ETAI 2013 Platoon presentation

Stojce Deskovski, University “St. Kliment Ohridski“, Macedonia

Zoran Gacovski, FON University – Skopje, Macedonia

Modeling and Control Algorithm for Platoon of Intelligent Vehicles


ETAI – 2013, Ohrid


1



1. Introduction

2. Dynamic vehicle model

3. Vehicle control system

4. Control of a platoon of vehicles

5. Simulation results

6. Conclusion and future work

O v e r v i e w :

2



• Grouping vehicles into platoons is a method of increasing the capacity of roads. An automated highway system is a proposed technology for doing this.

• Platoons decrease the distances between cars using electronic, and possibly mechanical, coupling. This capability would allow many cars to accelerate or brake simultaneously.

• This system also allows for a closer headway between vehicles by eliminating reacting distance needed for human reaction.

• Smart cars with artificial intelligence could automatically join and leave platoons. The Automated Highway System (AHS) is a proposal for one such system, where cars organize themselves into platoons of 8 to 25.

• Benefits from this AHS: greater fuel economy, reduced congestion, shorter commutes during peak periods, fewer traffic collisions, and ability for vehicles to be driven unattended.

1. Introduction (1)

3



1. Introduction (2)

• Intelligent vehicles have Adaptive or Advanced cruise control (ACC) system also called Intelligent cruise control (ICC) or Adaptive Intelligent cruise control (AICC) system.

• This vehicles are suitable to follow other vehicles on desired distance and to be organized in platoons.

• For control and stability analysis of Automated Guided Vehicles (AGV) and platoons of this vehicles we derived nonlinear dynamic vehicle model and its linearized model (Section 2).

• Concept of vehicle control system is discussed in Section 4.

• Section 4 is reserved for vehicle platoon modeling and control.

• Section 5 discusses simulation results given using Matlab/Simulink models of the vehicle and platoon of vehicles.

• Finally, in Section 6 we give conclusions and directions for future work.

4



MakeFull speed range ACC Partial cruise control

Models Notes Models Notes

BMW2007 5-series, 2010+ X5 excl

Diesel, 2013 3-seriesActive Cruise Control with

Stop & Go2000 7,5,6,3

Mercedes-Benz

2006 S, B, E, CLS, CL (2009+); A, CLA, M, G, GL

(2013+)Distronic Plus

1998 S,E, CLS, SL,CL, M, GL,CLK, 2012 C

VolkswagenPassat, Touareg (2011+) Golf

(2013+)not in US

Passat, Phaeton all generations, Touareg

AudiA8, A7, A6 (2011+); Q7 (2007+),A3 (2013+),Q5

(2013+)

Adaptive Cruise Control with Stop & Go

A3, A4 (see a demonstration YouTube) from navigation and

front camera sensors), Q7

PorschePanamera (2010+); Cayenne

(2011+), Cayman (2013+), Boxster(2012+)

Porsche Active Safe (PAS), PDK transmission only.

Volvo V40, S60, S80, XC60, XC70Also includes full power automatic braking under

20 mph

Cadillac XTS, ATS, SRX (2013+)Also includes full power automatic braking under

20 mph

2004 XLR, 2005STS, 2006 DTS (shuts off below 25 mph)

5

Vehicles models supporting adaptive cruise control. Vehicles with full speed range adaptive cruise control are able to bring the car to a full stop, and resume from standstill. Partial cruise control cuts off below a set minimum speed, requiring driver intervention

Vehicles models supporting adaptive cruise control. Vehicles with full speed range adaptive cruise control are able to bring the car to a full stop, and resume from standstill. Partial cruise control cuts off below a set minimum speed, requiring driver intervention



6

2. Dynamic Vehicle Model (1)2. Dynamic Vehicle Model (1)

z

ab

G mg

A

B

xrF

xfR

zrF

z

x

ox

oz

xrRxfF

zfF

Ah

h

O

AD

CMathematical model of longitudinal motion of the vehicle which is relevant for platoon modeling and control.

Mathematical model of longitudinal motion of the vehicle which is relevant for platoon modeling and control.

Fig.1 Forces acting on a vehicleFig.1 Forces acting on a vehicle

Application of Newton’s second law for the x and z directions gives: Application of Newton’s second law for the x and z directions gives:

sinxr xf xr xf Amu F F G R R D

0 cos zf zrmv G F F

(1)

(2)

Fx is the tractive forceFx is the tractive force



21sin cos ( )

2x r air wmu F mg f mg C u u

From (1), using (3) and (4) we get next nonlinear vehicle model for longitudinal motion:From (1), using (3) and (4) we get next nonlinear vehicle model for longitudinal motion:

where is a constant.where is a constant.

(5)

air r dC A C

2 21 1( ) ( )

2 2A d f w air wD C A u u C u u (3)

( ) cosx xf xr r zf zr rR R R f F F f mg (4)

Aerodynamic force

Rolling resistance

z

ab

G mg

A

B

xrF

xfR

zrF

z

x

ox

oz

xrRxfF

zfF

Ah

h

O

AD

C



8

2. Dynamic Vehicle Model (2)2. Dynamic Vehicle Model (2)

For specified operating (or nominal) state, real variables and functions in (5) we present like sum of nominal values and perturbations, i.e. (6)

Substituting (6) in (5), and using some approximations, model (5) will be divided in two parts:

For specified operating (or nominal) state, real variables and functions in (5) we present like sum of nominal values and perturbations, i.e. (6)

Substituting (6) in (5), and using some approximations, model (5) will be divided in two parts:

0 0 0 0 ; ; x xu u u F F F

Linearized modelLinearized model

Nominal motion0 21

sin cos ( )2

o o o ox r air wmu F mg f mg C u u

( )oair w xm u C u u u F d (8)

(7)

If nominal velocity, , is constant then from (7) we can find nominal tractive force:If nominal velocity, , is constant then from (7) we can find nominal tractive force:

ou

0 21sin cos ( )

2o o ox r air wF mg f mg C u u (10)

d – disturbance: (9)0 0( sin - cos )rd mgf mg

From (7) we can find state space model (12) and transfer function (14) of the vehicle. From (7) we can find state space model (12) and transfer function (14) of the vehicle.

Perturbed motion



0 1 0 0

1 1 10 x

x xF d

u uKm m m

( ) ( )

( ) 1x

u s KG s

F s s

(12)

(14)

Using the numerical values (15) we can find values of parameters in (12) and (14):Using the numerical values (15) we can find values of parameters in (12) and (14):

0 0 3

2

20 m / s, 0, 1000 kg, 1.2 kg / m ,

1.2 m , 0.5, 0.01, 9.81 m / s, 0f d r w

u m

A C f g u

242.1 N, 0.0694 (m/s)/N, =69.44s, oxF K

(15)

0 1 0 0

0 0.0144 0.001 0.001x

x xF d

u u

( ) 0.0694 ( )

( ) 69.44 1x

u sG s

F s s



10

3. VEHICLE CONTROL SYSTEM3. VEHICLE CONTROL SYSTEM

For vehicle with nonlinear dynamics (equation (5) for longitudinal motion) we implement combination of feed-forward control and feedback control approach, presented on Fig.3. For vehicle with nonlinear dynamics (equation (5) for longitudinal motion) we implement combination of feed-forward control and feedback control approach, presented on Fig.3.

Feedbackcontroller

Object(Vehicle)

)(tu

)(tox )(tu

+

++

-

)(tx

)(tx

)(tx

Control law for nonlinear object)(tou

Trajectory Generation

Feedforwardcontroller

)(tox

Fig.3 Concept of feed-forward and feedback control system of nonlinear object

Fig.4 SIMULINK diagram for the vehicle control



- Module reference inputs, generate reference acceleration ao, velocity vo, and

position xo, similar like the leader of the platoon.

- These signals go to the PID controller where are processed according to:

where are proportional, integral and derivative gains of the controller, a, v and x are real acceleration, velocity and position of the vehicle.

- Module Nominal control, Fig.4, consists of equation (10), and module Vehicle dynamics, which is based on full nonlinear model, equation (5).

- Simulink model in Fig.4 can be used for open loop, and closed loop simulation of the controlled vehicle.

- Module reference inputs, generate reference acceleration ao, velocity vo, and

position xo, similar like the leader of the platoon.

- These signals go to the PID controller where are processed according to:

where are proportional, integral and derivative gains of the controller, a, v and x are real acceleration, velocity and position of the vehicle.

- Module Nominal control, Fig.4, consists of equation (10), and module Vehicle dynamics, which is based on full nonlinear model, equation (5).

- Simulink model in Fig.4 can be used for open loop, and closed loop simulation of the controlled vehicle.

, , andp I DK K K

( ) ( ) ( )Ix p o o D o

Ku F K x x x x K v v

s



12

4. CONTROL OF A PLATOON OF VEHICLES (1)4. CONTROL OF A PLATOON OF VEHICLES (1)

4v 3v 2v 1v Lv

Lxoz

1 1Ldx x x

4x3x

1x

2x

2 1 2dx x x 3 2 3dx x x 4 3 4dx x x

2 2Ll x x 3 3Ll x x

4 4Ll x x

1 1Ll x x O

Lz

Lx

ox

L4a La1a2a3a

Fig.5 Configuration of platoon with 5 vehicles

In this paper we discuss the vehicle-following control approach, which is the focus of most current research and development work in the area.

Based on Fig.5, and mathematical model of individual vehicle together with its own control system - MATLAB/ SIMULINK model of the platoon of 10 vehicles is developed.

, , , ,1, 2,3,4i i i i ix v x a v i L - Position, velocity and acceleration with respect to ( ; , )o oG O x y

, , , ,1, 2,3,4i L i ri L i ri L il x x v v v a a a i L - Relative position, velocity and acceleration with respect to ( ; , )L LL L x y

1 , ,1, 2,3,4i i idx x x i L - Distances between vehicles

Equations (23), (24) and (25) can be used for generation of state-space model of string of several vehicles. This model is useful for stability analysis of the string using techniques of linear control theory. Equations (23), (24) and (25) can be used for generation of state-space model of string of several vehicles. This model is useful for stability analysis of the string using techniques of linear control theory.



13


Using vehicle model (5), or Fig.2, if and , we can find acceleration of the vehicle in this form:Using vehicle model (5), or Fig.2, if and , we can find acceleration of the vehicle in this form:0wV

2

0

1 1( ),

2x r air

x x x

u a F f mg C um

F F F

( ) ( ) ( )I

x p o o D oK

F K x x x x K v vs

Control force is determined by PID controller (20)xF

0

(21) (20)

Using (21) and (20) we can derive linear state space model of the i-th vehicle in the platoon:

1 1 11

[ ( ) ( ) ( ) ],

i i

i i

oi Ii i i i pi i i Di i i air i

x v

v a

a K x x hd K v v K a a C u am

Variables are input variables for the i-th vehicle and they are position, velocity and acceleration of the previous, or i-1 th, vehicle.

(23)(24)(25)

1 1 1, , andi i i ix v a a




1 1

2 2

1 1

2 211 11 1

1 1

2 222 2 2 2

0 0 1 0 0 00 0 0

0 0 1 1 0 00 0 0

0 0 0 0 1 00 0 0

0 0 0 0 0 10 0 0

0 0 0

0

oD airI P

I P

oD airI P P D

x x

dx dx

v v

v vK C uK KK K

a am m mm m

a aK C uK K K K

m m m m m

1

211

2

0 0

0 0

0 0

0 0

0

0 0 0 0

L

L

ILD

I

xhd

vhdKaK

mm

K

m

State space model of the string of two vehicles and vehicle-leader like generator of input variables xL, vL, aL

(26)

This string of two vehicles is stable because its eigenvalues, or poles, p1,…,p6, are real and negative:

-1.2690 ,-1.2690, -0.5306, -0.5306, -0.0149, -0.0149



15

String Stability (1)String Stability (1)

For a platoon of vehicles, beside individual vehicle stability, is defined string stability of the platoon. If the preceding vehicle is accelerating or decelerating, then the spacing error could be nonzero; we must ensure that the spacing error attenuates as it propagates along the string of vehicles because it propagates upstream toward the tail of the string.

For a platoon of vehicles, beside individual vehicle stability, is defined string stability of the platoon. If the preceding vehicle is accelerating or decelerating, then the spacing error could be nonzero; we must ensure that the spacing error attenuates as it propagates along the string of vehicles because it propagates upstream toward the tail of the string.

For string stability analysis it is useful to find transfer funcion from range error of i-th vehicle to range error of i+k th vehicle:

, 1 11

( )1

i k i k i k i ki k i i i k

i i i i

G sh GG s G G G

G shG

(29)

11

( ) , ,ii i i i i

i

vG s x x D

v

1

1

( ) ,i ki k i k i k i k i k

i k

vG s x x D

v

where:

For string stability must be satisfied

,, ( ) 1i k i i kor G s (30)

Above discussion for string stability can be easy applied to platoon described in this work.Deriving of transfer function (29) is presented on the next slide.Above discussion for string stability can be easy applied to platoon described in this work.Deriving of transfer function (29) is presented on the next slide.



16


1i kG 1i kG 1i kG iG 1iG 1i kG 1i kG 1i kG 1i kG 1i kG 1i kG 1i kG i kG 1iv

1

s

1

s

1

s

1

s

1

s

1

s

1i kv i kv 2i kv 1iv iv

1ix

1i i i i ix x h v

i kx 1i kx 2i kx 1ix ix

, ( ) i ki k

i

G s

1i k i k i k i k i kx x h v

1 2 1i k

i i i k i ki

vG G G G

v

i

i i

D

h v

i k

i k i k

D

h v

Equations for i-th vehicle:Equations for i-th vehicle:

11 1

i i i ix v G vs s

1 11

i i i i ii

v G v v vG

1i i i i ix x h v

Fig.1.1 for deriving transfer function , ( ) i ki k

i

G s

(1)

(2)

(3)

From (3) using (1) and (2) we can find: From (3) using (1) and (2) we can find:

1(1 )i i i i i

i

G shG vsG

(4)




Equations for i+k-th vehicle:Equations for i+k-th vehicle:

1 11

i k i k i k i k i ki k

v G v v vG

1i k i k i k i k i kx x h v

(5)

(6)

(7)

From (3) using (1) and (2) we can find: From (3) using (1) and (2) we can find:

1(1 )i k i k i k i k i k

i k

G sh G vsG

(8)

11 1

i k i k i k i kx v G vs s

Using transfer function from Fig.1.1:and relations (4) and (8) we will get:

, 1 2 11

( )1

i k i k i k i ki k i i i i k

i i i i

G sh GG s G G G G

G shG

1 2 1i k

i i i k i ki

vG G G G

v



18

5. SIMULATION RESULTS5. SIMULATION RESULTS For simulation MATLAB/SIMULINK is usedFor simulation MATLAB/SIMULINK is used

Fig.2 Simulink model of the vehicle

Fig.4 Simulink diagram for the vehicle control



Fig.6 Matlab/Simulink model of the platoon of 10 vehicles.

0 0 3

2

20 m / s, 0, 1000 kg, 1.2 kg / m ,

1.2 m , 0.5, 0.01, 9.81 m / s, 0f d r w

u m

A C f g u

Parameters for the vehicle model:- All vehicles are the same.

- Desired distances among vehicles dx i0=50m.

- Parameters of PID controllers are: KPi=700, KIi=10, and KDi=1800.



20

0 10 20 30 40 50 60 70 80 90 10018

20

22

24

26

28

t [s]

Veh

icle

vel

ociti

es,

vi [

m/s

]

Absolute vehicle velocities

Vehicle-Leader

Vehicle 9

Fig.7 Trapezoidal change of vehicle-leader velocity and responses of vehicles in the platoon.

Fig.7 Trapezoidal change of vehicle-leader velocity and responses of vehicles in the platoon.

Fig.7 shows velocity profile of the vehicle leader and responses of vehicles – followers.

Fig.7 shows velocity profile of the vehicle leader and responses of vehicles – followers.

0 20 40 60 80 100-1

-0.5

0

0.5

1

1.5

2

t [s]

Dis

tanc

e er

rors

bet

wee

n ve

hicl

es,[

m]

Distance errors between vehicles

Vehicle 9

Vehicle 1

Fig.8 shows distance errors between vehicles for the same inputs as in Fig.7Fig.8 shows distance errors between vehicles for the same inputs as in Fig.7

Fig.8. Distance errors between vehiclesFig.8. Distance errors between vehicles



21

0 10 20 30 40 50-500

0

500

1000

t [s]

Veh

icle

pos

ition

s, x

i [m

]

Absolute vehicle positions

Vehicle 1

Vehicle 9

Vehicle - Leader

Fig.9 Positions of the vehicles Fig.9 Positions of the vehicles

Fig.10 Positions of the vehicles Fig.10 Positions of the vehicles

Fig 9 shows positions of the vehicles in the platoon when each vehicle get information for acceleration, velocity and position only for previous vehicle.

Fig 9 shows positions of the vehicles in the platoon when each vehicle get information for acceleration, velocity and position only for previous vehicle.

0 10 20 30 40 50-500

0

500

1000

t [s]

Vehic

le p

ositio

ns,

xi [m

]

Absolute vehicle positions

Vehicle-Leader

Vehicle 1

Vehicle 9

Fig.10 shows the situation when only last three vehicles get information for acceleration, velocity and position from the vehicle-leader.

Fig.10 shows the situation when only last three vehicles get information for acceleration, velocity and position from the vehicle-leader.



22

6. Conclusions and future work 6. Conclusions and future work

1. In this paper we have developed a nonlinear and linearized model of the longitudinal motion of the vehicle.

2. Feed-forward control and feedback PID control approach is applied to design vehicle controller.

3. Using this vehicle model with its control system - model of platoon with ten vehicles is developed. In this model vehicles can get information for acceleration, velocity and position for previous vehicle and for movement of the vehicle–leader.

4. String stability of the platoon is discussed and transfer function of the string useful for stability analysis is presented.

5. Based on the developed models Matlab/Simulink models are created which can be used for simulation and performance analysis of the vehicle dynamics and platoon's control system.

6. This Simulink models can be useful for different experiments and testing of designated controllers.

7. In future work, we plan to develop more accurate models of the vehicles and platoons. We plan to design and test different then PID control laws, for example LQR and Fuzzy logic control. Practical realization using different sensors and wireless communication among vehicles will be our interest in the future.

1. In this paper we have developed a nonlinear and linearized model of the longitudinal motion of the vehicle.

2. Feed-forward control and feedback PID control approach is applied to design vehicle controller.

3. Using this vehicle model with its control system - model of platoon with ten vehicles is developed. In this model vehicles can get information for acceleration, velocity and position for previous vehicle and for movement of the vehicle–leader.

4. String stability of the platoon is discussed and transfer function of the string useful for stability analysis is presented.

5. Based on the developed models Matlab/Simulink models are created which can be used for simulation and performance analysis of the vehicle dynamics and platoon's control system.

6. This Simulink models can be useful for different experiments and testing of designated controllers.

7. In future work, we plan to develop more accurate models of the vehicles and platoons. We plan to design and test different then PID control laws, for example LQR and Fuzzy logic control. Practical realization using different sensors and wireless communication among vehicles will be our interest in the future.

Date post:	21-May-2015
Category:	Technology
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ETAI 2013 Platoon presentation

Technology