Problem 44895. Determine roll pitch yaw angles from a 3D rotation matrix

Created by Peter Corke

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","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\"?><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>Consider an aerospace application where the world reference coordinate frame {W} and a body-fixed coordinate frame {B}. The origins of {W} and {B} are coincident. The orientation of {B} is described in terms of roll-pitch-yaw angles defined as a sequence of rotations where yaw is about the Z, pitch is about the Y axis and roll is about the X axis.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Given an SO(3) rotation matrix describing the orientation of {B} with respect to {W} determine the roll-pitch-yaw angles.</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>"}]}

Solve

Solution Stats

18 Solutions
5 Solvers

Last Solution submitted on Dec 11, 2022

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

William on 29 Apr 2019

There is a flaw in the test suite. It tests the values in rpy2r rather than the results rpy from the solver's function. Also, the tolerance needs to be widened a bit.

Rafael S.T. Vieira on 14 Sep 2020

Actually that's not a flaw, William. Since it is not always possible to determine the exact three original angles. In the second test case for instance, there are infinite solutions due to a singularity. Therefore, he tests the rotation matrix since it will be equal for all possible solutions.

Solution Comments

Solution 2445591

1 Comment

1 Comment

Rafael S.T. Vieira on 14 Sep 2020

It's interesting that a precision error allows you to recover the original angles: atan2(cos(pi/2)*sin(pi/3),cos(pi/2)*cos(pi/3)) amazingly returns pi/3, which obviously should not be true since atan2(0,0) = 0 (?). The issue seems to be that cos(pi/2) is not zero (due to an approximation error), but just a really small value close to zero.

Problem Recent Solvers5

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44895. Determine roll pitch yaw angles from a 3D rotation matrix

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers5

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Problem 44895. Determine roll pitch yaw angles from a 3D rotation matrix

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers5

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Players

WeChat