Longitudinal Vehicle Dynamics Control for

Improved Vehicle Safety Name: Herman Hamersma

Supervisor: Prof Schalk Els

Date: 19 September 2013

Identifying the problem

𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹

=𝒕𝒕𝑹𝑹𝒕𝒕𝒕𝒕𝒕𝒕 𝒘𝒘𝒘𝒘𝒘𝒘𝒕𝒕𝒘𝒘𝟐𝟐𝒘𝒘𝑹𝑹𝒘𝒘𝒉𝒉𝒘𝒘𝒕𝒕 𝑹𝑹𝒐𝒐 𝑪𝑪𝑪𝑪

Aim of Research • Develop an autonomous longitudinal control

system for path planning and following • Control system will improve vehicles safety by

preventing the vehicle from exceeding vehicle’s limits.

Approach 1. Develop a longitudinal model of the Land Rover

in Adams (Automated dynamic analysis of mechanical systems).

2. Optimize the route the vehicle follows. 3. Develop control system and evaluate

performance in Adams. 4. Implement the control system on the Land

Rover. 5. Compare experimental results with simulated

results.

Modelling the Land Rover: Supply Forces

Measured engine torque Modelled engine torque

020

4060

80100

10001500200025003000350040004500-50

0

50

100

150

200

250

Throttle position [%]

Modelled engine torque

Engine speed [rpm]

Torq

ue [

Nm

]

0

50

100

150

200

Modelling the Land Rover: Demand Forces

Coast down test Demand forces

0 10 20 30 40 50 60 70 80 900

10

20

30Vehicle speed as a function of time

Time [s]

Spee

d [m

/s]

0 10 20 30 40 50 60 70 80 90-0.8

-0.6

-0.4

-0.2

0Vehicle acceleration as a function of time

Time [s]

Acce

lera

tion

[m/s

2 ]

17 18 19 20 21 22 23 24 25 26900

950

1000

1050

1100

1150

1200

1250

1300

Vehicle speed [m/s]

Dem

and

forc

e [N

]

Demand force as a function of vehicle speed

Measured Force

ax2+c fit

Engine Brake Torque Deceleration due to braking

500 1000 1500 2000 2500 3000 3500 4000 4500-40

-35

-30

-25

-20

-15

-10Engine brake torque as a function of engine speed

Speed [RPM]

Torq

ue [N

m]

Modelling the Land Rover: Demand Forces

-1 0 1 2 3 4 5 6 7-2

-1

0

1

2

3

4

5 g p

Hydraulic pressure [MPa]

Decele

rati

on

[m

/s2]

Measured dataFitted function

Adams Model - Summary

• Engine map modelled as a function of engine speed and throttle position

• Drag and rolling resistance modelled as a function of vehicle speed

• Engine braking torque was modelled as a function of engine speed

• Braking deceleration was modelled as a function of brake line pressure

Control System Development • Rollover threshold given by:

𝑨𝑨𝒚𝒚𝒉𝒉

=𝒕𝒕𝒘𝒘𝟐𝟐𝒘𝒘

• Lateral acceleration given by: 𝑨𝑨𝒚𝒚 =

𝑽𝑽𝟐𝟐

𝑹𝑹

• Thus, increase radius of path leads to a higher permissible speed or lowers lateral acceleration

• Leads to trajectory planning

Trajectory Planning • Racetrack discretised into sections

– Coordinates of right and left side of track – Position on section of the track indicated by α – α = 0 → LH side of track – α = 1 → RH side of track

300 350 400 450-640

-620

-600

-580

-560

-540

-520

-500

-480

Track discretisation

x-coordinate

y-co

ordi

nate

Left boundaryRight boundary

α = 0

α = 1

Trajectory Planning • Optimisation:

– Curvature requires second derivative – Use finite difference methods to approximate

curvature – Minimise the “global” curvature of the trajectory

– Standard quadratic form → use quadratic

programming to optimise

𝜿𝜿 = 𝜶𝜶 𝑻𝑻 𝑯𝑯 𝜶𝜶 + 𝒃𝒃 𝑻𝑻 𝜶𝜶

Trajectory Planning

0 200 400 600 800 1000

-700

-600

-500

-400

-300

-200

-100

0

100

Bird's eye view of Gerotek's ride and handling track

Distance x [m]

Dist

ance

y [m

]

Road boundariesTrajectory

50 100 150 200 250 300 350 400 450

-550

-500

-450

-400

-350

-300

-250

x-coordinate [m]

y-co

ordi

nate

[m]

Discretised track with minimum curvature trajectory

Longitudinal Control System

• The reference speed (V) must now be determined.

• Reference speed limited by: – Maximum lateral acceleration: – Friction available (friction circle) – Vehicle’s longitudinal performance capabilities

(supply and demand forces)

𝒕𝒕𝒚𝒚 =𝑽𝑽𝟐𝟐

𝑹𝑹

Maximum Lateral Acceleration

• Minimising the curvature is the same as maximising the radius

• To determine the radius of curvature:

𝒕𝒕𝒚𝒚 =𝑽𝑽𝟐𝟐

𝑹𝑹

𝑹𝑹𝒘𝒘 = 𝒙𝒙𝑹𝑹,𝒘𝒘 − 𝒙𝒙𝒘𝒘𝟐𝟐 + 𝒚𝒚𝑹𝑹,𝒘𝒘 − 𝒚𝒚𝒘𝒘

𝟐𝟐

Friction Available (Friction Circle)

• Friction force available is the vector subtraction of lateral force (generated by cornering) from the limit:

𝑨𝑨𝒙𝒙,𝒘𝒘 = 𝑨𝑨𝒙𝒙,𝒎𝒎𝒕𝒕𝒙𝒙 𝟏𝟏 − 𝑨𝑨𝒚𝒚,𝒘𝒘 𝑨𝑨𝒚𝒚,𝒎𝒎𝒕𝒕𝒙𝒙⁄ 𝟐𝟐

Vehicle’s Performance

0 50 100 1500

1

2

3

4

Vehicle speed [km/h]

Acc

eler

atio

n [m

/s2 ]

Maximum acceleration available as a function of speed

0 50 100 150-6.15

-6.1

-6.05

-6

-5.95

Vehicle speed [km/h]

Acc

eler

atio

n [m

/s2 ]

Maximum deceleration available as a function of speed

Speed Profile Algorithm

• Preview distance • Speed at each point

on the trajectory determined with limiting longitudinal acceleration

• Speed limit of 130km/h

𝒘𝒘𝒑𝒑𝑹𝑹𝑹𝑹𝑹𝑹 = 𝑽𝑽𝑽𝑽 −𝟏𝟏𝟐𝟐𝒕𝒕𝒎𝒎𝒕𝒕𝒙𝒙,𝑹𝑹𝑹𝑹𝒍𝒍𝒉𝒉𝑽𝑽𝟐𝟐 + 𝒕𝒕𝑹𝑹𝒍𝒍𝒄𝒄𝒕𝒕

𝑽𝑽𝒘𝒘+𝟏𝟏 = 𝑽𝑽𝒘𝒘𝟐𝟐 + 𝟐𝟐𝑨𝑨𝒙𝒙∆𝒄𝒄𝒘𝒘

0 500 1000 1500 2000 2500 3000 3500 4000 45000

20

40

60

80

100

120

140Reference speed for Gerotek

Distance travelled [m]

Spee

d [k

m/h

]

Reference speed

Maximum speed V2/R

ADAMS/View Simulation • Obtain GPS coordinates for various tracks around

the world – Silverstone – Imola – Zandvoort – Gerotek’s ride and handling track

• Generate a trajectory (path) and speed profile for each track

• Specify acceleration limits (longitudinal and lateral) • SIMULATE!

Simulation Results - Gerotek

0 500 1000 1500 2000 2500 3000 3500 40000

50

100

150

Distance travelled [m]

Spee

d [km

/h]

Speed as a function of distance travelled

ADAMS/View model speedLong ref speedMax lateral speed

0 500 1000 1500 2000 2500 3000 3500 4000-10

-5

0

5

10

Distance [m]

Acce

lerati

on [m

/s2 ]

Acceleration as a function of distance

LateralLongitudinalLimits

-1.5 -1 -0.5 0 0.5 1 1.5

-0.5

0

0.5

Friction circle

Lateral [g]

Long

itudi

nal [

g]

0 500 1000

-600

-400

-200

0

Path followed

x coordinates [m]

y coo

rdin

ates [

m]

Gerotek ride and handling simulation results

Simulation Results - Silverstone

0 500 1000 1500 2000 2500 3000 3500 40000

50

100

150

Distance travelled [m]

Spee

d [k

m/h

]

Speed as a function of distance travelled

ADAMS/View model speedLong ref speedMax lateral speed

0 500 1000 1500 2000 2500 3000 3500 4000-10

-5

0

5

10

Distance [m]

Acce

lera

tion

[m/s

2 ]

Acceleration as a function of distance

LateralLongitudinalLimits

-1 0 1-1

-0.5

0

0.5

1Friction circle

Lateral [g]

Long

itudi

nal [

g]

-500 0 500

-800

-600

-400

-200

0Path followed

x coordinates [m]

y co

ordi

nate

s [m

]Silverstone simulation results

Simulation Results Discussion • Trajectory planning used to minimise curvature • Lateral acceleration, friction and vehicle

performance limit used to determine maximum longitudinal acceleration

• Speed profile developed and implemented in Adams

• The model was able to negotiate several racetracks while maintaining control

Experimental Validation • Procedure:

– Record the path to be driven by driving at low speed.

– Define the maximum allowable lateral and longitudinal acceleration.

– Calculate the speed profile – Perform a severe double lane change

manoeuvre – Hope the vehicle brakes

Experimental Results

0 100 200 300 400 500 600-4

-2

0

2Path followed

x-coordinate [m]

y-co

ord

inat

e [m

]

-10 -5 0 5 10

-202

g-g diagram

Lateral acceleration [m/s2]

Lo

ng

itu

din

al

ac

cele

rati

on

[m

/s2 ]

0 100 200 300 400 500 6000

20

40Speed as a function of distance travelled

Distance travelled [m]

Sp

eed

[m

/s]

Measured speedDesired speed

0 100 200 300 400 500 6000

1

2Brake line pressure as a function of distance travelled

Distance travelled [m]

Bra

ke P

ress

ure

[M

Pa]

Measured pressureDesired pressure

0 100 200 300 400 500 600-4

-2

0

2

4Acceleration as a function of distance travelled

Distance travelled [m]

Acc

eler

atio

n [

m/s

2 ]

Longitudinal accelerationLateral acceleration

DLC - Lateral 5m/s2 ; Longitudinal 8m/s2

Experimental Results • Lateral acceleration of vehicle was kept below

prescribed limit • Vehicle reduced speed when exceeding speed

limit and tracked the speed limit • Control system was found to be

conservative(brakes early)

Conclusion • Aim was to develop a control system that limits lateral

acceleration by controlling vehicle speed • Longitudinal dynamics modelled in ADAMS:

– Engine map – Demand forces – Brakes – Engine braking

• Longitudinal control system developed • Control system performance was simulated in ADAMS • Control system implemented experimentally

Future Work • Investigate control system’s performance on test

track that resembles public roads

• Optimise the trajectory in real-time

• Integrate the developed control system with lane departure warning and obstacle detection

Thank you