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98 lines
2.8 KiB
Markdown
98 lines
2.8 KiB
Markdown
# Fast-RRT* Documentation
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- [Fast-RRT* Documentation](#Fast-RRT-documentation)
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- [`FindReachest()`](#findreachest)
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- [Psuedo Code](#psuedo-code)
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- [Written Explanation](#written-explanation)
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- [Visual](#visual)
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- [`CreateNode()`](#createnode)
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- [Psuedo Code](#psuedo-code-1)
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- [Written Explanation](#written-explanation-1)
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- [Visual](#visual-1)
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- [`Rewire()`](#rewire)
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- [Written Explanation](#written-explanation-2)
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- [Visual](#visual-2)
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- [`SampleFree()`](#samplefree)
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- [`Nearest()`](#nearest)
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- [`Near()`](#near)
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## `FindReachest()`
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### Psuedo Code
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<img src="findReachest.PNG" width="300">
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### Written Explanation
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Find the furthest possible node of `xNearest`'s parents from `xRand` that does not have an obstacle when a straight line is drawn between them.
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The selected node `xReachest` must be chosen from `xNearest`'s ancestors. The starting node may not be selected as `xReachest`.
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### Visual
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<img src="findReachestSketch.PNG" width="500">
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## `CreateNode()`
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### Psuedo Code
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<img src="createNode.PNG" width="300" >
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### Written Explanation
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Creates a node (`xCreate`) based on `xRand`, `xReachest`, and parent (`xReachest`) locations such that the path is drawn more near to the obstacle in few steps. Remember that these two nodes are guaranteed to have an obstacle between them.
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The node is created between `xRand` and `xReachest` where the path between `xRand` and `xCreate` becomes free of all obstacles.
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### Visual
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<figure>
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<img src="Capture1.PNG" width="380" >
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<img src="Capture2.PNG" width="380" >
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<figcaption> 1) xAllow and xForbid are set </figcaption>
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</figure>
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<figure>
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<img src="Capture3.PNG" width="380" >
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<figcaption> 2) xMid is established between xAllow and xForbid when the path is collision free to xRand</figcaption>
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</figure>
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<figure>
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<img src="Capture4.PNG" width="380" >
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<img src="Capture5.PNG" width="380" >
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<figcaption> 3) xMid is the new xAllow and xRand is the new xForbid</figcaption>
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</figure>
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<figure>
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<img src="Capture6.PNG" width="380" >
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<figcaption> 4) a new xMid is established between xAllow and xForbid </figcaption>
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</figure>
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<figure>
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<img src="Capture7.PNG" width="380" >
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<figcaption> 4) a new xMid is established between xAllow and xForbid when collision free to parent(xReachest) </figcaption>
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</figure>
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## `Rewire()`
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### Written Explanation
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Changes connection relationships of tree vertices.
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For any point in `xNear`, if replacing its parent node to be `xRand` reduces the cost of the path from `xStart` to `xNear`, then replace it.
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### Visual
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<img src="rewireSketch.PNG" width="150" >
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## `SampleFree()`
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Returns a sample `xRand` that is selected randomly from xFree.
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## `Nearest()`
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Nearest vector to `xRand` in terms of Euclidean distance.
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## `Near()`
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Return the set of vectors contained in specific radius around `xRand`.
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