IEEE Robotics & Automation Magazine - September 2011 - 49

are too close. The maintain speed and rear-end collision
prevention modules are based on a simple proportionalintegral differential (PID) control scheme. The positioning
system transmits the position information to the vehicles
over the wireless network.
Learning Human Driving Model
A set of experiments were performed in which five
human subjects drove a vehicle on the outer path in the
roundabout system in ten acceleration and ten braking
trials each. In these experiments, the subjects were
directed to either brake or accelerate at the human-decision point DP in Figure 3 while also avoiding a moving
target on the inner path. The data collected in these braking and acceleration trials were then analyzed to estimate
the parameters bq and cq and presented in the "Safety
Control Problem for Hidden-Mode Hybrid Systems" section. We denote the position measurement at time step k
as p(k) with dT ¼ 0.1 s as the time lapsed between two
consecutive steps. The acceleration/deceleration at time
step k is denoted as a(k) and is calculated as a(k) ¼
p(k) À 2p(k À 1) þ p(k À 2)=dT 2 . The average acceleration/deceleration
is calculated for the trial as a ¼
P
1=N À 1 Nk¼2 a(k): A total of 99 trial runs were obtained.
These trials were divided into a training set and a test set.
The model of the driver behavior was then obtained by
fitting two Gaussian distributions to the training data for
braking and acceleration trials and then using the test
data to verify the model. More than 1,000 randomly

Multivehicle
Laboratory

chosen training and test sets were considered. The average training and test errors are 0:56% and 0:96%, respectively. As the final model, we chose one with zero training
and test errors, in which 79 trials were used as the training set (40 braking and 39 acceleration trials) and 20 trials
were used as the test set (ten braking and ten acceleration
trials). The resulting values of the model parameters in
(2) are given by bB ¼À282.7 mm/s2 and bA ¼ 350.5 mm/
s 2 . The values of cB and cA are given by cA ¼ 139.6 mm/
s2 and cB ¼ 106.6 mm/s2 . We set d ¼ 3 corresponding to
three standard deviations.
Trials Experimental Conditions
A total of eight human subjects participated in the study.
This set of subjects is different from the set used to generate the human driving model. To start the experiment, the
subjects were given an introduction about the setup. This
was followed by a practice session in which the subject drove
the vehicle on an outer path. The autonomous vehicle was
run on the inner path at a constant speed of 500 mm/s. Subjects were free to drive the human-driven vehicle at any speed
between the points Pt1 and Pt2 : Between points Pt2 and
DP; the speed module keeps the vehicle speed at 600 mm/
s. This ensures that the human-driven vehicle does not
cross the decision point with minimum or maximum
speed. Thus, we instructed the human subjects to either
accelerate or decelerate as soon as they crossed the decision point DP to force the two vehicles in the bad set at
the same time.

U1, U2, Pt1

Autonomous Vehicle
Human-Driver
Interface

Set B
Outer Path

Inner Path

Steering
Wheel

Com

mand

Brake Pedal

Pt2

Throttle
Pedal

Human-Driven Vehicle

Signa

Human-Decision
Point, DP
LO = 14.22 m, L2 = 12.414 m, U2 = 13.314 m
LI = 11.62 m, L1 = 7.863 m, U1 = 8.763 m

Figure 3. Human-driver interface and roundabout system. LO is the length of the outer path, and LI is the length of the inner path.

SEPTEMBER 2011

IEEE ROBOTICS & AUTOMATION MAGAZINE

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2011