Robust Airborne Collision Avoidance through Dynamic Programm(45)

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for
an
en-
counter with two approaching intruders that are equally distant from the own aircraft horizontally and are separated from each other by 400ft. All aircraft are currently level, and no advisory has been issued. The actions taken by this strategy appear sensible for much of the state space. How-ever, it does especially poorly when the own aircraft is between the two intruders in altitude. When the own aircraft is in the position indicated in the .gure, the strategy results in a descend advisory because the closer intruder is above. This descend advisory, though, results in the aircraft de-scending into the other intruder. Of course, the system would later reverse the advisory to prevent collision, but this behavior is not ideal. Issuing a climb advisory or even delaying the alert would be preferable.
TCAS adopts a more sophisticated command arbitration strategy. It treats each threat individually, with the same threat detection, initial sense selection, and initial strength selection logic that would be used with a single intruder. The multithreat portion of the logic attempts to reconcile the senses and strengths associated with each intruder before displaying a composite
Altitude (ft)
1000 500 0 .500 .1000

Time (s)
Figure 32. Closest command arbitration strategy. Two intruder aircraft are on the left, and the own aircraft is
on
the
right.
All
aircraft
are
initially
level
and
no
advisory
has
been
issued.
The
parameters
from
Section
3
with zero terminal cycles were used.
advisory to the pilots. When all threats have the same sense, the logic simply uses the individual advisory with the greatest strength. When the senses of the individual advisories di.er, TCAS uses a set of rules to either (1) identify a single sense for all threats or (2) issue a “dual-negative advisory” that places vertical speed limits in both senses.

9.2 UTILITY FUSION
Instead of making decisions based solely on the actions recommended by the agents, the utility (or, alternatively, expected cost) each agent assigns to each action can be leveraged to arrive at a better overall
action
[51].
Let
J(n)(a) be the expected cost for executing action a as assigned by agent n. This value can be interpreted as the expected cost when executing action a for one step and then continuing with the optimal pairwise individual logic, ignoring all intruders other than intruder n.
Fusing these action costs requires de.ning a function f that combines the costs from all of the agents. The action to be executed is given by
arg min f(J(1)(a),...,J(N)(a)). (32)
a
There are di.erent ways to de.ne the combining function f, but it should have the following properties:
.
Exchangeability: f(. . . , a, . . . , b, . . .)= f(. . . , b, . . . , a, . . .) for all a and b.

.
Monotonicity: f(. . . , a, . . .) ≤ f(. . . , b, . . .) for all a<b.

.
One-step optimality: The recommended action should be optimal for a one-step horizon.

One way to de.ne f is
simply
as
a
summation
[50].
However,
it
does
not
seem
appropriate
to sum the immediate costs in this problem. For example, the penalty for alerting in this scheme would be incurred for each intruder. Double counting alert costs results in delaying the alert, which is especially undesirable in multithreat encounters. Depending on the encounter situation, it may be
important
to
alert
earlier.
Figure
33(a)
shows
a
slice
of
the
policy
for
this
strategy.

Alternatively, the combining function can return the maximum expected cost. At each time step, the strategy selects the action that guarantees the lowest expected cost against all individual intruders in isolation. One advantage of this approach is that it does not double count the alert costs.
　
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