Problem 42397. Megan's walk

Created by Alfonso Nieto-Castanon

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Can you make</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/fileexchange/51139-megan-simulator--xkcd-\"><w:r><w:t>Megan</w:t></w:r></w:hyperlink><w:r><w:t> (a stick-figure model of the popular XKCD character) walk straight?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"http://www.alfnie.com/software/ms_walk.jpg\"><w:r><w:t>http://www.alfnie.com/software/ms_walk.jpg</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Megan's pose is defined by a 20-element \"pose\" vector. In this problem you are tasked with defining two pose vectors x1 and x2 such that the cyclic trajectory defined as:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ x(t) = sin(2*pi*t)*x1 + cos(2*pi*t)*x2]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>results in Megan walking as straight and as far as possible.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The vectors x1 and x2 must contain real numbers with absolute values not higher than 2. Your code will be scored as a function of how far (and straight) Megan reaches when the cyclic trajectory above is repeated between t=0 and t=4 (four full cycles). Megan needs to walk forward a minimum of 100 units (approximately 1m) to pass this problem (see testsuite for details)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>I will update the links below with some of the best solutions:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:hyperlink w:docLocation=\"http://www.alfnie.com/software/ms_walk.mp4\"><w:r><w:t>Here</w:t></w:r></w:hyperlink><w:r><w:t> a video of this problem's reference solution walking example (distance 4.59m)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:hyperlink w:docLocation=\"http://www.alfnie.com/software/ms_walk_689805.mp4\"><w:r><w:t>Here</w:t></w:r></w:hyperlink><w:r><w:t> a video of LY Cao leapfrogging strategy (solution</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/689805\"><w:r><w:t>689805</w:t></w:r></w:hyperlink><w:r><w:t>; distance 14.43m)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:hyperlink w:docLocation=\"http://www.alfnie.com/software/ms_walk_689912.mp4\"><w:r><w:t>Here</w:t></w:r></w:hyperlink><w:r><w:t> a video of James \"walking with an attitude\" solution (solution</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/689912\"><w:r><w:t>689912</w:t></w:r></w:hyperlink><w:r><w:t>; distance 4.95m)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:hyperlink w:docLocation=\"http://www.alfnie.com/software/ms_walk_690182.mp4\"><w:r><w:t>Here</w:t></w:r></w:hyperlink><w:r><w:t> a video of LY Cao \"bitten by a radioactive spider\" solution (solution</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/690182\"><w:r><w:t>690182</w:t></w:r></w:hyperlink><w:r><w:t>; distance 39.95m!)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Good luck and have fun!</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Can you make <a href = "http://www.mathworks.com/matlabcentral/fileexchange/51139-megan-simulator--xkcd-">Megan</a> (a stick-figure model of the popular XKCD character) walk straight?<a href = "http://www.alfnie.com/software/ms_walk.jpg">http://www.alfnie.com/software/ms_walk.jpg</a>Megan's pose is defined by a 20-element "pose" vector. In this problem you are tasked with defining two pose vectors x1 and x2 such that the cyclic trajectory defined as:<pre> x(t) = sin(2*pi*t)*x1 + cos(2*pi*t)*x2</pre>results in Megan walking as straight and as far as possible.The vectors x1 and x2 must contain real numbers with absolute values not higher than 2. Your code will be scored as a function of how far (and straight) Megan reaches when the cyclic trajectory above is repeated between t=0 and t=4 (four full cycles). Megan needs to walk forward a minimum of 100 units (approximately 1m) to pass this problem (see testsuite for details)I will update the links below with some of the best solutions:<ul><li><a href = "http://www.alfnie.com/software/ms_walk.mp4">Here</a> a video of this problem's reference solution walking example (distance 4.59m)</li><li><a href = "http://www.alfnie.com/software/ms_walk_689805.mp4">Here</a> a video of LY Cao leapfrogging strategy (solution <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/689805">689805</a>; distance 14.43m)</li><li><a href = "http://www.alfnie.com/software/ms_walk_689912.mp4">Here</a> a video of James "walking with an attitude" solution (solution <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/689912">689912</a>; distance 4.95m)</li><li><a href = "http://www.alfnie.com/software/ms_walk_690182.mp4">Here</a> a video of LY Cao "bitten by a radioactive spider" solution (solution <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/690182">690182</a>; distance 39.95m!)</li></ul>Good luck and have fun!

Can you make <http://www.mathworks.com/matlabcentral/fileexchange/51139-megan-simulator--xkcd- Megan> (a stick-figure model of the popular XKCD character) walk straight?

http://www.alfnie.com/software/ms_walk.jpg

Megan's pose is defined by a 20-element "pose" vector. In this problem you are tasked with defining two pose vectors x1 and x2 such that the cyclic trajectory defined as:

x(t) = sin(2*pi*t)*x1 + cos(2*pi*t)*x2

results in Megan walking as straight and as far as possible.

The vectors x1 and x2 must contain real numbers with absolute values not higher than 2. Your code will be scored as a function of how far (and straight) Megan reaches when the cyclic trajectory above is repeated between t=0 and t=4 (four full cycles). Megan needs to walk forward a minimum of 100 units (approximately 1m) to pass this problem (see testsuite for details)

I will update the links below with some of the best solutions:

* <http://www.alfnie.com/software/ms_walk.mp4 Here> a video of this problem's reference solution walking example (distance 4.59m)
* <http://www.alfnie.com/software/ms_walk_689805.mp4 Here> a video of LY Cao leapfrogging strategy (solution <http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/689805 689805>; distance 14.43m)
* <http://www.alfnie.com/software/ms_walk_689912.mp4 Here> a video of James "walking with an attitude" solution (solution <http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/689912 689912>; distance 4.95m)
* <http://www.alfnie.com/software/ms_walk_690182.mp4 Here> a video of LY Cao "bitten by a radioactive spider" solution (solution <http://www.mathworks.com/matlabcentral/cody/problems/42397-megan-s-walk/solutions/690182 690182>; distance 39.95m!)

Good luck and have fun!

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Solution Stats

79 Solutions
7 Solvers

Last Solution submitted on Nov 28, 2022

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James on 22 Jun 2015

For anyone who is looking for some pointers on this problem: http://xkcd.com/138/

Solution Comments

Solution 699828

2 Comments

2 Comments

James on 13 Jul 2015

Alfonso, I've submitted the same values of x1 and x2 four times, and I've received four different distances. The solution numbers are 697837 and 699826-699828. I ran into this issue on my own computer, but thought it was just due to a much earlier version of MATLAB mucking things up. I'm not nearly smart enough to figure out why this is happening. Any thoughts?

Jan Orwat on 13 Jul 2015

I've seen same behaviour. Different results occur due to wind. Set parameter 'defs_windnoisy' to 0 when evaluating drawMegan() and distance becomes "stable" (4609 in case of this solution). Most unstable solution I've found was getting distance between 330 up to around 2700.

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Problem 42397. Megan's walk

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Problem 42397. Megan's walk

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