![](bg3.png)
To improve the IDM model, we introduce the
RSS (Responsibility-Sensitive Safety) model and use
it to calculate a more reasonable desired safe distance
(Shalev-Shwartz et al., 2017) (Shalev-Shwartz et al.,
2018).
2.2 RSS Model
Definition 1. (Safe longitudinal distance — same di-
rection) A longitudinal distance between a car c
r
that
drives behind another car c
f
, 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 a
max,brake
per-
formed by c
f
, if c
r
will accelerate by at most a
max,accel
during the response time and from there on will brake
by at least a
min,brake
until a full stop then it won’t col-
lide with c
f
.
Lemma 2. Let c
r
be a vehicle which is be-
hind c
f
on the longitudinal axis. Let ρ,
a
max,brake
,a
max,accel
,a
min,brake
be as in Definition 1.
Let v
r
,v
f
be the longitudinal velocities of the cars.
Then, the minimal safe longitudinal distance between
the front-most point of c
r
and the rear-most point of
c
f
is:
d
min
=
v
r
ρ +
1
2
a
max,accel
ρ
2
+
(v
r
+ρa
max,accel
)
2
2a
min,brake
−
v
2
f
2a
max,brake
+
(2)
2.3 SafeIDM
According to the definition of the minimum longitu-
dinal safe distance in RSS, it is possible for the min-
imum safe distance d
min
to be very small when the
current front vehicle speed is high. Using this defi-
nition of safe distance can greatly improve the issue
of abrupt braking caused by high speed but small cut-
in distances front vehicle in the original IDM model.
The desired following distance in SafeIDM can be de-
fined as follows:
s
∗
= 1.1 ∗d
min
+ s
0
(3)
Compared to the original IDM model, the
SafeIDM model provides a more reasonable acceler-
ation output when dealing with aggressive cut-in sit-
uations. However, this does not guarantee the safety
of the vehicle since the IDM model assumes that the
acceleration output is highly smoothed (typically us-
ing a fourth-order approximation). Additionally, the
SafeIDM model does not consider the safety of the
rear vehicle. We will discuss viable methods for en-
suring safety in longitudinal safety model in Chapter
4 and provide the complete algorithm in Chapter 5.
3 COUNTERFACTUAL
INFERRENCE
The longitudinal safety distance of an unmanned de-
livery vehicle is influenced by various factors, Fig.
2. In the context of this article, inferring the maxi-
mum braking amount of the front vehicle can signifi-
cantly contribute to determining an effective strategy
for the ego vehicle to adopt.To address this concern,
we present two hypotheses:
Hypothesis 1. When the front vehicle merges into
the lane occupied by the ego vehicle, it is essential
to consider the potential occurrence of accidents and
the associated liability concern. If, during the merg-
ing maneuver, the distance between the front vehicle
and the ego vehicle is too small, and the front vehicle
abruptly applies the brakes (resulting in a calculated
minimum longitudinal safety distance exceeding the
current distance), the responsibility for the ensuing
accident does not rest with the ego vehicle(as this can
be categorized as a deliberate collision).
Hypothesis 2. When following the ego vehicle, the
rear vehicle should consider the maximum braking
amount that the ego vehicle may adopt to maintain
a safe distance as much as possible. Compared with
unmanned delivery vehicles, human drivers have rich
driving experience in complex interaction scenarios,
such as aggressive cut-in scenario. Therefore, human
drivers adopt the practice of closely following due to
the presumption that, in this situation, the ego vehi-
cle does not require the implementation of excessive
braking strategies (in the vast majority of cases).
Based on Hypothesis 1, we can deduce the max-
imum braking amount that the front vehicle can uti-
lize in aggressive cut-in scenarios by solving the fol-
lowing equation in reverse, resulting in the calculated
d
min
exactly matching the current longitudinal dis-
tance between the ego vehicle and the front vehicle.
Similarly, based on Hypothesis 2, we can deduce
the maximum braking amount that the rear vehicle as-
sume the ego vehicle may take.
In order to not always use the worst-case assump-
tion, we propeses a graded risk strategy for the in-
ferrence of the braking amount of the front vehicle,
which means the braking behavior can be happend in
the condition of the longitudinal safety distance is sat-
isfied when the braking amount is in the set of [-0.5,
-1, -1.5, -2.0, -2.5, -3, -3.5, -4.0, -4.5, -5] as small as
possible(from the perspective of absolute values), if
the longitudinal distance between the ego vehicle and
the front vehicle is larger than the longitudinal safe
distance calculated by the assumption of the front ve-
hicle would brake at the maximum braking amount of
CFRLI-IDM: A Counterfactual Risk Level Inference Based Intelligence Driver Model for Extremely Aggressive Cut-in Scenario in China
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