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FIGURE 4.2
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Second style of remote control.
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REMOTE CONTROL ALGORITHMS
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4.3 Complex Remote Control
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In this style of remote control the robot carries out a series of actions to accomplish a task speci ed by the user. For this simulation the mouse will be used as a laser designator. If you are familiar with laser targeting devices used by the military you will recognize this style of remote control. The device uses a laser to designate a target for a missile. The missile locks onto the target and moves there. We will emulate this by using the mouse to designate the target we want the robot to go to. The robot will lock onto the mouse position and go there. The robot will also be able to draw on the screen while moving to help you see the actions that took place (this can also make the robot act as a sketcher). The robot will use its GPS and compass to calculate the difference between its current position and heading and the target s position and direction. 4.3.1 THE MATHEMATICS Figure 4.3 shows a representation of the calculations that are necessary for this algorithm. The robot s location is represented by the coordinates Rx, Ry. Rx is the robot s horizontal position on the screen in relation to the top left-hand corner which is position 0, 0. Ry is the vertical position. The target is located at Tx, Ty. The difference between the x-coordinates of the robot and target is dX. The difference in their y-coordinates is dY. As you can see from Fig. 4.3, the two values can be used to calculate the distance R between the robot and the target. This is an application of the pythagorean theorem.
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Target (Tx, Ty) North dA dY R TA CH
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dX Robot (Rx, Ry) CH = Robot's compass heading dA = Angle to tum TA = Target's angle from x-axis dX = Tx Rx dY = Ty Ry TA = Tan 1 (dY/dX)
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dX 2 + dY 2
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FIGURE 4.3
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Laser targeting with the robot.
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BUILDING BLOCKS
RobotBASIC has a function that can do this calculation for us, PolarR (dX, dY) which returns the value for R. The function PolarA (dX, dY) returns the angle in relation to the horizontal axis that is formed by the line between the robot s center and the target s center, as shown in Fig. 4.3 (angle TA). This angle can be used to calculate a turn direction and amount so the robot can face the target. As you can see in Fig. 4.3 this is the angle dA. However, there are two complications. The rst problem is that angle TA is measured from the east direction (this is common in computer languages). That is, east is 0 , not 90 , as our robot (and humans) normally think of it. This angle, which is the value returned by PolarA() is not a 360 angle like in a compass; it is 180. The positive angles are measured counter-clockwise from east and negative ones are clockwise from east. So north is 90 , south is 90 and west is 180 . We will have to convert the angle reported by PolarA() to a compass heading so that the robot can be turned to that heading. Adding 90 to the angle reported by PolarA() will solve this problem, but before doing this another issue has to be resolved. The angle value returned by PolarA() is given in radians, not degrees (again, this is common practice in computer languages). It is simple to convert between degrees and radians in this manner: 1 /180 radians
So, when you want to convert an angle in degrees to radians you do
Angle_In_Radians = Angle_In_Degrees * pi()/180
To convert from radians to degrees you do:
Angle_In_Degrees = Angle_In_Radians * 180/pi()
Refer to Sec. C.8 for the function Pi(), it essentially returns the value . This means we can calculate TA in degrees using:
TA = PolarA (dX,dY)*180/pi()
Remember, we also need to convert TA relative to north instead of east. Since east is 0 in relationship to the x-axis, but it is 90 in relationship to north, we must add 90 to convert TA to a compass heading. So, the equation becomes:
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