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  • 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. Pola Department 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 has constantly increased and that number is expected to raise even more in the next years.

    More vehicles on the roads means more time wasted in tra�ic congestion, less safety and higher pollution.

    Vehicles adopting di�erent level of automation can reduce considerably tra�ic issues.

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

    2 22

  • Why Human-Inspired?

    Objective: let the ACC mimic the human behavior

    Incorporate the human psycho-physical response in a car-following situation

    Improve the controller response to the surrounding environment

    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 straight road.

    Collision A collision is the event corresponding to a distance between two vehicles less than s = L+ L0, where L0 ≥ 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 the position, velocity and acceleration of vehicle n, respectively. The state vector of the follower vehicle is defined 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 0 0 1 −τ 0 0 0 1 0 0 0 0 1

     ︸ ︷︷ ︸

    A

    x(k) +

     0 0 τ 0

     ︸ ︷︷ ︸

    Bu

    u(k) +

     0 τ 0 τ

     ︸ ︷︷ ︸

    Bd

    d(k) +

     0 τ 0 0

     ︸ ︷︷ ︸

    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

    x 2 [m/s]

    0

    50

    100

    150

    200

    x 1 [

    m ]

    Domains

    q1

    q2

    q3

    q4

    unsafe

    Definition of the time head-ways needed to stop the vehicle in di�erent situations:

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

    Definition of the corresponding space head-ways thresholds:

    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: Hybrid Systems, 2017.

    9 22

  • Microscopic Hybrid Automaton

    -15 -10 -5 0 5 10 15

    x 2 [m/s]

    0

    50

    100

    150

    200

    x 1 [

    m ]

    Domains

    q1

    q2

    q3

    q4

    unsafe The space head-way thresholds are used to define the discrete states 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 controlled invariant.

    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 di�erent weights.

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

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

    where

    ān(k + i) =

    { an(k), if 0 < v̄n(k + i− 1) < vmax 0, otherwise

    13 22

  • 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 ỹ = y − yr .

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

    exp(wTPCj z) (7)

    where

    PCj = P C+ for positive accelerations, PCj = P

    C− for negative accelerations;

    zT = [1 y3 y 2 3 y

    3 3 ]

    T , wT = [1 y4 y 2 4 y

    3 4 ]

    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

    min u(h), h=0,...,Nj

    1

    2

    ỹT (Nj)Pj ỹ(Nj) +Mj Nj∑ h=0

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

    + +

    1

    2

    Nj−1∑ h=0

    ( ỹT (h)Gj ỹ(h) + u

    T (h)Rju(h) )

    s.t.

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

    x(h) ∈ Ω, ∀ h ∈ N, u(h) ∈ U, ∀h ∈ N.

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

    15 22

  • 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 horizon Nj = 10 ∀ j Leader speed profile: a first acceleration from velocity 5m/s to velocity 18m/s and a deceleration to velocity 3m/s

    17 22

  • Speed and Acceleration Profiles

    0 10 20 30 40 50 60

    Time [s]

    0

    5

    10

    15

    20

    25

    S p

    e e

    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

    A c c e

    le ra

    ti o

    n [

    m /s

    2 ]

    Acceleration profile (follower)

    Fuel optimization

    No fuel optimization

    18 22

  • 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

    19 22

  • Distance Profile

    0 10 20 30 40 50 60

    Time [s]

    0

    10

    20

    30

    40

    50

    60

    D is

    ta n c e [ m

    ]

    Distance profile

    p fuel opt.

    p no fuel opt.

    20 22

  • Presentation Outline

    1 Introduction

    2 Model

    3 Controller Design

    4 Simulations

    5 Conclusions

    21 22

  • Conclusions

    Main result A 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.

    22 / 22

  • Thanks for your a�ention!

    Introduction Model Controller Design Simulations Conclusions