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03psps-01 Question 4 Radius

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    In homework 3.4, you're asked to simulate circular robotic motion.
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    We gave you some equations to help you along in your simulations.
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    I want to give you those formulas again and explain where some of them came from.
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    The first equation I want to talk about is this one.
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    The radius of curvature is equal to the length of the vehicle over the tangent of alpha
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    where alpha is our steering angle. Let me write that up here.
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    So where does this equation come from.
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    To derive it, the key realization is that the front and rear tire do not travel along the same circle.
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    Here's my rear tire, and here's my front tire.
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    They are, of course, separated by a distance that we called "L."
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    Let's draw the circles that these tires travel along.
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    Well, this rear tire is actually going to travel along a smaller inner circle
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    while this tire is going to travel along a larger outer circle.
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    Since we defined our radius of curvature as the distance from the back tire to the center,
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    Let's label this r, and we can see that the line connecting these tires defines an axis,
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    and here we have our steering angle, alpha, from here.
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    Now we can do a little bit of geometry.
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    Let's make a right triangle.
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    Well, if this angle here is alpha, then this much be a 90 degree angle,
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    because a radius intersecting with a tangent line always forms a right angle.
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    That means that that this angle here must be equal to 90 degrees minus alpha,
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    which means this angle, since this is a right triangle must be alpha.
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    Well, we're almost there. The tangent of this angle is equal to the opposite side,
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    which is the length, over the adjacent side, which is the radius.
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    So tangent of alpha is equal to L over r.
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    We manipulate this equation a little bit, and we find that the radius of curvature
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    is equal to the length of the vehicle over the tangent of the steering angle.
タイトル:
03psps-01 Question 4 Radius
概説:

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Team:
Udacity
プロジェクト:
CS373 - Artificial Intelligence
Duration:
02:08
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English subtitles

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