Vision Zero: Can Roadway Accidents be Eliminated without
Compromising Traffic Throughput?
Shai Shalev-Shwartz, Shaked Shammah, Amnon Shashua
Mobileye, 2018
Abstract
We propose a new economical, viable, approach to challenge almost all car accidents. Our method relies on amathematical model of safety and can be applied to all modern cars at a mild cost.

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Introduction

In 1997 the Swedish Parliament introduced a “Vision Zero” policy that requires reducing fatalities and serious injuries
to zero by 2020. One approach to reduce the number of serious car accidents, which has been advocated by the “Vision
Zero” initiative, is to enlarge the tolerance to human mistakes by combining regulative and infrastructure changes. For
example, installing speed bumps in urban areas, which reduces the common speed from 50 kph to 30 kph, may makethe difference between a mild injury and a fatality when a car hits a pedestrian. Another example is not allowing agreen light for two routes at the same time (like “turn right on red” scenarios). The disadvantage of this approach isthat it compromises the throughput of the road system — for example, reducing the speed limit from 50 kph to 30 kph
increases traveling time by 66%.
Another approach to reduce the number of car accidents is to rely on Advanced Driving Assistant Systems (ADAS).
For example, a Forward Collision Warning (FCW) system alerts the driver when the car is dangerously close to a frontal
car and an Automatic Emergency Braking (AEB) system applies a strong autonomous braking at the last moment incase an accident is likely to happen. A recent study of the Insurance Institute for Highway Safety (IIHS) showsthat vehicles equipped with FCW and AEB systems have a 64% fewer front-to-rear crashes with injuries [1]. The
advantage of the ADAS approach is that it does not affect the throughput of the road system.
The main goal of this paper is to propose a roadmap for reaching an ADAS system that can substantially reduce
fatalities and serious injuries, at a reasonable cost, while sustaining the usefulness and throughput of the road system.
We emphasize that the industry as a whole keeps enhancing ADAS systems and comes up with novel new approaches(a notable example is Toyota’s Guardian [3]). Our goal is to put on the table a complete proposal with a clearly statedgoal, which is fully accessible to the public and to regulatory bodies, and which comes with some formal mathematicalguarantees.
Our starting point is exiting AEB systems. As mentioned previously, AEB systems already eliminate roughly 64%
of front-to-rear crashes. While this is an impressive achievement, we believe that the main reason some crashes are
not eliminated is because AEB is an “emergency” system rather than a “preventive” system. That is, AEB systems
are designed to react to an imminent collision (hence the term “emergency” in the acronym) rather than to prevent a
dangerous situation to occur in the first place. Indeed, the AEB test specifications by regulatory bodies (like ENCAP[2]) are geared towards avoiding or mitigating a collision that is expected if no action is taken. To balance safety
and comfort, normally the brake activation is applied at a very short time-to-collission (TTC) in order to reduce thechance of a false detection causing an unexpected brake activation1 . As a result, AEB avoids collisions at relatively low
speeds and somewhat mitigates collisions at higher speeds but even those are much lower than highway driving speeds.
Electronic Stability Control (ESC), on the other hand, is designed to reduce skidding, operates in a “preventive” fashion
1 Car makers adopt a variety of ”braking profiles”, but as shown in [5] all braking profiles begin braking at TTCs not higher than 2s.

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by limiting the maneuverability of the vehicle. Most drivers do not feel constrained and mostly are not even aware that
ESC was activated while those who seek full unencumbered control of the vehicle can always deactivate ESC if they
so desire.
The first step in our roadmap is therefore a “preventive” collision avoidance system in which a mild brake activation
is applied before the imminent danger occurs while keeping the comfort of driving intact. We wish to do so whileproviding formal guarantees of safety in the sense of proving that if all cars comply with the proposed system thencollisions rates will drop considerably below current AEB rates. Our approach embraces the “prevention” rationalof the “Vision Zero” initiative — unlike AEB systems, that are activated at the last moment, we would like to keep
vehicles from entering dangerous situations in the first place. A notable advantage of this “preventive” approach over
AEB is that unlike AEB systems that prevent an accident by braking very strongly (1.5g in some systems) and as aresult might cause someone else to hit us from behind, the preventive approach will eliminate the danger, of being hit
from behind, in advance by applying a mild brake. At the same time, we embrace the “keep the normal flow of traffic”
rational approach of ADAS systems in general, and AEB in particular, as we refrain from reducing speed without
distinction. Instead, we intervene in the driver’s decisions only when he/she is not “careful” according to the specificscenario.
At the heart of our approach is the Responsibility Sensitive Safety (RSS) model described in [4]. RSS formalizes
an interpretation of reasonable human common sense. RSS is a rigorous mathematical model formalizing an interpretation of a set of principles of reason, and has been designed to achieve several goals: first, the interpretation of how
humans interpret caution. Second, the interpretation should lead to a desired result (we call “Utopia”) that, if all agentscomply with RSS parameters, accidents, resulting from decision making processes, could be eliminated. Third, theinterpretation should be useful, meaning it will enable agile driving rather than enforcing an overly-defensive driving
which inevitably would block traffic and in turn limit the scalability of system deployment. Finally, the interpretation
should be efficiently verifiable in the sense that we can rigorously prove that a car will always obey the interpretationof human caution without the need to role out future actions of all agents involved.
Originally, RSS has been designed as a safety seal for the decision making process of self driving cars. However,
we show in this paper how a variant of RSS can be leveraged to ADAS, to enhance the safety of human drivers aswell while providing formal mathematical guarantees for safety when all agents comply with RSS. In a nutshell, RSS
introduces a parameter-based methodology for defining safe distances which when breached constitute a “dangerous”
situation. Safe distance was originally couched in a specific ”braking profile” that fits a robotic control. In this paper
we extend the definitions of RSS to include any braking profile and in particular we propose a jerk-bounded profilethat allows for relatively large TTC yet supports smooth braking. The benefit of couching a braking profile within
the RSS framework is that all the formal guarantees associated with RSS apply as well. Thus, rather than proposing
some heuristic of a braking profile, RSS enables a preventive braking system with formal guarantees. Furthermore, we
argue that the proposed RSS-for-ADAS system may be similar to ESC in the sense where most drivers would have noproblem with mild interventions of the car as a safety mechanism, and the few drivers which would like full unabatedcontrol for competitive driving will be able to shut off the system and be exposed to a higher level of accident risk.
The rest of the sections describe the roadmap for an ADAS system that enforces compliance with RSS rules. We
envision two stages of deployment where at first we propose merely an enhancement of existing AEB systems inthe sense of handling front-to-rear crashes only using existing front-facing sensing (camera or camera+radar). Our
proposal for stage 1, can lead to a significantly higher elimination rate of front-to-rear crashes, comparing to existing
AEB systems. The main improvement of stage 1 is due to the preventive approach, which will allow technology
providers to balance the false positive / false negative tradeoff in a better way. By considering the sensing capabilities
of existing systems, we estimate that the elimination rate of front-to-rear accidents will be roughly 99%. For the second
stage we envision a full surround camera sensing fused with a crowd sourced map, to enable the full implementationof RSS. The advantage of the full implementation is that RSS comes with the elegant mathematical guarantee, statingthat if all players fully comply with RSS rules, then accidents resulting from driving decision making process would
become rare, thus achieving Vision Zero 2 for all possible crashes. The cost of installing a camera surround system,in high volume, would be around 5 − 10 times the cost of existing AEB systems which is negligible compared to the
2 As we explain later, accidents can still occur if some agents do not comply with RSS rules due to hardware failure, sensing error, software
bugs or some “act of god”. But, it is reasonable to estimate that such failure will happen in less than 1% of the dangerous situations, and under thisassumption, at least 99% of the accidents would be eliminated.

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cost of accidents to society.

2Stage I: preventing front-to-rear crashes by Automatic Preventive Braking (APB)

The goal of stage I is to prevent front-to-rear crashes as an enhancement of existing AEB systems. As of 2018, AEB
systems are activated when the Time-To-Collission (TTC) to the front vehicle/pedestrian is very small. Typically, anumber between 1 to 2 seconds. The time to contact is the distance between the cars divided by their relative speed.
It follows that if the front and rear vehicles are driving at the same speed, the TTC is infinity. To illustrate why thisapproach is problematic, consider an extreme case, in which the rear vehicle is driving slightly faster than the frontvehicle. Say, the rear vehicle is driving at 10 m/s (= 36 kmh) while the front vehicle is driving at 9.99 m/s. If the
distance between them is x, then the TTC is x/0.01 = 100 x. Taking an AEB system which is being activated at TTC
of 2 seconds, we obtain that the system will not be activated as long as the distance is larger than 2/100m = 2 cm.
It follows that driving behind a car at a speed of 36 kmh and at a distance of 3 cm is considered “safe” by an AEB
system. This does not feel right.
The source of the aforementioned problem in AEB systems is that they do not consider a “what would happen if”
type of reasoning. Indeed, if the front car would suddenly brake, the AEB system would need a time to respond tothe change and it will most likely be too late. The common sense of a safe human driver is to be a little bit paranoid— a good driver keeps a safe distance from a frontal car so as to be ready for the unexpected. Of course, being
over protective is also not good, as it leads to an extremely defensive driving. The secret sauce is to be ready for theunexpected, yet reasonable, events, while ignoring completely un-reasonable events.
RSS [4] is a mathematical, interpretable, model, formalizing the “common sense” arguments above. In particular,
RSS formalizes• What is a dangerous situation ?
• What is the proper response to a dangerous situation ?
• What are the reasonable assumption a good driver can make on the future behavior of other road agents ?
• What does it mean to be cautious ?
For a detailed exposition of RSS we refer the reader to [4]. We do not intend to repeat all the definitions in this paper,
but only to introduce a generalization of RSS that will be useful for human drivers.
We first consider the simplest case of a front car, cf , driving in front of a rear car, cr , where both cars driving
at the same direction along a straight road3 , without performing any lateral maneuvers4 . RSS defines the notion of adangerous situation by relying on the following definition:
Definition 1 (RSS Safe Distance) A longitudinal distance between a car cr that drives behind another car cf , where
both cars are driving at the same direction, is safe w.r.t. a response time ρ if for any braking of at most amax,brake ,performed by cf , if cr will accelerate by at most amax,accel during the response time, and from there on will brake byat least amin,brake until a full stop then it won’t collide with cf .
Relying on the above definition, RSS states that:• A situation is dangerous if the distance is not safe.
• The proper response to a dangerous situation for the rear car is to brake (after a response time) by at leastamin,brake until either reaching a full stop or gaining again a safe distance3 see [4] on homomorphism from general to straight roads.
4 to support lateral maneuvers see Sec.3.

3Crucially, RSS’s proper response does not depend on the underlying driving policy. In fact, it can be embedded on
top of any driving policy. Our main observation is that we can embed RSS on top of a human driving policy. Basically,
whenever a human driver brings the car to a non-safe distance, the RSS-ADAS system will apply braking so as tobring the car back to a safe distance.
The problem with this naive implementation is that applying a strong brake without any warning might be dangerous by itself.5 To tackle this problem, we first propose a generalization of RSS (Section 2.1), and then we specify aparticular member of this RSS family that enables to intervene in advance but in a smooth manner without inconveniencing the human driver (Section 2.2). Another advantage of this approach is that it mitigates the danger of false
positives.

2.1

Generalized RSS

In the original definition of RSS, the rear car is assumed to accelerate during the response time and then to brake until
reaching a full stop. This is an example of a braking profile. More generally:
Definition 2 (Braking profile) A braking profile, B, is a mapping from initial kinematic state of the car (mainly,
initial velocity, v0 , and acceleration, a0 ) to a pair Tb , v, s.t. v : [0, ∞) → R is the future velocity of the car andTb < 0 is the first time in which v(t) = 0.
Some examples for braking profiles are given below:v0
and• The braking profile applied by the front car in the original definition of RSS is defined by Tb = amax,brakev(t) = max{v0 − tamax,brake , 0}.

• The braking profile applied by the rear car in the original definition of RSS is defined by Tb =and
if t ≤ ρ
v0 + tamax,accelv(t) = v0 + ρamax,accel − (t − ρ) amin,brake if t ∈ (ρ, Tb )0otherwise

v0 +ρamax,accel,
amin,brake

We now define a generalization of RSS’s safe distance.
Definition 3 (Generalized RSS Safe Distance w.r.t. Braking Profiles Bf , Br ) A longitudinal distance between a car
cr that drives behind another car cf , where both cars are driving at the same direction, is safe w.r.t. braking profiles
Bf , Br if in case the front car applies braking profile Bf and the rear car applies braking profile Br , then the cars
will reach a full stop without colliding.
The proper response is defined as follows:
Definition 4 (Proper response) Suppose the first time that the distance between cf and cr is non-safe is t0 , andw.l.o.g. set t0 = 0. Then, the proper response for the front car is to have its velocity at least vf (t), where vf is thevelocity defined by Bf , and the proper response for the rear car is to have its velocity at most vr (t), where vr is thevelocity defined by Br .
It is easy to verify that if both cars apply proper response then there will be no accident.

2.2

Jerk-bounded Braking Profile

In this section we describe the jerk-and-acceleration-bounded braking profile, denoted Bj . The idea is that we start
decreasing our acceleration linearly (with slope jmax ), until reaching a max brake parameter (denoted amin,brake ), andthen we continue to brake with a constant deceleration until reaching zero velocity. In the following we provide closed
form formulas for calculating this braking profile.
5 This is one of the main reason why existing AEB systems are tuned to have an extremely low probability of false positives. The price forextremely low false positive rate is a much higher false negative rate (meaning, the system fails to detect a car which is at a non-safe distance).

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Braking with a Constant Jerk Suppose we start braking at jerk of jmax . Suppose also that we can immediately
arrive to zero acceleration (leave the throttle), hence below we assume a0 ≤ 0. Then, the dynamics of the car is asfollows:a(t) = a0 − jmax t
t

Z t
1
1
v(t) = v0 +a(τ )dτ = v0 + a0 τ − jmax τ 2 = v0 + a0 t − jmax t2
2
2
τ =0
0

t
Z t
1
1
1
1
2
3
x(t) = x0 +v(τ )dτ = x0 + v0 τ + a0 τ − jmax τ= x0 + v0 t + a0 t2 − jmax t3
2
6
2
6
τ =0
0
Braking profile Based on these equations, braking distance will be defined as follows. Let T be the first time inwhich either a(T ) = −amin,brake or v(T ) = 0, that is,pa0 + a20 + 2jmax v0
a0 + amin,brake, T2 =.
T = min{T1 , T2 } where T1 =
jmax
jmax
The time for reaching full brake is
(
Tb =

T2

if T = T2

v0 +a0 T − 12 jmax T 2
amin,brakeotherwise

And the speed is as follows:12

v0 + a0 t − 2 jmax tv(t) = v0 + a0 T − 12 jmax T 2 − (t − T )amin,brake
0

if t ≤ T
if t ∈ (T, Tb )otherwise

Braking distance Finally, the car will move the following distance until reaching a full stop:
2
v0 + a0 T − 21 jmax T 2
1
1
2
3
v0 T + a0 T − jmax T +2
62amin,brake

2.3

Safe distance w.r.t. Bf and Bj

Suppose that the front car brakes with braking profile Bf (braking with a constant deceleration of amax,brake ), and therear car relies on braking profile Bj . Then, the safe distance formula is
"
#


2
1
2 2
v
v
+
a
T
−
j
T
1
1
0
0
max
f
2
v0 T + a0 T 2 − jmax T 3 +−2
6
2|amin,brake |2|amax,brake |+2.4

The Automatic Preventive Braking (APB) System

As soon as the distance becomes non-safe (according to the jerk-based formula), the APB system will start to brakewith a jerk of jmax until one of the following happens: (1) the car stops (2) the distance becomes safe, or (3) the driver
turns off the RSS system (by a button or some other mechanism).
An inductive proof, similar to the one given in [4], can show that if we start with a safe distance from a frontvehicle, and apply the proper response of the APB System, then under the assumption that the front vehicle will notbrake stronger than amax,brake , we will never hit the front vehicle from behind.

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2.5

A better balance between false positives and false negatives

It is worth noting that the same hardware that implements AEB nowadays can be adjusted to implement APB. Since
AEB systems brake abruptly at the last seconds before a crash, an activation of the AEB system is scary and dangerous(someone might hit us from behind), and hence AEB systems are tuned to have an extremely small rate of false
positives (a false positive event is when the system detects that we are going to crash into a “ghost” vehicle, which
is not really there). The price for an extremely small rate of false positives is a higher rate of false negatives (a false
negative event is when the system fails to detect a car, even though we are going to crash into it). Furthermore, sincefalse positive events are much more dangerous when driving at a high speed, AEB systems are only activated whendriving at a low speed.
In contrast, because the braking profile of APB is jerk bounded, the danger of false positives is much milder (thedriver will not be jolted, and a car from behind will also not be surprised because of the bound on the jerk). Therefore,
we can tune the system to have much less false negatives than an AEB system, and we can also activate the APB
system when driving at a high speed.

3Stage II: Beyond Front-Rear Accident Prevention

In stage II of the system, we require a surround (camera-based due to the required resolution) sensing system and acrowd sourced High Definition (HD) map. The surround system enables to prevent a car from performing a reckless
cut-in and to merge in junctions unsafely. The major contribution of the map is that the system has full knowledge on
where to expect potential dangers: it knows in advance where there should be lanes that might merge to our lane, who
has the priority, where to expect traffic lights, where to expect occluded pedestrians, etc. Planning in advance enables
the system to adjust speed mildly in advance and not to be surprised. In addition, a map enables to know the geometryof the road even without explicitly detecting lane marks. Finally, RSS is a formalization of reasonable common sense
in such scenarios. With the use of a crowd sourced map, we can gain access to road conditions and the actual dataon the behavior of road users at every road, thus helping regulators to define the appropriate rules for every road (forexample, to specify “school zone” areas in an automatic way).
Unlike geo-fenced autonomous driving applications limited to particular areas, an ADAS system would require
the support of an HD-map in all driving locations. An HD map that can offer coverage of the entire globe and isperpetually maintained fresh and updated by means of crowd sourced data. With a surround sensing and a map, we
can implement the full stack of RSS. The details can be readily inferred following [4] and the exposition of Stage-I
above.

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Utopia is (almost) Possible — Toward Reaching Vision ZeroThe premise of RSS is that “utopia is possible”, in the sense that if all agents fully comply with RSS’s proper response,6
then accidents resulting from wrongful driving decisions would become rare. And so, geographic regions enforcing
RSS on all vehicles (by regulation), will benefit from a substantially high level of road safety. It should be noted that
accidents can still occur as a result of conditions outside the driving decision making process, such as accidents caused
by vehicles that do not apply proper response due to a hardware failure (e.g. malfunctioning braking system) or due toperception mistakes (e.g., a system does not detect a car at a non-safe distance in front of us). However, suppose thatthe probability of such a failure is one in every 100 dangerous situations. While this level of accuracy is insufficient
for autonomous driving (an accident once in every 100 dangerous situation is a very bad result), it can be shown that
if this failure rate is maintained in ADAS systems, where the driver is still active and responsible, we can obtain an
elimination rate of roughly 99% of car accidents. This is a huge step toward fulfilling the “Vision Zero” initiative.
6 By “following proper response” we mean that the agents’ actual decelerations match the requirements of proper response.

6References[1] IIHS.
Gm
front
crash
prevention
systemscutpolice-reported
crashes.
https://www.iihs.org/iihs/news/desktopnews/gm-front-crash-prevention-systems-cut-police-reported-crashes,2018.
[2] 2020 ROADMAP. The european new car assessment programme. https://cdn.euroncap.com/media/16470/ratingsgroup-report-2015-version-10-with-appendix.pdf, 2015.
[3] PAUL SEREDYNSKI. As early autonomy questions roil the industry, toyota hews to driver-enhancement philosophy. https://www.sae.org/news/2018/06/tu-auto-interview-with-toyotas-ryan-eustice, 2018.
[4] Shai Shalev-Shwartz, Shaked Shammah, and Amnon Shashua. On a formal model of safe and scalable self-drivingcars. https://arxiv.org/abs/1708.06374, 2017.
[5] ADAC Report. Comparative test of advanced emergency braking systems. ADAC Vehicle Testing.

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