1 challenge the future m.wang, w.daamen, s. p. hoogendoorn and b. van arem driver assistance systems...
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1Challenge the future
M.Wang, W.Daamen, S. P. Hoogendoorn and B. van Arem
Driver Assistance Systems Modeling by Optimal Control
Department of Transport & PlanningDelft University of Technology
2Challenge the future
Outline
• Context
• Control framework for car-following support
• Adaptive Cruise Control (ACC) model
• EcoACC control model
• Simulation results
• Summary and outlook
3Challenge the future
Context
• Global interests in Advanced Driver Assistance Systems
(ADAS).• ACC are earliest ADAS in market.• Public concern on environment stimulates Eco-driving
assistance systems, i.e. EcoACC.• Needs for model EcoACC and evaluate the effects on driving
behavior.
4Challenge the future
Existing ACC
• Feedback controller, not optimal behavior
• Often be switched off at low speeds
• Cannot satisfy multiple control objectives
• Not able to model Eco-driving
5Challenge the future
This paper
An optimal control framework to model ACC/EcoACC
systems based on assumptions that:• Other vehicles driving at constant speed within a prediction
horizon;• Accelerations are controlled to minimize a cost function;• Costs are chosen to reflect multiple control objectives.
6Challenge the future
On-board system
On-board sensors
V2V&V2I Comm.
State estimation & prediction
Optimization at vehicle level
Reference control signal
Vehicle maneuver
Local traffic state
Other sensors
Vehicle actuactor
Schematic diagram for vehicle followingcontrol
7Challenge the future
Control framework
• (Local traffic) system state:
x = (x1, x2)T = (si , Δvi)T
si - following gap
Δvi - relative speed to predecessor
• State dynamics:
ui-1 - follower acceleration
ui - follower acceleration
si
Δvi = vi-1 – vi
i-1i
1
i i
i i i
s vd d
v u udt dt
x
8Challenge the future
Control framework2
• Objective function
s.t. state dynamics
• Applying Pontryagin’s Minimum Principle entails solving coupled ODE:
1) state dynamics with initial conditions x(t0)
2) co-state dynamics with terminal conditions λ(t0+T)
λ : co-states or marginal costs of the state x
0
0
*0min , ( )
t T
tuJ L u dt G t T
x x
9Challenge the future
ACC model
Functional requirements:
•Maintaining desired speed at cruising mode;
•Maintaining desired time gap at following mode.
Control objectives:
•Maximize travel efficiency;
•Minimizing risk;
•Maximizing comfort.
10Challenge the future
ACC running cost
with s*: desired gap, s*= v t* + s0; v0 : desired speed.
• The controller aims to:1) Minimize accelerations
2) Maintain a gap close to some desired gap s*
3) Match the speed of the predecessor.
• Applying the solution approach yields:
The optimal control law equals the marginal cost of relative speed.
3* 2 2 2 21 2
0
1( ) ( )
2 2 2 2ComfortSafety Efficiency
L s s v v v u
* vu
11Challenge the future
Tuning of prediction horizon
• Leader with constant speed of 72 km/h
• Initial gap: s (0) = 50 m
• Initial speed difference: Δv (0) = 0 km/h
• Desired time gap: t* = 1.5 s
• Desired speed: v0 = 120 km/h
• Prediction horizon: T = [2:20] s
s
Δv
LeaderControlled vehice
12Challenge the future
Simulation results
13Challenge the future
Choice of prediction horizon
• Large enough to ensure expected behavior;
• Not too large to avoid computational complexicity.
• A prediciton horizon of 5 s is recommanded from the results.
Intel Core 2, 2.4 GHz
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EcoACC model
Control objectives:
•ACC controller objectives + minimizing fuel consumption
Running cost:
•ACC controller running cost + Eco cost
Calculation of Eco cost:
•Spatial fuel consumption rate•Microscopic fuel consumption model from ARRB
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Comparison of ACC/EcoACC
0 5 10 15 20 25 3050
55
60
65
70
75
time (s)
v (k
m/h
)
Simulation setup:
•Disturbance in leader speed;
•Initial speed difference: Δv (0) = 0 km/h;
•Initial gap: s (0) = 30 m; 100 m;
•Desired time gap: t* = 1.5 s;
•Desired speed: v0 = 120 km/h;
•Prediction horizon: T = 5 s.
•Comparison
• 1) ACC;
• 2) EcoACC1, Eco cost weight = 5;
• 3) EcoACC2, Eco cost weight = 10.
16Challenge the future
Simulation: I nitial gap 100 m
0 5 10 15 20 25 3030
40
50
60
70
80
90
100
time (s)
s (m
)
0 5 10 15 20 25 30-30
-20
-10
0
10
time (s)
v
(km
/h)
0 5 10 15 20 25 3050
60
70
80
90
100
110
time (s)
v (k
m/h
)
0 5 10 15 20 25 30-3
-2
-1
0
1
2
3
time (s)
u (m
/s2 )
leader
ACC
EcoACC1 with 4 = 5
EcoACC2 with 4 = 10
17Challenge the future
Results (with reference to ACC)
EcoACC1 EcoACC2
Scenario 1(30m)
Mean speed -0.5% -1.2%
Fuel consumed -3.5% -5.1%
VKT* -0.5% -1.2%
Scenario 2(100m)
Mean speed -0.3% -0.8%
Fuel consumed -9.9% -15.2%
VKT -0.3% -0.8%
*VKT: Vehicle Kilometers Travelled
18Challenge the future
Summary
• An optimal control framework to model/design ADAS and Eco-DAS.
• Flexible state and running cost specifications reflecting control objectives.
• In our simple examples, the Eco costs result in higher fuel efficiency and similar distance
traveled.
• Stochastic case
• Local and string stability
• Cooperation between vehicles M. Wang, S.P. Hoogendoorn, W. Daamen, R.G. Hoogendoorn and B. van Arem. Driver Support and Cooperative Systems
Control Design. 2012 American Control Conference. Montreal, Canada.
Outlook
19Challenge the future
Questions?