4.1. Detection Range of the ADAS Applications
ADAS support the driver by assisting in longitudinal and lateral driving tasks, e.g., braking and steering, to increase safety and comfort while driving. Adaptive cruise control (ACC) is a typical ADAS function that adjusts the subject vehicle’s speed to ensure a safe distance from a preceding vehicle. Another important ADAS function that focuses on longitudinal driving tasks is the forward vehicle collision warning system (FVCWS), which monitors the speed and distance of the vehicle driving ahead to prevent a collision, or at least reduce its severity. While detecting a non-moving vehicle is optional according to ISO 15623 [
29], static obstacles discussion is included in this paper.
Since LiDAR systems provide accurate distance information, they are mainly used for ACC and FVCWS applications [
30,
31]. Because forward detection often requires a more extended range than monitoring the surrounding environment, the following discussions of the requirement are based on the assumption that an individual sensor located in the middle of the vehicle front is used.
The function of ACC is to control the driving speed to adapt to a preceding vehicle [
32]. The maximum required detection range
of the ACC function is calculated with the maximum driver-selectable set speed
and the maximum selectable time gap
by [
32]:
The standard ISO 15622 [
32] specifies that the minimum selectable time gap for the subsequent control shall be ≥0.8 s, and the system shall provide at least one time gap between 1.5 s and 2.2 s for speeds higher than 8 m·s
−1 (30 km·h
−1). For example, a detection distance of 85 m is required to have a time gap of 2.2 s at a speed of 38.8 m·s
−1 (140 km·h
−1).
The function of the FVCWS is to warn the driver when a preceding vehicle appears in the trajectory of the subject vehicle and becomes a potential hazard [
29]. The standard ISO 15623 [
29] specifies the range requirements regarding scenarios where a warning rises. Among them, three typical scenarios for the FVCWS according to different states of the obstacle vehicle are indicated in
Table 3.
In the first scenario, the preceding vehicle is traveling at the same speed as the subject vehicle, where the warning distance is only related to the subject vehicle’s speed and the driver’s brake reaction time .
In the second scenario, the preceding vehicle is regarded as a stationary obstacle. The subject vehicle’s deceleration must be taken into account by determining the warning distance.
In the last scenario, the preceding vehicle is decelerating with a relative speed relative to the subject vehicle, while the subject vehicle is traveling with . Scenario one and scenario 2 are the two boundary conditions of scenario 3 when and , respectively.
Increasing the brake reaction time T and the subject’s vehicle deceleration
increase the required warning distance. ISO 15623 utilizes the result in the study of Johansson et al. [
33] to determine the brake reaction time T. The study indicates that the reaction time of 98% of tested people is under 1.5 s. Moreover, the minimum subject vehicle deceleration
is given with 5.3 m·s
−2 by evaluating the emergency brake performance of cars on a dry, flat road surface in ISO 15623 [
29]. Different braking capabilities have to be additionally considered for other vehicles like trucks. The maximum warning distances for the three scenarios are presented in
Figure 2.
Although the driving speed on several motorways is not limited in Germany, most countries regulate the maximum driving speed. Typical speed limits are between 90 km·h
−1 and 130 km·h
−1. According to [
34], the maximum limit of the listed countries is 140 km·h
−1, chosen as the subject vehicle speed for scenario 3 in
Figure 2. Scenario 2 is a boundary condition of scenario 3 when the preceding vehicle decelerates until it stops. Therefore, concerning all scenarios and a subject vehicle speed of 140 km·h
−1, a minimum detection range of 200 m is required to avoid a forward collision.
Noticeably, overtaking maneuvers on rural roads require an extensive detection range to avoid a forward collision when the oncoming traffic is considered. For example, the German rural road is classified into four types [
35]. Two of them are designed with overtaking lanes, which means the overtaking maneuver can be achieved without the influence of the oncoming traffic. The other two rural roads have a maximum design speed of 90 km·h
−1 without overtaking lanes. Assuming that both the subject and oncoming vehicles are traveling at 100 km·h
−1 (which is the legal maximum and more applicable than the reduced design speed), a warning distance of 180 m is required.
4.2. Field of View Requirements for ADAS
Compared with straight roads, detection in curves requires an increased horizontal FOV. The ACC system shall enable the subject vehicle to follow a preceding vehicle on curves with a minimum radius of 500 m [
32]. The geometric relations to cover the complete lane width in a curve are shown in
Figure 3a. Equation (7) can be used to determine the half horizontal viewing angle
to completely cover the width of the own lane up to the apex of the inner curve, assuming that the subject vehicle’s position is in the middle of the lane. A larger horizontal angle is required to capture more distance in a curve.
In Equation (7),
is the curve radius, and
is the lane width. The lane width typically varies between 2.75 m and 3.75 m depending on the design speed and the number of parallel lanes [
35,
36]. Based on the maximum value of 3.75 m,
Figure 3b shows the required whole horizontal angle to cover the complete lane width as a function of the curve radius. Accordingly, the minimum horizontal FOV required for the ACC function is approx. ±5° concerning a 500 m curve radius.
The forward vehicle collision warning system (FVCWS) function is classified by curve radius capability that an obstacle can be detected in a curve with a certain radius in the subject vehicle’s trajectory. System classes Ⅰ, Ⅱ, and Ⅲ refer to the curve radii of >500 m, >250 m, and >125 m, respectively. Detecting a preceding vehicle with a lateral offset of up to 20% of its width must be possible from the minimum distance, which varies between 5 m and 10 m depending on the system class [
29].
Figure 4 illustrates these geometric requirements.
The minimum detection height
and the maximum height
from the ground are given in [
29] with 0.2 m and 1.1 m, respectively, to determine the vertical FOV for the FVCWS function. Concerning a vehicle width
of 2 m [
37], the resulting FOVs for the FVCWS function are listed in
Table 4.
The results in
Table 4 indicate that a smaller curve radius requires a larger FOV in horizontal and vertical views to detect potentially dangerous objects in the current lane. Concerning a minimum curve radius of 125 m, the horizontal angle to cover the full lane width must be more than 20° (see
Figure 3b), which is below the Class Ⅲ FVCWS. In summary, ADAS functions that focus on principal longitudinal driving tasks require a FOV of 32.6° × 10.2° concerning curve radii ≥ 125 m.
4.3. Angular Resolution Requirements
The angular resolution is defined by the minimum angular distance between two objects which can be resolved by LiDAR systems [
31]. According to the description in chapter 3, the angular resolution refers to the angle of two adjacent scanning points for scanning LiDAR systems and two adjacent detector pixels for non-scanning LiDAR systems.
Angular resolutions of 0.1°~0.2° are stated for LiDAR systems [
9,
10,
11,
12,
13]. Since it directly affects the detection performance, object detection algorithms based on LiDAR point clouds must be considered when determining the required angular resolution.
Table 5 compares the average precision and processing time for commonly used open-source LiDAR-based object detection algorithms. The algorithms are trained and tested on the KITTI validation set [
38] via OpenPCDet toolbox, using RTX 3080 GPU and i7-10700K CPU.
The KITTI dataset contains 7481 LiDAR frames (images) for training and 7518 LiDAR frames for testing. Among them, 80,256 objects are labeled, including eight categories, e.g., ‘Car’, ‘Truck’, ‘Pedestrian’, and ’Bicyclist’. The statistic of the dataset shows that cars, pedestrians, and bicyclists are the most predominant categories [
38]. Hence, they are focused on in this paper.
The average precision shown in
Table 5 is evaluated using the PASCAL metrics [
43], resulting from all the 7518 testing LiDAR frames in the KITTI dataset. In object detection tasks, recall is defined as the proportion of detected relevant elements over the total number of the relevant elements. Precision is the proportion of detected relevant elements among all detected elements. The average precision is computed from the precision/recall curve and defined as the mean precision at 40 equally spaced recall levels.
According to the results listed in
Table 5, each algorithm has minor differences in the detection performance of traffic objects. The average precision of all algorithms for identifying cars, pedestrians, and bicyclists has a standard deviation of 0.59%, 3.95%, and 1.77%, respectively. The PointPillars algorithm requires the shortest processing time for each image. Under the hardware conditions above, the processing of each image requires 0.027 s with GPU and 0.0286 s with CPU. This leads to a ~35 Hz data processing rate. An automotive sensor has to deal with real-time dynamic information to capture moving objects or obstacles. A minimum frame rate of 25 Hz has to be considered while selecting the frame rate for an automotive LiDAR [
44]. Concerning this requirement, the data processing has to be greater than 25 Hz to achieve real-time detection. PointPillars is the only algorithm that achieves a frame rate of over 25 Hz real-time detection on the tested system. Despite its average precision by pedestrians and bicyclists being slightly lower than other algorithms, considering the importance of real-time detection for automotive applications, it is selected as an example to obtain the angular resolution requirement in this paper.
Classification and position tasks are usually used to evaluate a detection result, e.g., “is there a car in the scenario?” and “where is it?” [
45]. The result is often visualized as a bounding box for each detected object with a confidence score.
The confidence score is the product of the probability that an object contained in a bounding box (P
object) and the intersection over union (IoU). If no object is contained in a box, the confidence score equals zero. Otherwise, it equals the IoU. The IoU indicates the overlap ratio between the predicted box
and the ground truth
, given with [
46]:
Lang et al. [
42] introduce the PointPillars algorithm in their study at first, and the threshold of the IoU is set to 0.5. According to Equation (8), an IoU of 0.5 refers to a maximum 33.3% offset between the predicted box and the ground truth, e.g., in the horizontal direction, leading to a maximum 0.67 m offset of car detections concerning a width of 2 m. The threshold of an IoU can be set to more than 0.5 to obtain a more accurate location prediction. Since many LiDAR-based object detection algorithms and evaluation metrics prefer to apply an IoU threshold of 0.5 to consider a correct detection [
39,
40,
41,
45], the angular resolution limits are acquired with 0.5 confidence as a reference in this paper.
Three of the most common road users are chosen for the detection. For cars and bicyclists, the detection is evaluated for two perspectives due to these participants’ different width and depth dimensions. Under an identical distance, the object at a larger cross-section perspective may be easily detected, leading to a minimum angular resolution requirement. Since pedestrians show a similar width and depth, only one perspective is taken into account.
The raw point clouds are downsampled to different angular resolutions to find a limit for the 0.5 confidence score. The Velodyne HDL-64E LiDAR used in the KIITI dataset has an angular resolution of 0.08° in the horizontal and 0.4° in the vertical direction. These values decide the finest possible angular resolution for the image and the minimum interval for downsampling. The upper limits for horizontal and vertical angular resolution are selected at 1.04° and 1.6°, respectively, providing enough tolerance for determining the angular resolution limit. For every object and perspective, 52 downsamplings are executed. The detection results for the three object types are shown in
Figure 5.
The right column in
Figure 5 shows the confidence score for various angular resolutions for the scenario shown in the corresponding scene in the left column. The threshold of the confidence score is set to 0.4. Since detections with a lower confidence score cannot be treated as positive classifications, they are shown as blank fields in the heatmap. The Velodyne LiDAR has a different angular resolution in the horizontal and vertical directions. Since using quadratic pixels is a more general approach to realize than using rectangular ones, especially with flash LiDAR systems, the required angular resolution for the confidence score of 0.5 is determined using this pixel shape.
The required number of LiDAR points is determined from the calculated results shown in the right column of
Table 6. In combination with the aspect ratio of the detection objects, this table gives the required number of quadratic shaped pixels (last column in
Table 6). The point numbers leading to a score between 0.45 and 0.55 are averaged. With a maximum variance of 5%, the estimated findings are able to offer a detection confidence of 0.5. The object aspect ratio is determined using the dimension of the raw point cloud shown in the middle column in
Figure 5. Since car windows usually do not appear in LiDAR point clouds (they do not backscatter the LiDAR irradiation), only the lower half of the vehicle body is considered.
Due to the different sizes of the objects, bicyclists and pedestrians require a finer angular resolution than cars for a successful detection at the same distance. In addition, objects are more difficult to detect in the rear view than in the side view. The resulting dependency between object distance and required angular resolution is shown in
Figure 6.
As shown in
Figure 6, the standard deviation of the required angular resolution for all scenarios reduces with an increasing distance. According to the discussion in
Section 4.1, a minimum range of 200 m is able to prevent a collision for traveling speeds of up to 140 km∙h
−1. This distance requires an average angular resolution of 0.07° with a standard deviation of 1.8% for all scenarios. The highest criterion among them is bicyclist detection in the rear perspective view. An angular resolution of less than 0.04° is required. This value will be considered for evaluating laser safety in the following section.
4.4. Laser Safety and Comparison of the Detection Range
Besides the influence of the radiation pattern, the output power, which is limited by eye safety, strongly affects the detection range. According to the IEC 60825-1 standard, automotive LiDAR systems are certified with laser class 1 as safe for the human eye [
29]. The following parameters are criteria that influence the determination of the accessible emission limit (AEL) under the consideration of eye safety [
15]:
The most significant hazard for wavelengths between 400 nm and 1400 nm is thermal damage to the eye’s retina. For pulsed LiDAR systems that operate with a wavelength <1400 nm, the output power limit is determined by applying the most restrictive of these three conditions [
15], namely:
The maximum AEL for a single pulse (AEL.single);
The average power for a pulse train (AEL.s.p.T) of an emission duration T;
The AEL for a single pulse multiplied by a correction factor C5 (AEL.s.p.train).
Among them, the emission duration T varies from 10 s to 100 s regarding the divergence angle of the laser beam [
15]. The correction factor C5 is determined by the effective number of pulses for a given exposure duration [
15]. Only AEL.
single and AEL.
s.p.T have to be compared for LiDAR systems that operate with a wavelength > 1400 nm. For the wavelengths > 1400 nm, radiation penetrates into the aqueous humour, where the heating effect is dissipated due to the water absorption [
15]. The following parameters are assumed to compare the limitation of the output power for LiDAR systems with different radiation patterns indicated in
Section 3:
Pixel number: 815 × 255;
Frame rate: 30 Hz;
Beam divergence in spot scanning LiDAR systems: <1.5 mrad;
Single pulse duration: 5 ns;
Number of light sources for each pattern: 1.
As discussed in
Section 4.2 and
Section 4.3, LiDAR systems require a FOV of 32.6° × 10.2° for ADAS functions. It is known that detecting a small object at a long distance requires a finer angular resolution than other situations. To detect a bicyclist with a rear perspective at 200 m, an angular resolution of 0.04° × 0.04° is necessary (see
Section 4.3). Accordingly, the pixel number of the considered LiDAR systems is 815 × 255. The pulse repetition rate of flash LiDAR systems is equivalent to the systems frame rate, defined here at 30 Hz.
Meanwhile, blade irradiation scanning LiDAR systems need only to scan in one direction. Hence, the pulse repetition rate of blade irradiation scanning LiDAR systems is 815 × 30 Hz for horizontal and 255 × 30 Hz for vertical scanning. For spot scanning LiDAR systems, the angle between two adjacent scanning points is the angular resolution. Thus, the laser’s beam divergence must be less than the angular resolution. Concerning a 0.04° angular resolution (see
Section 5), the beam divergence must be less than 0.70 mrad. Hence, the AEL of the spot scanning LiDAR systems is evaluated according to [
15] for beam divergences < 1.5 mrad.
On the contrary, the AEL of blade irradiation scanning and flash LiDAR systems is obtained according to [
15] for extended source radiations. Moreover, a typical single pulse duration of 5 ns is assumed [
16] to determine AEL.
single.
Figure 7 shows the maximum accessible exposure limits as a function of the wavelength for the three radiation patterns concerning the retinal hazard region (wavelength up to 1400 nm).
The AEL values in
Figure 7 indicate the energy limitation falling into the eye, assuming a 7 mm pupil aperture and 100 mm measuring distance. The most critical value of the three curves (two curves for wavelength > 1400 nm) has to be considered for a specific wavelength. The pupil aperture only occupies part of the irradiated area, depending on the distance and the beam divergence angle. Hence, the most restricted AEL value is not identical to the emitted energy of LiDAR systems which increases the possible emission of a LiDAR system.
Equation (9) indicates the calculation of the total accessible emitted energy at the pupil, which is donated by
.
where
is the energy limitation on the retina from
Figure 7.
is the ratio of the pupil area
and the size of the area irradiated by the laser
in a certain distance. For
, all emitted energy may fall into the observer’s eye, leading to
.
To further compare the detection range of the three radiation patterns mentioned in
Section 3, the following assumptions are made:
Optical efficiency of the emitter: 90%.
Optical efficiency of the detector: 90%.
Reflectivity of the object: 10% with Lambertian scattering characteristic (
Section 3).
Aperture of detector optical system: Ø 25.4 mm (1′′).
Pupil diameter: Ø 7 mm.
Atmospheric attenuation and scattering: neglected.
Pixel gap: neglected.
Intensity distribution of the emitter: homogeneous, K = 1.
A typical wavelength of 905 nm can be stated for automotive LiDAR systems [
1,
9,
47,
48]. Therefore, a wavelength of 905 nm is considered for exemplary systems. According to
Figure 7, the emission energy for a spot scanning LiDAR system is limited to 0.1608 nJ at this wavelength. The limit is 77.49 nJ for vertical and 247.7 nJ for horizontal blade irradiations. In contrast, the emission energy of flash LiDAR systems can be up to 445.3 nJ.
The type of detector determines the required receiving energy of LiDAR systems. The comparison of the maximum detection range for different radiation patterns has to be assumed to use identical detectors. For example, SPADs are appropriate for LiDAR systems to achieve a long detection range due to their single-photon sensitivity. The energy of a single-photon saturates the detector, causing it to enter the death time (see
Section 2.2). During this death time, other photons received by the detector no longer generate electrical signals. In this case, the required energy for one detection equals the energy of a single photon. Multiple measurements can compensate for the uncertainty caused by single-photon measurements (see
Section 2). The energy of a single photon
at 905 nm is 2.2 × 10
−19 J, according to Equation (10), with
as Plank’s constant and the light speed
.
The nominal ocular hazard distance (NOHD) is the distance from the output aperture, beyond which the emitted energy remains below the AEL [
15]. For each assumed NOHD, the corresponding maximum energy output can be calculated according to Equation (9). This leads to a detection range (calculated with the equations in
Table 2) for each scanning type depending on the chosen NOHD (
Figure 8).
For spot irradiation, a laser beam with a divergence angle of 0.04° extends to the pupil diameter of 7 mm in about 10 m. All the emitted energy is able to fall on the retina up to this range. Hence, the total emitted energy equals the AEL value and leads to a constant detection range of ~103 m. As the NOHD increases further, the spot irradiation covers a larger area than the pupil aperture, allowing an increased energy output and an extensive detection range. Concerning a detection range of 200 m, an NOHD of ~20 m is required.
For blade and flash irradiation, the detection range increases significantly with the NOHD. With the given assumptions, horizontal and vertical blade irradiation enables a detection range of the required 200 m with an NOHD of 0.03 m. These distances can easily be maintained with a suitable housing or mounting position of the system. For flash irradiations, the eye-safety distance (NOHD) is 0.17 m.