MINIMIZING DRIVER INTERFERENCE UNDER A
PROBABILISTIC SAFETY CONSTRAINT IN
EMERGENCY COLLISION AVOIDANCE SYSTEMS
Jeff Johnson, Yajia Zhang, Kris Hauser
School of Informatics and Computing
Semiautonomous Active Safety Systems
Mercedes-Benz Pre-Safe
system
Volvo S60 adaptive cruise control
Collision Avoidance in General
• Robustly deliver driver from dangerous situations
• How to deal with uncertainty in the environment and in vehicle
control?
• Minimally interfere with driver operations
• Interference may train a driver to rely on the system and become
inattentive
• Driver inattention is a major factor in serious traffic crashes [NHTSA
2001]
Our Approach
•
Safety-Constrained Interference Minimization Principle
(SCIMP): Maintain minimum safety threshold while minimizing
interference
• Implemented two scenarios under this framework:
Collision avoidance braking
Intersection crossing
Safety-Constrained Interference
Minimization Principle
For some safety threshold α, and the user’s desired control
ud, pick the α-safe control u that is closest to ud
P(safe) ≥ α
u = ud
α=0
Control space
Safety-Constrained Interference
Minimization Principle
For some safety threshold α, and the user’s desired control
ud, pick the α-safe control u that is closest to ud
P(safe) ≥ α
u=
Control space
ud
α = 0.5
Safety-Constrained Interference
Minimization Principle
For some safety threshold α, and the user’s desired control
ud, pick the α-safe control u that is closest to ud
P(safe) ≥ α
α = 0.9
u
ud
Control space
Safety-Constrained Interference
Minimization Principle
• More formally, satisfy this optimization:
Minimize the
difference between
the driver’s control
and the control to
be executed…
…such that the safety of the
system is at least α
Safety-Constrained Interference
Minimization Principle
• More formally, satisfy this optimization:
Minimize the
difference between
the driver’s control
and the control to
be executed…
…such that the safety of the
system is at least α
Interference metric
Safety-Constrained Interference
Minimization Principle
• More formally, satisfy this optimization:
Minimize the
difference between
the driver’s control
and the control to
be executed…
…such that the safety of the
system is at least α
Probability of safety of
optimal control that
starts at ut = u
Safety-Constrained Interference
Minimization Principle
• If P(safe|u) ≥ α cannot be satisfied
choose the safest control:
Properties of SCIMP
• If the user’s control is safe, then u = ud
• Safety and interference tuned through single parameter α
• But computing P(safe) is hard:
• It is the probability that a given control will result in state that is at
least α-safe
• Stochastic partially-observable optimal control problem
• Tractability requires an approximation
P(safe) Approximation
Indicator function, whether system
can remain safe under state x given
control u
Probability of a given
state x
• Integrate over optimal hypotheses assuming the
underlying state hypothesis is true
• Reduces the problem to an integral over deterministic
optimal control problems
• When uncertainty is relatively low, this provides a very
good approximation
Collision Avoidance Braking
• The problem: Employ a braking policy that avoids collision
with an obstacle obstructing the vehicle’s path
• Obstacle, vehicle moving in same direction along fixed path
• Vehicle equipped with speedometer and range sensing device
• System state estimated with EKF
• Two road surface types: wet and dry
System Structure: EKF Formulation
State vector x
• Vehicle position pc
• Vehicle velocity vc
• Obstacle position po
• Obstacle velocity vo
• Obstacle acceleration ao
Observation term z
• Relative distance d
• Speedometer reading v
Braking term 0 ≤ u ≤ 1 indicates how hard to brake:
u = 0, no brake
u = 1, brake with maximum deceleration
Dynamics
pc = pc + vct + ½uacmaxt2
vc = vc + ukacmaxt
acmax = acmax
po = po + vot + ½aot2
ao = ao
Sensor model
d = po – pc
v = vc
Additive noise
xt+1 = f(xt, ut) + ε1
zt = h(xt) + ε2
Policy
• Estimate stopping position of
vehicle under maximum braking
• Estimate position of obstacle at time
vehicle comes to full stop
• If overlap, brake to maintain safe
stopping distance
• Smooth brake output
• S(x, u) is given by whether there is
a collision for a given state and
control
Five Test Scenarios
Stationary obstacle
Transient obstacle
False negative
Hard braking obstacle
False positive
Two road surface types:
Dry pavement: acmax = -5 m/s2
Wet pavement: acmax = -3 m/s2
Policy Evaluation
CV: Collision velocity
Interference Index: c1DT + c2ET + c3SD
• DT: Penalizes erratic braking
• ET: Penalizes slow driving
• SD: Penalizes early stopping
• c1…3: Proportionality constants
• We compared an Ideal, Basic, and SCIMP policies.
Sample Results
Transient obstacle
Emergency braking obstacle
Interference Index
Ideal
3
Basic
2
SCIMP
1
No control
0
-1
-2
0
5
10
15
Collision Vel (m/s)
20
Interference Index
4
4
Ideal
3
Basic
2
SCIMP
1
No control
0
-1 0
5
10
15
-2
-3
-4
Collision Vel (m/s)
False negative
20
Sample Results
False negative
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
4
Ideal
Basic
SCIMP
No control
N/A
0.6
0.7
0.8
0.9
Alpha
Between obstacles
Interference Index
Interference Index
False positive
1
Ideal
3
Basic
2
SCIMP
1
No control
0
-1
-2
0
5
10
15
Collision Vel (m/s)
20
Intersection Crossing
• The problem: Employ
a longitudinal control
policy that allows a
vehicle to safely traverse
an intersection
• How do we compute
S(x, u)?
Path-Time Space: Construction
Agent
vehicle
Overlap path
parameter
t2
Deceleration
p2
Overlap duration
t1
Acceleration
p1
p2
p1
Obstacle
vehicle
Path-Time Space: Construction
Agent
vehicle
Overlap path
parameter
t2
Deceleration
p2
Overlap duration
t1
Acceleration
p1
p2
p1
Obstacle
vehicle
Analytical Planner
• Exact, optimal,
and polynomialtime
• Can be used in
the indicator
function S(x, u)
when computing
P(safe)
Optimal Acceleration-Bounded Trajectory Planning in Dynamic Environments Along a
Specified Path
Johnson, Hauser; ICRA 2012
Analytical Planner
Results
Agent-obstacle side impact
6
5
4
3
2
1
0
-1 0
-2
-3
-4
Ideal
Basic
Probabilistic
No Control
2
4
6
Collision Vel (m/s)
8
10
Interference Index
Interference Index
Between obstacles
6
5
4
3
2
1
0
-1 0
-2
-3
-4
Ideal
Basic
Probabilistic
No Control
2
4
6
Collision Vel (m/s)
8
10
Summary
• Safety-Constrained Interference Minimization Principle
• Generalized, mathematical framework for semi-autonomous
collision avoidance
• Reduces collision velocity relative to non-probabilistic method
• Tunable via single parameter
• Implemented two scenarios:
• Collision Avoidance Braking
• Intersection Crossing
Future Work
• Ground interference
index on data from
human drivers
• Study human reactions
to semiautonomous
longitudinal control
(short-term and longterm adaptations)
The DriveSafety DS-600c Driving Simulator
Transportation Active Safety Institute (TASI)
THANK YOU.
This work is partially supported by the Indiana
University Collaborative Research Grant fund of
the Office of the Vice President for Research.