vb.net read usb barcode scanner FIGURE 9.5b The robot is about to approach the extended borderline. in Software

Draw QR-Code in Software FIGURE 9.5b The robot is about to approach the extended borderline.

FIGURE 9.5b The robot is about to approach the extended borderline.
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A line de ned by the previous equation has in nite length. When we derived the equation for the boundary lines we did so to enable the above calculation, however, even though the in nite line may intersect the circle (Line B in Fig. 9.5a and also as in Fig. 9.5b), the segment that we are interested in (the actual boundary line) may not do so. It is necessary to check further to see if the intercept between the line and the circle is actually within the segment being considered. This is accomplished by checking to see if the calculated intercept x-coordinates are within the x-coordinates of the two points that de ne the line-segment. If both calculated intercept x-coordinates are outside the boundary line-segment then the boundary line does not intersect the circle even though its in nite extension does, as is about to occur in Fig. 9.5b (see the Line 47 in Fig. 9.6). Figure 9.6 shows how all of the above can be implemented in code. The math can be a little complex, but once the nal equations have been developed, the implementation is fairly straightforward.
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15 18 19 20 22 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
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//====================================================== TestViolation: Violation = false rGPS Rx,Ry for j = 1 to MaxDim(Boundary,1)/2 -1 //--for each line mm = (j-1)*2 X1 = Boundary[mm] Y1 = Boundary[mm+1] X2 = Boundary[mm+2] Y2 = Boundary[mm+3] If j=1 then X1 = -X1 //due to MPolygon specs //--Line formula Y = mX+b m = 1.0*(Y2-Y1)/(X2-X1) b = Y1-m*X1 //--quadratic X=(-B+Sqrt(B*B-4*A*c))/2/A //-X=(-B-Sqrt(B*B-4*A*c))/2/A //--if there is a solution then the //--circle and line intersect (possibly) A = 1+m^2 B = 2*m*(b-Ry)-2*Rx C = Rx^2+(b-Ry)^2-625 //625=(20+5)^2 BB = B^2-4*A*C if (BB) >= 0 BB = Sqrt(BB) XX1 = (-B+BB)/2/A //--first intercept XX2 = (-B-BB)/2/A //--second intercept //--check if intercept is actual //--not on extended line if Within(XX1,X1,X2) OR Within(XX2,X1,X2) Violation = true break //no need to check any more boundary lines endif endif next Return //======================================================
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FIGURE 9.6 GPS con nement part II (line numbering starts at 15 there is no missing code).
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Lines 25 to 28 are where we obtain the x, y coordinates of both ends of the line (this will be done for each line that de nes the boundary). Lines 31 to 32 are where we calculate the values m and b. Lines 37 to 39 are where we set the quadratic equation coef cients that will be used to solve the formula. Notice (Line 39) that the value 625 25^2. 25 is the robot s radius (20) plus an added buffer of 5. We write 625 directly so as to save time. This algorithm is very calculations intensive and any time saving we can do (such as this one) would help make the algorithm faster. This is an example of compromise between ef ciency and good programming practice. In good practice we ought to have set a constant for the robot s radius (e.g., R_Radius 20) and a constant for the buffer (e.g., Buffer 5) then we would write Line 39 as:
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C Rx^2 (b Ry)^2 (R_Radius Buffer)^2
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Unfortunately this requires a lot more time to execute than just writing the number as a literal. Also since this line of code will be executed many times (for each boundaryline and every time the robot moves) the time penalty would be high. Line 41 determines if the formula has a solution. If it does, the program enters the inside of the if-block (Lines 42 55). If it does not, the next boundary is considered (using the for-next loop). Lines 42 to 44 are where the equation is solved to obtain the x-coordinate of the two possible intercept points (they could be equal which means the same point i.e., one point). Lines 47 to 50 are where we check to see if the intercept points are within the boundary line-segment and not just part of the extended in nite line. If either point is, then there is a violation and we abort any further checking by exiting out of the for-next loop using the Break statement. Otherwise we proceed with checking the other lines [see Sec. C.8 for details on the Within() function].
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Combine the code from Figs. 9.4 and 9.6 (without the line numbers) then run the program. Remember, the robot does not see the boundary lines except through the mathematics described in this chapter. It may appear that the robot is avoiding the boundary as if it was an object but this is only because we made boundary avoidance the same as obstacle avoidance. Convince yourself of this by commenting out Line 77 in Fig. 9.4. This prevents the boundary plotting and you will see the robot avoiding an invisible wall.
9.4 Summary
In this chapter we have explored: Various methods for keeping the robot within or outside of an area. The advanced ground sensor capability of the robot. How to use the GPS to con ne the robot within an area. Mathematical concepts for calculations involving circles and lines. Now, try to do the exercises in the next section. If you have dif culty read the hints.
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