IEEE Robotics & Automation Magazine - December 2010 - 31

ri ,^ei ) ¼ f
r 2 Ri j 9 r 2 r^i j r ¼ di (r,^ei )g ,
d~i (^
describing how the agent's estimated action r^i is updated
based on the estimated event vector ^ei :
~ ri ,^ei ):
r^þ
i ¼ di (^

(2)

During the second phase, all predicted behaviors ~qi are
compared against the measured one qi . A behavior qi (t) complies with model Hi if
jjqi (t) À ~qi (t)jj

e, for all t 2 Tk ,

σi (0)
e1i

Fast

ei3
ei5

Left

ei4

si1 = Front Lane Occupied
si2 =

Right

ei2

¬ei2

where Tk ¼ ½tk , tkþ1 ) is the kth observation period, e is a suitable
precision, and jj Á jj is the Hausdorff norm. When no predicted
behavior complies with the model, the agent is certainly
uncooperative; if there is a unique behavior complying with the
model and not depending on the region outside Ah 's visibility
range, the agent is certainly cooperative; otherwise, it is possibly
cooperative, and thus the value uncertain is chosen.
Consider four cars in the highway example [Figure 10(a)].
Misbehavior of car 00, running a FAST maneuver along the
second lane, while its next right lane is free, has to be
detected (the car should start a RIGHT maneuver to return
to the first lane). A FAST maneuver of a car in the second
lane implies that the region on its right is occupied by
another car. Three local monitors on the other cars try to
learn whether the car 00 is cooperative or not but have no
full view of its neighborhood of car. Figure 10(b) reports the
local maps of occupancy, M00;01 , M00;02 , and M00;03 , that each
monitor has reconstructed.

Slow
I 4unobs

Left Lane Occupied

si3 = Right Lane Occupied

e1i

= s1i ∧

ei3 = ¬si3

¬si2

ei2 = si1∧

ei4 = ¬si1

V0

¬si2

ei5 = si3

(a)

I 4obs

V0

Figure 8. Example of partial visibility of a local observer. The
observer on the car 00 has difficulty discerning whether the
pilot of car 04 is correctly driving or it is faking the presence of
other cars that are outside the observer's view.
(b)

Ai
·
qih,1 = H(qih,1, Iih,1)
..
. vi
(c)

· +
(qi, σi ) = Hi (qi, σi, vi)

·
qih, nh = H(qih, nh, Iih, nh)

qi

Mh
Vh
qi
vi obs
(d)

Figure 7. Automaton of the traffic rules of a society of cars
that follow a collision avoidance and motion coordination
protocol to guarantee their passengers' safety. (a) Protocols'
automaton, (b) initial configuration, (c) intermediate
configuration, and (d) final configuration.
DECEMBER 2010

∼
∼
(qi, Mi,h) = Hi (qi,vi,Vh)

ψ

Mi,h

Figure 9. Architecture of a local monitor onboard of agent Ah
that is able to estimate the cooperativeness of an agent Ai by
using only local information.
IEEE Robotics & Automation Magazine

31



Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2010

IEEE Robotics & Automation Magazine - December 2010 - Cover1
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