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n previous chapters, our robot was programmed to roam anywhere it could. In this chapter we will discuss ways of con ning the robot to a certain area (or out of an area) but without erecting walls, fences, or other barriers that protrude out of the ground. The robot should be able to move anywhere while avoiding obstacles but should not be allowed to move out of (or into) a speci ed area. There are various ways to delimit such a con nement for a robot: Draw lines around the boundary or use infrared beams, or bury an electric wire in the ground around the perimeter, or any other means where the robot can use sensors to know the limit has been reached and take action to stay away from the boundary. If the area is surrounded by a drop off, such as a table or the passageway of the second oor of a house, we give the robot the ability to detect a drop off to enable it to stay away from cliff edges. Give the robot a set of coordinates de ning the prohibited/allowed areas and then have the robot use a GPS (global positioning systems) to calculate if it is allowed to enter/exit an area.

Inverse Cosine (Arc Cosine)

Equation (2.31) can be used to calculate the true anomaly, and because of the small eccentricity, this can be approximated as M 2e sin M (3.22)

The two-line elements for the Intelsat series, obtained from Celestrak at http://celestrak.com/NORAD/elements/intelsat.txt are shown in Fig. 3.7.

In this chapter we will develop some algorithms that simulate a means of con ning the robot using the standard sensors that our robot has, but we will also explore the possibilities that more advanced sensors can provide.

10-02.

Fig. 37-3

Most people are familiar with the electronic fence systems that con ne dogs to a yard. A perimeter is de ned by some means (usually a radio signal) and a device on the dog s collar triggers some kind of pain to the dog (how cruel) that makes the dog shy away from the perimeter effectively con ning the dog to the yard and house. We are not going to be so mean to our robot. We will surround the desired perimeter with a red line and tell the robot not to move beyond the line. This line simulates a buried wire carrying a very low power radio frequency (RF) signal. A real robot would need a small radio receiver whose antenna is placed so that it can detect the wire. The simulated robot senses the line with the rSense() function we have explored in Chap. 7, simulating the ability to sense the RF signal. The details of the physical mechanism are not important to developing the algorithm for the behavior. Once the algorithm for teaching the robot the required behavior has been established, the actual mechanism for marking the boundary can be whatever is suitable. The aim is to explore how to make the robot recognize a boundary and stay within it. 9.1.1 AN INITIAL ALGORITHM The program in Fig. 9.1 is an attempt at achieving the requirement discussed above. The idea is to use rSense() to detect when the robot is approaching the boundary and then turn away. The turning direction depends on which sensor combination is triggered:

From Fig. 3.7 the inclination is seen to be 0.0079 , which makes the orbit almost equatorial. Also the revolutions per day are 1.00271159, or approximately geosynchronous. Other values taken from Fig. 3.7 are: 124.94126775 days; 190.2817 ; e year 2005; 311.0487 ; w

From Table 2.2 the Julian day for Jan0.0 2005 is JD00 2453370.5 days. The Julian day for epoch is JD 2453370.5 124.94126775 2453495.44126775 days. The reference value is (see Eq. 2.20) JDref 2415020 days. Hence T in Julian centuries is: T JD JDref

If the right sensor is triggered or the right and front together then turn left. If the left sensor is triggered or the left and front together then turn right. If all the sensors or just the front one are triggered, the robot turns around. To prevent the possibility of repeating a behavior endlessly, we will give the robot some randomness by turning 180 30 .

[0 x ]

36525 38475.442 36525 1.05340017 The decimal fraction of the epoch gives the UT as a fraction of a day, and in degrees this is: UT 0.94126775 338.85637 Substituting these values in Eq. (2.34) gives, for the GST: GST 99.9610 36000.7689 T 0.0004 T2 UT 360

MainProgram: linewidth 7 rectangle 50,50,650,550,red rlocate 100,100,90 rInvisible red goSub Confine End //======================================================== Confine: while true while not rSense() rforward 1 wend S = rSense() if S = 4 OR S = 6 then rTurn 1 if S = 1 OR S = 3 then rTurn -1 if S = 2 OR S = 7 then rTurn 150 + random(60) wend Return

201.764 (mod 360 )

[ 1 y 1]

3.32104 rad 190.28044 Equation (3.20) then gives:

Notice the use of the line S = rSense(). This saves the sensors condition in the variable S. We then use this variable to test for various situations. We could have written each if-statement like this:

and Eq. (3.21):