A Microscopic Human-Inspired

Adaptive Cruise Control for Eco-Driving

ECC 2020, Saint Petersburg, Russia

M. Mirabilio, A. Iovine, E. De Santis,M. D. Di Benedetto, G. PolaDepartment of Information Engineering,Computer Science and Mathematics (DISIM),Center of Excellence DEWS,University of L’Aquila, L’Aquila, Italy

May 12-15, 2020

Presentation Outline

1 Introduction

2 Model

3 Controller Design

4 Simulations

5 Conclusions

1 22

Traffic Control Problem

In the last decades the number of vehicles hasconstantly increased and that number is expectedto raise even more in the next years.

More vehicles on the roads means more timewasted in traic congestion, less safety and higherpollution.

Vehicles adopting dierent level of automation canreduce considerably traic issues.

F. Borrelli et al., "Control of connected and automated vehicles: State of the art and future challenges." Annual Reviews inControl, 2018.

2 22

Why Human-Inspired?

Objective: let the ACC mimic the human behavior

Incorporate the human psycho-physical responsein a car-following situation

Improve the controller response to the surroundingenvironment

Improve passengers feelings

3 22

Presentation Outline

1 Introduction

2 Model

3 Controller Design

4 Simulations

5 Conclusions

4 22

Reference Framework

We consider N vehicles, indexed by n ∈ 1, ..., N, with same length L and proceeding on a straightroad.

CollisionA collision is the event corresponding to a distance between two vehicles less than s = L+ L0, whereL0 ≥ 0 is an additional safety margin.

5 22

Dynamic Model

Given the sampling time τ , kτ denotes the k−th sampling time. Let pn(k), vn(k) and an(k) be theposition, velocity and acceleration of vehicle n, respectively. The state vector of the follower vehicle isdefined as

xn+1(k) =

xn+11 (k)xn+12 (k)xn+13 (k)xn+14 (k)

=

pn(k)− pn+1(k)vn(k)− vn+1(k)

an+1(k)vn(k)

(1)

We define the set of feasible states as:

X = x ∈ R4 : x1 ≥ s, |x2| ≤ vmax, |x3| ≤ amax, 0 ≤ x4 ≤ vmax, vmax, amax > 0 (2)

6 22

Dynamic Model

The discrete-time evolution of the continuous state is described by

x(k + 1) =

1 τ 0 00 1 −τ 00 0 1 00 0 0 1

︸ ︷︷ ︸

A

x(k) +

00τ0

︸ ︷︷ ︸

Bu

u(k) +

0τ0τ

︸ ︷︷ ︸

Bd

d(k) +

0τ00

︸ ︷︷ ︸

E

e(x(k)) (3)

Where:

u is the control input: acceleration variation, or jerk;

d = an is the acceleration of the ahead vehicle;

e(x(k)) = c1 + c2(x4(k)− x2(k))2, c1, c2 > 0, is the friction term.

7 22

Microscopic Hybrid Automaton

Given a pair (n, n+ 1) of vehicles, the hybrid automaton describing the follower is:

H = (Q,R4, U,D, f, Init,Dom, E) (4)

Legend

Q = qj , j = 1, 2, 3, 4 is the set of discrete states;

R4 is the continuous state space;

U = [−umax, umax] is the input space;

D = [−amax, amax] is the disturbance space;

f = fj , qj ∈ Q is the set of vector fields with fj : R4 × U ×D → R4;

Init ⊆ Q× R4 is the set of initial discrete and continuous conditions;

Dom : Q→ 2R4

is the domain map;

E ⊆ Q×Q is the set of edges.

8 22

Microscopic Hybrid Automaton

-15 -10 -5 0 5 10 15

x2 [m/s]

0

50

100

150

200

x1 [

m]

Domains

q1

q2

q3

q4

unsafe

Definition of the time head-ways needed to stopthe vehicle in dierent situations:

TE : R4 → R, TR : R4 → R, TS : R4 → R (5)

⇓

Definition of the corresponding space head-waysthresholds:

emergency distance ∆E : R4 → R;

risky distance ∆R : R4 → R;

safe distance ∆S : R4 → R;

interaction distance ∆D : R4 → R.

A. Iovine et al., "Safe human-inspired mesoscopic hybrid automaton for autonomous vehicles." Nonlinear Analysis: HybridSystems, 2017.

9 22

Microscopic Hybrid Automaton

-15 -10 -5 0 5 10 15

x2 [m/s]

0

50

100

150

200

x1 [

m]

Domains

q1

q2

q3

q4

unsafeThe space head-way thresholds are used to define the discretestates and their domains:

1. q1: Free driving;

2. q2: Following I;

3. q3: Following II;

4. q4: Closing in.

Property

The set Ω =(⋃4

j=1Dom(qj) ∩X)

is robustly controlledinvariant.

10 22

Presentation Outline

1 Introduction

2 Model

3 Controller Design

4 Simulations

5 Conclusions

11 22

Problem Definition

Methodology: Model Predictive Control

12 22

Problem Definition

For every qj ∈ Q:

a prediction horizon Nj ∈ N is chosen;

a cost function Jj is chosen so that the various objectives receive dierent weights.

We make a prediction of the leader acceleration in the near future:

d(k) = [an(k), an(k + 1), ..., an(k +Nj − 1)]T

where

an(k + i) =

an(k), if 0 < vn(k + i− 1) < vmax

0, otherwise

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Problem Definition

We define the output vector and the corresponding output reference vector as:

y = [x1 x2 x3 x4 − x2]T , yr = [∆Sdes 0 0 vdes]T (6)

The reference error is y = y − yr .

The instantaneous fuel consumption (or emission rate) is computed by the term:

exp(wTPCj z) (7)

where

PCj = PC+ for positive accelerations, PC

j = PC− for negative accelerations;

zT = [1 y3 y23 y33 ]T , wT = [1 y4 y

24 y34 ]T .

A. Trani et al., "Estimating vehicle fuel consumption and emissions based on instantaneous speed and acceleration levels",Journal of transportation engineering, 2002.

14 22

Problem Definition

minu(h), h=0,...,Nj

1

2

yT (Nj)Pj y(Nj) +Mj

Nj∑h=0

exp(wT (h)PCj z(h))

+

+1

2

Nj−1∑h=0

(yT (h)Gj y(h) + uT (h)Rju(h)

)s.t.

x(h+ 1) = Ax(h) +Buu(h) +Bddh(k) + Ee(x(h)), ∀ h ∈ N,x(0) = x

x(h) ∈ Ω, ∀ h ∈ N,u(h) ∈ U, ∀h ∈ N.

x = x(k) is the current state at time k.

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Presentation Outline

1 Introduction

2 Model

3 Controller Design

4 Simulations

5 Conclusions

16 22

Simulations Results

Fuel optimization VS no fuel optimization

Two vehicles scenario

Sample time τ = 0.3s and prediction horizonNj = 10 ∀ jLeader speed profile: a first acceleration from velocity5m/s to velocity 18m/s and a deceleration to velocity3m/s

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Speed and Acceleration Profiles

0 10 20 30 40 50 60

Time [s]

0

5

10

15

20

25

Sp

ee

d [

m/s

]

Speed profile

Leader

Follower fuel opt.

Follower no fuel opt.

0 10 20 30 40 50 60

Time [s]

-4

-3

-2

-1

0

1

2

3

4

5

Acce

lera

tio

n [

m/s

2]

Acceleration profile (follower)

Fuel optimization

No fuel optimization

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Discrete State Profile

0 10 20 30 40 50 60

Time [s]

0.5

1

1.5

2

2.5

3

3.5

4

4.5

q [ ]

Discrete state profile (follower)

Fuel optimization

No fuel optimization

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Distance Profile

0 10 20 30 40 50 60

Time [s]

0

10

20

30

40

50

60

Dis

tance [m

]

Distance profile

p fuel opt.

p no fuel opt.

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Presentation Outline

1 Introduction

2 Model

3 Controller Design

4 Simulations

5 Conclusions

21 22

Conclusions

Main resultA Human-Inspired ACC for eco-driving for autonomous vehicles.

Goals

merging of hybrid automaton with predictive control strategy;

fuel optimization;

ACC able to mimic a human driver behavior.

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