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An easy solution is to simply let the robot follow the wall for a little while and stop If you study Fig 121 you will see that if the robot stops too early it will just try to face the beacon again and start over Obviously, the robot does not have to follow the wall until it gets to the other side; it only has to follow it for a reasonable length of time The question is How long is reasonable If the object is small, then a short time is best because we don t want to go all the way around the object If we always use a short time though it is conceivable that some combination of objects could occur that would trap the robot.

6.13. What is the effective aperture of an isotropic antenna operating at a wavelength of 1 cm 6.14. Determine the half-power beamwidth of a half-wave dipole. 4l,

6.15. A uniformly illuminated rectangular aperture has dimensions a b 3l. Plot the radiation patterns in the principal planes.

This might happen if the robot does not go far enough around the object to get a clear (or at least clearer) path to the beacon In such situations, the robot might simply continue to retrace its steps repeatedly moving toward the goal until blocked, following the wall but not far enough, moving toward the goal again, but essentially in the same situation as before One way to solve such a problem is to introduce some randomness into the robot s behavior If you examine the code in Fig 126 you will notice that it is the same as the code in Chap 8, but in place of a while-loop we are now using a for-loop The while-loop in Chap 8 caused the robot to follow the wall forever The for-loop causes this code to be executed between 20 and 270 times These numbers were.

Fig. A-13

6.16. Determine the half-power beamwidths in the principal planes for the uniformly illuminated aperture of Prob. 6.15. Hence determine the gain. State any assumptions made. 6.17. Explain why the smooth-walled conical horn radiates copolar and crosspolar field components. Why is it desirable to reduce the cross-polar field as far as practical, and state what steps can be taken to achieve this. 6.18. When the rectangular aperture shown in Fig. 6.9 is fed from a waveguide operating in the TE10 mode, the far-field components (normalized to unity) are given by

GoAround: If BeaconFound Then return rTurn -random(150) if TurnDir > 0 FN = 6 else FN = 12 endif for i=1 to 20 + random(250) while (rFeel() & FN) or (rBumper() &4) rTurn -TurnDir wend rForward 1 while not rFeel() rTurn 5*TurnDir rForward 1 wend next Return

E ( ,

3 1 3 1 , , , . 2 2 2 2

E( ,

chosen experimentally based on the general size and number of objects expected to be in the room An if-statement at the beginning of the subroutine causes the routine to exit and not attempt to follow a wall if the beacon has already been found The line after the if-statement is very important It causes the robot to turn away from the wall a random amount (0 150 ) This single statement prevents the robot from being stuck in many situations because the random turning of the robot eventually puts it into an orientation where the sensors allow it to move Remove the line when you test this algorithm and you will see the robot eventually encounter a situation where it cannot free itself 1217 DETERMINING IF THE BEACON IS FOUND The routine in Fig 127 determines if the robot has reached the beacon.

where X and Y are given by Eqs. (6.19) and (6.20). The aperture dimensions are a 3l, b 2l. Plot the radiation patterns in the principal planes. 6.19. Determine the half-power beamwidths in the principal planes for the aperture specified in Prob. 6.18, and hence determine the directivity. 6.20. A pyramidal horn antenna has dimensions a 4l, b illumination efficiency of 70 percent. Determine the gain. 2.5l, and an