total information potential V, for the ith robot is the sum of the received signal amplitudes
A&k from all other robots.
N N 1(3.2)
V,= ZAik = Z 2 (3.2)
k=l,k1i k=l,ksidk +
where oy is a regularity constant to avoid V, peaking to infinity when dk 0.
This is compared to the threshold calculated according to the desired radius to
specify the sign on the direction of the IF, which is the gradient of the potential.
Approximating the discontinuous sign function with arctan, the expression for the IF for
the ith robot becomes
Fi = arctan(y -V ) -- (3.3)
api
3.2.3 Results
The application of IPIM for spreading of robots eliminates the need for them to
know their positions explicitly. But many implementation issues like the mode of
communication as well as the way to find the gradient for IF must be formulated for the
simulation of the algorithm completely. Hence, the results presented in this section were
obtained by transmitting relative position information between robots. Transmitting the
relative positions instead of absolute positions allows the center of the circle to vary
according to the initial position of the robots.
3.2.3.1 Spreading algorithm
Figure 3.3 shows the spreading of robots starting from their initial positions to the
final positions. Figure 3.4 shows the trajectories of all the robots. It can be seen that the
spreading is almost uniform at the end and the robots form approximately concentric
circles around the center of the circle. It can also be observed that the radius of the