonomous vehicle.
(a)-(b) | (b)-(c) | |||
---|---|---|---|---|
Average value | Desv. est. | Average value | Desv. est. | |
LE (m) | 0.167 | 0.081 | 0.062 | 0.017 |
AE (°) | 2.668 | 1.293 | 0.886 | 0.241 |
Curvature (m−1) | 4.157 10−3 | 2.355 10−3 | 0.950 10−3 | 0.948 10−3 |
Estimation of the geometric characteristics of the barrier (a) using only the points detected ahead of the vehicle, (b) using points detected in front of and behind the vehicle, and (c) using the points detected ahead of the vehicle and estimating the location of the points behind it.
This paper has described the use of laser scanner technology to maintain the position of an autonomous vehicle even when the GNSS and inertial systems signals are not sufficiently accurate. This system is complementary to conventional guidance systems and works in parallel without interfering with obstacle detection systems. A method to increase the robustness of the data needed for autonomous driving along a reference element has been presented. Specifically, the proposed two major advances over other similar approaches are as follows: The method does not require the sensor to have vision of the reference element behind the vehicle. The method does not require absolute positioning (e.g., GNSS) or landmarks in the infrastructure
Since the environment is structured, it has been possible to base the system on a single sensor of relatively low cost compared to others available in the market (16 detection layers versus costly scanners with 64). Moreover, the implementation performed does not imply high computational complexity, so it can be executed in real time.
Finally, tests have shown the appropriate behaviour of the implemented algorithms and how they improve the solution in the case where only data ahead of the vehicle is considered.
External forces
External momentums
Linear velocities along Cartesian axes
Angular velocities around Cartesian axes
Vehicle mass
Moments of inertia of the vehicle around the three axes of the reference system
Moments of inertia of the vehicle
Vertical movement of
Mass of
Vertical stiffness of tyre
Forces transmitted by suspension spring
Forces transmitted by suspension shock absorber
Rotation speed of wheel
Moment of inertia of wheel
Longitudinal force at tyre
Moment at tyre
The authors declare that there are no competing interests regarding the publication of this paper.
This work has received the support of the Spanish Ministerio de Economía y Competitividad (TRA2013-48314-C3-2-R).