explained above provide us with the individual received amplitudes. Hence, a better
communication scheme where a simple receiver can detect directly the IP at the robot's
position is required.
5.1.2 Gradient Calculation
Assuming a receiver that can directly detect the IP at the robot's position, a method
to find IF at that position is formulated here. The gradient of the potential with respect to
the robot's position p, can be estimated from the measurements taken by three antennas
on the robot using first order difference approximation of the derivatives. To improve
accuracy in the calculations, a rectangular grid of receiver antennas may be used to
calculate the gradient in the same way.
5.1.3 Results
The spreading algorithm for circular region was found to be working satisfactorily
with the use of an M sequence for communication between robots and a rectangular grid
antenna for gradient calculation. The parameters used in the simulation are tabulated in
table 5.1. The spreading speed of the spreading algorithm was also verified by calculating
the variance of the estimated pdf over the circular region at every iteration as shown in
figure 5.1. It can be seen that the spreading speed is almost the same here as compared to
the spreading speed when the position information of robots were transmitted (figures
3.13, 3.14 and 3.15). The variance of the estimated pdf after the robots reach their final
positions was found to be 4.5246e-004. This is slightly higher than the variance obtained
when the spreading algorithm was simulated by transmitting position information of
robots.