11

EcoEco--Driving using Model Driving using Model

Predictive ControlPredictive Control

Presented byPresented by

M. A. S. KamalM. A. S. Kamal

Researcher, Researcher, Fukuoka Industry Science and Fukuoka Industry Science and Technology FoundationTechnology FoundationLab of Prof. Taketoshi Kawabe Lab of Prof. Taketoshi Kawabe Kyushu UniversityKyushu University

22

Presentation OutlinePresentation Outline

Background and MotivationBackground and Motivation

Ecological Driving using MPCEcological Driving using MPC

Modeling of Vehicle Control ProblemModeling of Vehicle Control Problem

Case Studies and SimulationCase Studies and Simulation Driving on Single Lane road Driving on Single Lane road

Driving on MultiDriving on Multi--lane road. lane road.

Driving on Road with upDriving on Road with up--down slopedown slope

Conclusions Conclusions

33

Background Background

&&

MotivationMotivation

44

Emission From CarsEmission From Cars

Emission From CarsEmission From Cars

Emission of CO2 from Transportation is one of the major sources of Environment Pollution and Global Warming.

It is a demand of time to make Transportation

Systems more Environmentally friendly

Transportation

PSIndustry

55

Fuel Efficient VehiclesFuel Efficient Vehicles

Progress for efficient Vehicles have been continuing

66

Realization of EcoRealization of Eco--DrivingDriving

Major Factors influencing consumptionsMajor Factors influencing consumptions TTraffic Management Systems, raffic Management Systems, VVehicle maintenance, ehicle maintenance, RRoute Selections, oute Selections, Driving StyleDriving Style..

Proper Proper Driving or Vehicle Control Style Driving or Vehicle Control Style may save fuel consumption significantly.may save fuel consumption significantly.

77

Ecological DrivingEcological Driving

According to Recent Studies:According to Recent Studies:EcoEco--Driving may save fuelDriving may save fuel

By 10By 10--25%. 25%.

Various Approaches are introduced to Various Approaches are introduced to Motivate a driver for EcoMotivate a driver for Eco--Driving:Driving:

Example: Example:

Driving Tips; ECO indicator; Fuel Ranking;Driving Tips; ECO indicator; Fuel Ranking;

88

EcoEco--Driving AssistanceDriving Assistance

Driving TipsOn-board Assistance

for Driver

ECOECO indicator

ECOECO

99

OnOn--board Performance Indicatorboard Performance Indicator

Driving Efficiency

1010

Existing Assistance SystemExisting Assistance System

CARWINGS and ECO Pedal

1111

Support on Sloppy RoadSupport on Sloppy Road

1212

Limitation of Existing AssistanceLimitation of Existing Assistance

They only focus on fuel consumption They only focus on fuel consumption characteristics of the Enginecharacteristics of the Engine

They do not analyze current road traffic They do not analyze current road traffic situationsituation

They do not anticipate future traffic They do not anticipate future traffic conditionsconditions

They are not suitable for changing They are not suitable for changing situationssituations

Therefore, A more Comprehensive EcoTherefore, A more Comprehensive Eco--Driving System is necessary for Optimum Driving System is necessary for Optimum AchievementAchievement

1313

Ecological Driving using MPCEcological Driving using MPC

1414

Proposed EcoDrivingProposed EcoDriving

EcoDriving should be based onEcoDriving should be based on

Fuel Consumption Fuel Consumption Characteristics of the EngineCharacteristics of the Engine

Road gradients, alignment and Road gradients, alignment and LanesLanes

Situation of current trafficSituation of current traffic

Anticipation of Future SituationAnticipation of Future Situation

Traffic Signal aheadTraffic Signal ahead

Safety Safety

1515

ITS TechnologiesITS Technologies

Necessary InformationPosition, Speed, acceleration of surrounding vehicles.Status of Signal (or Timing)Road gradient and alignment

Possible TechnologiesGPS, Camera, Laser, etcCommunication Among VehiclesCommunication with Infrastructure

Algorithm ?

1616

Vehicle control problemVehicle control problem NonNon--linear linear Requires AnticipationAnticipation of traffic Discontinuous Events Constraints

Model Predictive Control Model Predictive Control is the most suitable Options.

Selection of AlgorithmSelection of Algorithm

1717

At t, using current state and initial inputs, states in the prediction horizon t to t+T is predicted.

Inputs are optimized using performance index.

Only the first input is used to control the vehicle.The process is repeated in next steps.

Concept

t0t tt1 t2 inputState

Prediction Horizon TPrediction Horizon T

t

Model Predictive ControlModel Predictive Control

11

1818

Modeling of Vehicle DynamicsModeling of Vehicle Dynamics

))(),(),(()( tqtutxftx =&

HVHVHVHVPVPVPVPV

Tpphh vxvxx ],,,[=

Simplified Vehicle Control System:A Host Vehicle; A Preceding Vehicle; Signal;

Assuming following non-linear state equation

State

Input )(tu Time varying parameter )(tq

1919

Modeling of the Modeling of the Host Vehicle

Rh

Th

hh FFdt

dvM =

)(sin

)(cos2

1 2

h

hhVaDR

h

xMg

xMgvACF

+

+=

Host Vehicle

hhT

h uMF =

g

DC

VA

huhM

Air density

Drag Coefficient

Frontal Area

Slope angel

Rolling Coefficient

Gravitational force

Control inputVehicle Mass

2020

Prediction Model of the Prediction Model of the Preceding Vehicle

)(tqadt

dvp

p ==

Time varying parameter q(t) represents acceleration of the preceding vehicle.

Influence of other traffic and status of traffic control

signal is reflected in q(t).

Values of q(t) needs to be estimated based on current situation of road and traffic.

2121

HVPV

HVPV

Prediction Model of Prediction Model of PV

In the above two cases

=+0

)()(

tqttq mp

Vv 0ifOtherwise

In absence of a PV, it is assumed a dummy Vehicle idling at the RED signal

2222

HVPV

Stopping model of PV at RED signal

How a vehicle approaches the stopping point in a red signal was observed experimentally

0 20 40 60 80 100l [m]

0

10

20

30

40

50

60

v b [

km/h

]

30 patterns of 3 driversAverage stopping pattern is approximated as:

012

2

33

44

55

* )(

alala

lalalalvb

+++

++=

Average braking rate:

)()(

)( **

* lvdl

ldvla b

bb =

2323

Braking rate of PV at RED signal

Braking rate of any stopping vehicle of velocity vb at l can be obtained as

2

**

)(

)()()(

=

lv

lvlala

bbb

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8Approximated braking rate for various v andl

)()( latq b=

24240 20 40 60 80 100

l [m]

0

10

20

30

40

50

60

v b [

km/h

]

Prediction of PV at RED signal

Predicted stopping pattern at various v and l

0 20 40 60 80 100l [m]

0

10

20

30

40

50

60

v pb [

km/h

]

Experimentally observed pattern

2525

Modeling Modeling

+==

q

v

uxgxgvACM

x

quxfx

p

hhhvaDh

h

))(sin()(cos2

1

),,( 12

&

HVHVHVHVPVPVPVPV

maxmin uuu h

State equation can be written as:

Input of host vehicle is limited by

2626

Engine Characteristic MapEngine Characteristic Map

29.1%

28.5%27%

25.5%

24%

Best efficiency points

Efficiency

Engine power

A typical Engine Map is constructed keeping the fuel consumption rate tested on 10-15 Mode matches the rating of the vehicle

2727

Fuel Consumption ModelFuel Consumption Model

C

P

29.1%28.5% 27

% 25.5%24

%

Best efficiency points

Efficiency

Engine power

Engine Efficiency () depends on torque and speed.

For a CVT Vehicle, it is assumed, the gear ratio is maintained at maximum efficiency for any output power.

Total moving forces on the vehicle:

Where C: calorific value of gasoline.

MaMgMgAvCF aD +++= 2

2

1

Therefore, the consumption [ml/s] can be obtained as:

Power required to run the vehicle:

cPFvP +=

2828

Fuel Consumption ModelFuel Consumption Model

0

1

2

3

4

5

0 20 40 60 80 100

Velocity [km/h]

Con

sum

ptio

n [

ml/

s]

a = 0.0

a = 0.4

a = 0.8

a = 1.2

a = 1.6

a = 2.0

a = 2.4

)( 012

2

012

23

3

cvcvca

bvbvbvbfV

+++

+++=

Validation

Where, sin gva += &

The fuel consumption data obtained from the map and approximated in terms of v and a

2929

Performance IndexPerformance Index

( )+

=Tt

tudquxLJ )(),(),(min

Fuel EconomyCost for acceleration/braking

Desired Speed*

Dynamic weights w1, w2, w3, w4 focus their relative contextual merits.

( )( ) ( )( ) .

2

1

204

23

22

2012

23

31

VhphdRh

hVaDhhhh

lxxvhwvvw

gvACM

uwbvbvbvbv

wL

++

++++=

Safe Clearance

3030

Optimization of the control inputsOptimization of the control inputs

Generalized Minimum Residual Algorithm is used to derive the Generalized Minimum Residual Algorithm is used to derive the solution with a given initial values vector.solution with a given initial values vector.

),,(),,(),,(:),,,,( puxCpuxfpuxLpuxH TT ++=

Required condition in finding the optimum control inputs:

The Hamiltonian Function is given by :

3131

Optimization ProblemOptimization Problem

.0

),(

),,,(

:

),(

),,,(

:),,(

11

111

00

0010

=

=

NN

NNNNTu

Tu

uxC

uxH

uxC

uxH

txUF

Condition for Optimal solution with given initial values

Continuation/Generalized Minimum Residual (C/GMRES)Continuation/Generalized Minimum Residual (C/GMRES) [5] is used to finds the solutions of the above.

[9] T. Ohtsuka, [9] T. Ohtsuka, A Continuation/GMRES method for fast computation of nonlinear A Continuation/GMRES method for fast computation of nonlinear receding horizon control,receding horizon control, Automatica 40 (2004) 563Automatica 40 (2004) 563--574.574.

),(),(),(:),,,( uxCuxfuxLuxH TT ++=Hamiltonian:

3232

Flow of Vehicle Control ProcessFlow of Vehicle Control Process

Measure states of the vehicle,

At time t=kh

Using the model of vehicle dynamics, Information of road slope, Performance index and Constraint,

For a prediction horizon T, from t=kh to, t=kh+T

Optimize the current and future vehicle control inputs using C/GMRES

Implement best current input to control the vehicle

k=k+1

3333

Test EnvironmentTest Environment

Functions can be Extended through API Routine to control a car in a special way

AIMSUNAIMSUN Microscopic Traffic SimulatorMicroscopic Traffic Simulator

Vehicles run as per Gipps model

3434

AIMSUN NG

Host Vehicle

Model Predictive Control

Other Traffic

Interactions

API

Control input

Measurement

EDASTraffic Signal

Interactions

Interactions

Simulation Interface

3535

SimulationsSimulations

=1200[kg]

=1.184[kg/m3]

=0.012

=34.5e+6[J/l]

=0.7[PS] =514.85[W]

=9.8[m/s2]

=2.5[m2]

=0.32

Modeling Parameters

M

DC

A

g

C

cP

8

=12[s]

=50[km/h]

=110

=7.7

=0.39

= 0.1[s]

= 2.75[m/s2]

Algorithms Setting

Tdv

0w

maxu

h

1w

2w

Constraint is converted into inequality constraint as:

( ) 02

1),( 2max

22

2 =+= uuuuxC

3636

Simulation ISimulation I

HVPV FV

4.1 kmS13S14 S2 S1

Single Lane Test Route

Test Route in AIMSUN: about 600 vehicles/h

Comparison Conducted1.Gipps Model Vehicle2.The proposed EcoDriving3.EcoDriving without stopping model of PV

Observations1.Fuel savings by host vehicle2.Effect on following vehicle

3737

Gipps Model Gipps Model

0 100 200 300 400 5000

20

40

60

velo

city

[km

/h]

HVPVFV

0 100 200 300 400 5000

100

200

Ran

ge [

m]

(HV-PV)(HV-FV)

0 100 200 300 400 500t [s]

-2

0

2

u 1 [

m/s

2 ]

3838

The Proposed EcoThe Proposed Eco--DrivingDriving

0 100 200 300 400 5000

20

40

60

velo

city

[km

/h]

HVPVFV

0 100 200 300 400 5000

100

200

Ran

ge [

m]

(HV-PV)(HV-FV)

0 100 200 300 400 500t [s]

-2

0

2

u 1 [

m/s

2 ]

3939

EcoDrive without PV stop ModelEcoDrive without PV stop Model

0 100 200 300 400 5000

20

40

60

velo

city

[km

/h]

HVPVFV

0 100 200 300 400 5000

100

200

Ran

ge [

m]

(HV-PV)(HV-FV)

0 100 200 300 400 500t [s]

-2

0

2

u 1 [

m/s

2 ]

4040

Fuel Comparison of Host VehicleFuel Comparison of Host Vehicle

254.4

220.3

228.8

200

215

230

245

260

[m

l]

.

(10%)(10%)

13%

Gipps EcoD

EcoD

4141

Effect of Eco Driving on Following VehicleEffect of Eco Driving on Following Vehicle

254.8

219.7

235.1

200

215

230

245

260

[m

l]

.

GippsEcoD

EcoD

4242

Simulation IISimulation II

S1 S2 S3S12 S13

J1 J2J13

S14

J12J11

Test Route 4.00 km

Test Route 4.1 km14 sections13 junctions2-3 Lanes90 sec Signal cycle50 sec Green Timing

Vehicle flow10002000 vehicle/hourVehicle TypesTruck, Car, and Taxi

Test Route & Network Setting in AIMSUNTest Route & Network Setting in AIMSUN

4343

Simulation ResultsGipps Eco Driving

04.

Signal status

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

v p [km

/h]

Velocity of Preceding Vehicle

0 50 100 150 200 250 300 350 400 450 5000

40

80

120

160

xp-x

h [m

]

Range clearance

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

v h [km

/h]

Velocity of Host Car

0 50 100 150 200 250 300 350 400 450 500-4

-2

0

2

4

uh

Control Input

0 50 100 150 200 250 300 350 400 450 500time [s]

0

90

180

270

Fuel [ml]

04.

Signal status

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

v p [km/h]

Velocity of Preceding Car

0 50 100 150 200 250 300 350 400 450 5000

40

80

120

160

xp-x

h [m]

Range clearance

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

vh [km/h]

Velocity of Host Car

0 50 100 150 200 250 300 350 400 450 500-3

-1.5

0

1.5

3u

h

Control Input

0 60 120 180 240 300 360 420 480 540time [s]

0

60

120

180

Fuel [m

l]

Cumulative Consumption

4444

Average Fuel ConsumptionAverage Fuel Consumption

140

170

200

230

260

290

320

350

0 20 40 60 80 100

Vehicles on observation

Fue

l [m

l]

EcoDrive GippsMean Value Mean Value

4545

0

5

10

15

20

25

30

Fre

quency

13 14 15 16 17 18 19 20

Km/h

EcoDrive

Gipps

15.73 [km/h]

17.6 [km/h]

Average Fuel ConsumptionAverage Fuel Consumption

100[km/l]

4646

Simulation IIISimulation IIIEcological Driving over UpEcological Driving over Up--Down Down

SlopesSlopes

4747

Fundamental Concept Fundamental Concept

Assumption: Vehicle is not interfered by other vehicle or traffic signals.

4848

ModelingModeling

State equation of a vehicle:

,

))(),(()(

2

1

=

=

x

xx

tutxftx&

+=

uM

F

xuxf

R

2

),(

)(sin2

11

22 xMgMgAxCF DR ++=

Air Rolling Slopes

Where forces

++

=0

)( 22 cPxxmFP& )0( >u

Power of the Engine:

5

)0( u

Air density

Drag Coefficient

Frontal Area

Slope angel

Rolling Coefficient

Gravitational force

Power required at stand still.

g

DC

A

Location

Velocity

Control input (accel/brake)

: Motion resistance forces

: Vehicle Mass

2xu

MRF

cP

1x

And, )( maxmax uuu

4949

Performance IndexPerformance Index

( )+

=Tt

tudquxLJ )(),(),(min

Fuel EconomyCost for acceleration/braking

Desired Speed*

Dynamic weights w1, w2, w3 focus their relative contextual merits.

( )( )23

22

2012

23

31

2

1

Rh

hVaDhhhh

vvw

gvACM

uwbvbvbvbv

wL

+

++++=

5050

Model Predictive ControlModel Predictive Control

Measure states of the vehicle,

At time t=kh

Using the model of vehicle dynamics, Information of road slope, Performance index and Constraint,

For a prediction horizon T, from t=kh to, t=kh+T

Optimize the current and future vehicle control inputs using C/GMRES

Implement best current input to control the vehicle

k=k+1

Even at each timeOptimum inputs for the horizonis generated, the whole process is repeated in short interval.

5151

SimulationsSimulations

=1200[kg]

=1.184[kg/m3]

=0.012

=34.5e+6[J/l]

=0.7[PS] =514.85[W]

=9.8[m/s2]

=2.5[m2]

=0.32

Modeling Parameters

M

DC

A

g

C

cP

The proposed algorithm is evaluated through simulation

8

=12[s]

=50[km/h]

=3

=34

=1

= 0.1[s]

= 2.75[m/s2]

Algorithms Setting

Tdv

1w

maxu

h

2w

3w

5252

Simulations ResultsSimulations Results

0

4

8

12

16

Elevation

[m]

0 400 800 1200x1 [m]

-6

-3

0

3

6

Slo

pe

[%]

Road shape and Slope

5353

SimulationsSimulations ResultsResults

0 400 800 1200x1 [m]

44

46

48

50

52

54

56

x2 [km

/h]

MPC

FSD

ASCD

0 400 800 1200x1 [m]

-0.3

0

0.3

0.6

u [m

/s2]

MPC

FSD

ASCD

The Vehicle approaches at velocity 50 [km/h] MPC is compared with two hypothetical Systems :

(a) FSD (Fixed Speed Drive)(b) ASCD (Automatic Speed Control Drive)

5454

Cumulative Fuel ConsumptionCumulative Fuel Consumption

0 400 800 1200x1 [m]

-0.3

0

0.3

0.6

u [m/s2]

MPC

FSD

ASCD

0 400 800 1200x1 [m]

0

10

20

30

40

Fuel C

onsu

med

[ml]

MPC

FSD

ASCD

Fuel saving features:

(a) Avoid excessive input

(b) Avoid hard braking

(c) Speeding up before up slope

(d)Use down slope to speed up again

5555

ResultsResults ComparisonComparison

29.75

32.5332.89

27

29

31

33

Fuel

[m

l]

MPC FSD ASCD

0

4

8

12

16Elevation

[m]

Fuel savings only on up-hill

Fuel savings by MPC over:

(a)FSD 9.32%(b)ASCD 10.55%

5656

Additional Results IAdditional Results I

0 400 800 1200

-8

-4

0

4

Elevation

[m]

0 400 800 1200x1 [m]

44

46

48

50

52

54

56

x2 [km/h]

MPC

FSD

ASCD

0 400 800 1200x1 [m]

-0.3

0

0.3

0.6

u [m/s

2]

MPC

FSD

ASCD

29.68

32.5232.73

27

29

31

33

Fu

el [m

l]

MPC FSD ASCD

MPC has similar benefit over FSD and ASCD

5757

Additional Results IIAdditional Results II

0 400 800 1200

0

2

4

6

8

Elevation

[m]

0 400 800 1200x1 [m]

46

48

50

52

54

x2 [km/h]

MPC

FSD

ASCD

0 400 800 1200x1 [m]

0

0.25

0.5

0.75

1

u [m/s

2]

MPC

FSD

ASCD

(c)

31.7731.8 31.79

31.2

31.4

31.6

31.8

Fu

el

[ml]

MPC FSD ASCD

Almost the same fuel consumption by MPC, FSD and ASCD

5858

Additional Results IIAdditional Results II

0 400 800 1200

-6

-4

-2

0

2

4

Elevation

[m]

0 400 800 1200x1 [m]

46

48

50

52

54

x2 [km/h]

MPC

FSD

ASCD

0 400 800 1200x1 [m]

-0.5

-0.25

0

0.25

0.5

u [m/s

2]

MPC

FSD

ASCD

18.71

19.819.91

16

17

18

19

20

Fue

l [m

l]

MPC FSD ASCD

About 6% Fuel savings

5959

Test Test

RouteRoute

MAS Kamal, Fukuoka IST

Yuniba Dori

6060

0 500 1000 1500 2000 2500 m-5

0

5

10

15

20

25

30

35

Road Elevation from Digital Map

MAS Kamal, Fukuoka IST

6161

Results: North to South Results: North to South

MAS Kamal, Fukuoka IST

0 450 900 1350 1800 2250 2700x1 [m]

5101520253035

Ele

vatio

n [m

]

-6

-3

0

3

6

Slo

pe

[%]

44

48

52

56

Velo

city

, x2 [k

m/h

]

EcoDFSDASCD

-0.4

0

0.4

0.8

1.2

Inpu

t, u [m

/s2 ]

EcoDFSDASCD

118.06

123.55124.27

113

116

119

122

125

Fu

el [

ml]

EcoD FSD ASCD

Fuel savings about 5.0%

6262

Results: South to North Results: South to North

MAS Kamal, Fukuoka IST

0 450 900 1350 1800 2250 2700x1 [m]

5101520253035

Ele

vatio

n [m

]

-9

-6

-3

0

3

6

Slo

pe

[%]

44

48

52

56

Velo

city

, x2 [k

m/h

]

EcoDFSDASCD

-0.8

-0.4

0

0.4

0.8

Input

, u [m

/s2 ]

EcoDFSDASCD

78.15

82.87

84.07

74

77

80

83

86

Fu

el [

ml]

EcoD FSD ASCD

Fuel savings about 7.04%

6363

Test RouteTest Route

MAS Kamal, Fukuoka IST

Test Route 1.7km

Elevation of the road segment

202

202

54

Nishi Ward,

Fukuoka City,

Japan

Test Route onthe Map

6464

Simulation ResultSimulation Result

MAS Kamal, Fukuoka IST

0

20

40

60

x 2 [

km/h

]

-3

0

3

u [m

/s2 ]

0

20

40

60

x 4 [

km/h

]

-404

Slo

pe [%

]

0 50 100 150 200 250t [sec]

0

50

100

Fue

l [m

l]

0Sig

nal

0

20

40

60

x 2 [

km/h

]

-3

0

3

u [m

/s2 ]

0

20

40

60

x 4 [

km/h

]

-404

Slo

pe [%

]

0 50 100 150 200 250t [sec]

0

50

100

Fue

l [m

l]

0Sig

nal

Gipps Vehicle EDAS Vehicle

6565

Comparison Comparison

MAS Kamal, Fukuoka IST

27.6

78.7

24.6

68.9

0

20

40

60

80

100

120

Gipps Eco Drive

Other sectons

Sloppy section

Test Route 1.7km

Elevation of the road segment

202

202

54

Nishi Ward,

Fukuoka City,

Japan

Fuel Consumption [ml]

6666

ConclusionsConclusions

A novel concept of EcoDriving using MPC A novel concept of EcoDriving using MPC has been presented.has been presented.

Vehicle is controlled based on Fuel Vehicle is controlled based on Fuel consumption, anticipation of future state consumption, anticipation of future state and information of road shape.and information of road shape.

Simulation Results reveal the significant Simulation Results reveal the significant improvement in fuel consumption improvement in fuel consumption compared to other methods.compared to other methods.

Further fine tuning of the system will be Further fine tuning of the system will be followed by real experiments.followed by real experiments.

MAS Kamal, Fukuoka IST