Page 69 - Innovations in Intelligent Machines

58 P.B. Sujit et al.
Theorem 2. The negotiation terminates in a finite number of negotiation
cycles.
Proof. From Theorem 1 we observe that, at each negotiation cycle, at least
one of the agents gets all accept and so decides upon a target for its next step.
Since there are a finite number of agents, in a finite number of negotiation
cycles each agent would decide upon a target to attack. If the target are not
available then they continue to search task. Hence, all the agents would decide
upon a task in a finite number of negotiation cycles. The maximum number
of negotiation cycles an agent can go through is N.

4.3 Simulation Results

A simulation study is conducted on a battlefield scenario of size 100 × 100.
Through these simulations we show that the negotiation scheme performs
better than greedy strategy in terms of average number of targets destroyed.
The simulation is carried out using 7 UAVs for 100 different sets of target posi-
tions with each set having 20 targets. The a priori knowledge about number
of targets present in the space and their initial positions are not available to
the UAVs. We also study the performance of negotiation and greedy schemes
for various sensor radius.
From Figure 5 we can see that the negotiation scheme outperforms the
greedy strategy. The number of targets using negotiation scheme is higher and

20
Ns = 30
18 r Ns r = 20
and s =40
r
Ns r =10 G s = 40 = 50
Average number of targets destroyed 12 8 G s = 20 G s = 30
16
G s r
Ns =50
r
14
r
r
10
r
6
4
G s = 10
r
2 G > Greedy strategy
N > Negotiation scheme
0
0 50 100 150 200 250 300 350
Time taken to destroy targets
Fig. 5. Average number of target hits for 100 different target positions