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.