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parking maneuver using two circle method
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Parking Maneuver Using TWO CIRCLE METHOD

 

The algorithm decided upon is based on the concept that a parallel parking

Procedure is comprised of two arcs of equal length by identical circles, C1 and C2. C1 is R distance in only the positive y-direction from the goal parking position. C2 is the circle relating to the initial position whose center is located a distance R in the negative y direction. In both the initial and desired positions, the line connecting the center of the robot to its respective circle center is perpendicular to the x-axis. The initial position begins at the center of C2 minus a distance R in the y direction. These circles are equal in size, with radius R, the turning radius of our model car.

The center of C1 is assumed from here on to be the origin. The robots coordinates are then based off of this origin, plus some padding. Using angle A, the angle that is part of the triangle connecting C1, C2 and the Y-axis, trigonometry is used to obtain the distance the center of C2, (x1, y1) is from the origin. Calculating C2 (x1, y1) uses the following equations:

Sin (A) = y1/2R

A=sin-1 (y1/2R)

Cos (A) = x1/2R

x1=2Rcos (A)

For each possible configuration of the two circles, the turning point is going to create a symmetric divide forcing the two arc lengths along each circle to have the same length. The arc length is determined using angle A through the following equation: Arc Len = R[(π/2)-A]. It always performs movements in the backward direction because that was all that was required within the scope of this project.

 

 

Calculation Behind Parking

Arc Len = R[(π/2)-A]

A=sin-1 (y1/2R)

x1=2Rcos (A)

Y1=?

R=PQ + Spot width/Car width + In-between distance + Half Car width

Now,

Y1=R + Half Car width + PQ

=R + Half Car width + R (Car width + Half Car width + In-between distance)

= 2R Car width distance between car and obstacle.