Wide Open LiDAR Eyes
One of the main differences between LiDARs and their “cousins,” the cameras, is the additional dimension we get in LiDAR’s 3D point cloud. Accordingly, in my previous articles, I analyzed this 3rd dimension, both from the perspective of how far should a LiDAR “see” and why it is so important that we have a common language when discussing range performance.
This time, I want to discuss the horizontal dimension of LiDAR’s point cloud, specifically the HFOV (Horizontal Field of View).
Since Velodyne presented in 2007 the HDL-64E, which became the first commercially available, mass-produced real-time 3D LiDAR, most of their products have still been rotating systems that provide 360-degree HFOV, aka “spinners.”
Similarly, many other companies, such as Ouster, Robosense, and Hesai, started from 360-degree systems. As a result, these barrel-like systems became one of the most known identifiers of autonomous test vehicles.
However, in the last few years, we witnessed that most companies changed the mechanical scanning method to alternative, mainly solid-state scanning techniques, with a narrower FOV.
I’ll repeat this point: Most new systems have narrower HFOV than earlier LiDAR generations.
Moreover, among currently announced automotive LiDAR systems appears to be a considerable variance of HFOV values, as you can see in the following chart, where I presented the FOV dimensions of 88 different LiDAR systems or configurations:
The median values of HFOV and VFOV are 107deg and 25deg accordingly, while the standard deviation values are 106deg and 16deg.
Another representation of the spread of HFOV values is in the histograms below. In contrast to some agreement in the VFOV figures among most vendors, there is a significant diversification in the HFOV values:
However, when we look at the recent 29 design wins, as analyzed by Yole Développement, 66% percent of them have mechanical scanning methods, including the spinners.
As a result, I raise two questions:
- Should we aim to return to a bigger HFOV of 360 degrees in a mass-produced consumer automotive application?
- In case the LiDAR’s HFOV can be narrower than 360 degrees, “How wide should its “eyes” be opened”? In other words, what is the required value of the HFOV?
In addition, there is another open question of how we should define the HFOV of a LiDAR system, but I’ll leave it out of the scope of this article.
I’ll start with the second question since it deals with the requirements. Next, I’ll check if 360-degrees systems are essential to comply with these requirements.
How Wide Should be LiDAR’s “Eyes”?
To answer this question, we first need to define the appropriate conditions:
- Vehicle type — private vehicle (consumer vehicle/passenger car).
- LiDAR assembly type and location— front-looking: at the grill / behind the windshield / roof-top locations.
- Driving domain — see below.
- Scenario definition — see below.
Driving Domain Selection
We can divide automotive use cases into two major categories: The Highway domain and the Urban domain. By “Highway domain,” I mean high-speed freeways, motorways, expressways, etc. The “Urban domain” complements the Highway, including urban, suburban, rural roads, and streets.
Accordingly, the conditions in each domain significantly differ in terms of relevant driving speeds and what kind of potential obstacles the vehicle may encounter along its route.
For example, in an Urban domain, a scenario with a 90 degrees intersection is widespread. Accordingly, the HFOV requirements in the Urban domain will be higher to detect a perpendicularly approaching vehicle. However, such a scenario isn’t relevant in the Highway (as defined by the Vienna convention), and the HFOV requirements will be much lower. On the contrary, the driving speeds on the Highway are much higher, which require much longer detection ranges than in the Urban domain.
Consequently, the product requirements that come out of analyzing the two domains will differ. There are two primary options to settle this down:
- Assembling in the vehicle two different kinds of systems, one per each domain.
- Assembling a single robust system. To avoid over-spec or under-spec, the system design should include two types of performance areas: a wide short-range area for the Urban domain and a narrow long-range ROI (Range of Interest) area for the Highway domain. See examples in the following figure:
The pros and cons of each option are a topic for a whole new article, so I’ll leave them out for now. For marketing reasons, most datasheets focus on the wider type of HFOV appropriate for the Urban domain. Therefore, I’ll also analyze this use case rather than the narrower ROI requirements.
Scenario Definition
As I noted before, one of the most challenging scenarios, in terms of HFOV, for a LiDAR system is an intersection.
When two vehicles approach an intersection, we can draw an imaginary triangle between them, called a “Clear Sight Triangle,” that ensures both drives (or perception suites) can see each other.
Specifically, in the case of uncontrolled or yield-controlled intersections, the relevant Clear Sight Triangle is called an “Approach Sight Triangle.” In parallel, at a stop-controlled intersection used a “Departure Sight Triangle.” Both are defined by AASHTO (American Association of State Highway and Transportation Officials) in its Policy on Geometric Highways and Streets (2018, 7th edition), aka the “Green Book,” or “The Bible of Road Design.”
There are ten different intersection scenarios, but I’ll analyze only the two most extreme:
- Left turn at an uncontrolled intersection — in this case, the speed of the ego vehicle is the highest.
- Left turn at a yield-controlled intersection — in this case, required the longest clear sight triangle legs, resulting in larger viewing angles, even compared to stop-controlled intersections or crossing maneuvers.
Assumed driving conditions in an Urban scenario:
- Midblock driving speed: 100km/h (a high enough estimator, based on worldwide urban speed limits)
- Number of lanes to be crossed in the major road: 4
- Road grade: -5% (a measure of the road incline, source)
- Road surface: wet
Left Turn at an Uncontrolled Intersection
In this type of intersection, the driver of a vehicle, or the perception algorithms, should be able to detect potentially conflicting vehicles in a sufficient time to stop before reaching the intersection. Accordingly, we need to calculate the legs of the Approach Sight Triangle and then the angle between them.
The first leg corresponds to the stopping distance of the ego vehicle. To calculate it, I’m using the same formula I presented and explained in “How Far Should LiDAR “See”?”:
- Friction coefficient — For a wet asphalt road, the average friction coefficient is 0.5 (see table in (“How Far…”).
- Initial speed — According to AASHTO, field observations indicate that vehicles approaching uncontrolled intersections typically slow to approximately 50% of their midblock running speed. This occurs even when no potentially conflicting vehicles are present. I’ll use this statistical estimation for the ego-vehicle, but I take a more conservative estimate of only a 25% slowdown for the human driver in the opposing car. Therefore, the driving speeds are 50km/h and 75km/h, accordingly.
- Reaction time — The reaction time of the algorithms is less than 200ms. Nevertheless, I assume a much longer reaction time of 2.5 seconds to avoid abrupt breaks and frightening the driver in the opposing vehicle that may see a car speeding at the intersection and starting to brake only at the end.
Accordingly, using the formula above, we can calculate that the overall stopping distance of the ego vehicle on a wet road is 54.4m.
To find the other leg of the clear sight triangle, I need to calculate the distance the opposing vehicle passes during the same time required for our vehicle to stop. I know the speed of the second vehicle, but I need to calculate the overall stopping time:
By using the numbers I assumed above, the stopping duration is 5.3 seconds. At the same time, the opposing vehicle passes 111.1m at 75km/h.
Finally, we have both legs of the clear sight triangle and can calculate, using simple trigonometry, that the angle between them is 64 degrees, meaning the whole required HFOV is 128 degrees.
This result covers most of the relevant use cases, such as:
- Right turns and crossing maneuvers at uncontrolled intersections.
- Intersections with stop control on minor/major/all-way roads.
- Intersections with traffic signal control.
- Roundabouts.
- Left turns from major roads.
However, intersections with yield control we need to analyze separately.
Left Turn at a Yield Controlled Intersection
To make things simpler and shorter, to calculate the travel legs, in this case, I use the rules of thumbs presented in the “Green Book.”
Based on the assumption that drivers making turns without stopping will slow to a turning speed of 16 km/h, the leg length along the minor road should be 15m.
The time required for a passenger car to perform a left turn onto a four-way roadway with a 5% grade is 8.9 seconds. You can contact me for the detailed calculations or look at chapter 9.5.3 in the “Green Book.”
During the time gap, the opposing vehicle travels 247.2m, which means our clear sight triangle angle is 86.4 degrees, and the overall required HFOV is almost 173 degrees.
That’s huge!
How to Support Such a Huge HFOV?
Although implementing an HFOV of 128 degrees is challenging, it’s doable. Moreover, if we look again at the statistics, many existing systems have already reached this ballpark:
However, mainly for cost and efficiency reasons, 173 degrees is impractical for most scanning techniques … except for the mechanical one.
Can it be that the requirement of 173 degrees was the reason that spinning “Buckets” on the roof became so distinctive for autonomous test vehicles?
The short answer is — No. The longer one is below.
Analyzing the “Bucket”
Despite their unmatchable large HFOV, mechanically scanning systems have several critical drawbacks that are deal-breakers when we consider mass-produced consumer vehicles:
- Price — Due to their Opto-mechanical complexity, the spinners’ assembly, alignment, and calibration costs are higher than other techniques.
- Reliability — Since the spinners include a giant, but fragile moving optical module, their sustainability to mechanical vibrations and shocks is low.
- Design — Although spinners are standard in test vehicles, the chance that consumers will accept them in their private cars is pretty low. It’s worth reminding that the first adopters of LiDAR sensors among car manufacturers (OEMs) are the premium class vendors, such as BMW, Audi, and Volvo. In these vehicles, a sleek design is part of the required package. Accordingly, such OEMs aim to integrate the sensors as seamlessly as possible, which isn’t possible when assembling a “bucket” on the roof.
Finally, since having a 360-degrees sensor on the roof isn’t an option, it requires a seamless integration along the vehicle’s perimeter. But, in this case, about half of the FOV is blocked anyway.
Therefore, despite compliance with the 173 degrees HFOV requirement, mechanically scanning systems aren’t appropriate for consumer vehicles.
Instead, the vehicle surroundings should be covered using alternative solutions, such as assembling a cocoon of several LiDAR systems, as presented in the following figure:
Note: 360-degree sensors might still be a feasible option for robotaxis or autonomous trucks, where price, design, and even vibrations (for robotaxis) requirements are looser.
Should We Divide the HFOV any Further?
If we consider the cocoon as an acceptable solution to comply with the 173 degrees requirement, why can’t we divide the FOV for even more sections, using more systems with narrower HFOV? For example, using two systems with an HFOV of 64 degrees instead of a single system with 128 degrees.
The main reason is efficiency. A single system will be more efficient than several systems that cumulatively cover a similar FOV for the following principal reasons:
- Price — reducing the number of components, shortening the testing procedures, and cutting operational overhead by decreasing the number of systems contributes to a lower cost.
- Mechanical dimensions — a single external case and common internal components contribute to smaller dimensions.
- Wiring — A single system requires less wiring in the car, which is a big issue for OEMs.
- Synchronization — A single system needs to be synchronized to other sensors in the vehicle.
- ROI Integration — Integrating an ROI region at the vehicle’s front is more straightforward with a single front-looking system than two systems located at the corners. Moreover, both wide segment and ROI segment can be implemented in a single front-looking system, while with two systems assembled at the corners, most probably will be required a third system for the ROI.
- Best performance at the most critical directions — In many systems, the angular or range performance is slightly lower at the edges than at the center of the FOV, mainly due to optical reasons. Assembling two systems at the corners of the vehicle means that the edges of the FOV cover the vehicle’s front.
In conclusion, an optimal system should comply with most of the requirements but avoid an over-spec. For our matter, in my opinion, a single system with 128 degrees HFOV at the front of the vehicle will be much more cost-effective than two systems covering 64 degrees each. On the other hand, three systems with 120–130 degrees to cover all of the vehicle’s surroundings are preferable to two 180-degrees systems. This is due to the price, reliability, and design issues related to the design of ultra-wide FOV systems.
Summary
In this article, I presented the methods and primary considerations for analyzing the requirements of an automotive LiDAR Horizontal Field of View (HFOV). Based on the use cases I showed, you can see that the most practical requirement for LiDAR HFOV is about 128 degrees, especially when achieving it using a solid-state scanning technique.
Do you have any comments or questions? Do you want to see the statistical data of the systems in Charts 1 and 2? Contact me on LinkedIn!
Bonus trivia fact: The authors of Application of Light Detection and Ranging Technology to Highway Safety used LiDAR systems to test clear sight triangles in 2002, two years before the first DARPA Grand Challenge, and before anyone considered using them for autonomous driving.
Disclaimer: The analysis performed in this article is high-level and aimed mainly to present the way of thinking and principle calculations. It shouldn’t be considered as-is for a real-product design.
