Problem 44831. Composing relative poses in 2D: problem 2

Created by Peter Corke

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>We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>There is a playing field with a reference frame denoted by {F}. The rigid-body displacement from {O} to {F} is given by the homogenous transformation</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>TF</w:t></w:r><w:r><w:t> .</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction. The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>TB</w:t></w:r><w:r><w:t> .</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis. The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>TS</w:t></w:r><w:r><w:t> .</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>There is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>What is the range and bearing of the landmark as observed by the laser scanner?</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>"}]}

We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.There is a playing field with a reference frame denoted by {F}. The rigid-body displacement from {O} to {F} is given by the homogenous transformation <tt>TF</tt> .There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction. The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation <tt>TB</tt> .The robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis. The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation <tt>TS</tt> .There is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.What is the range and bearing of the landmark as observed by the laser scanner?

We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.

There is a playing field with a reference frame denoted by {F}.  The rigid-body displacement from {O} to {F} is given by the homogenous transformation |TF| .

There is a robot with an attached body-fixed coordinate frame {B} whose origin is in the centre of the robot, and whose x-axis points in the robot's forward direction.  The rigid-body displacement displacement of {B} relative to {F} is given by the homogenous transformation |TB| .

The robot carries a laser scanner which reports the range and bearing of landmarks with respect to its coordinate frame {S} with zero bearing angle corresponding to its x-axis.  The scanner is displaced from the centre of the robot and the displacement of frame {S} relative to {B} is given by the homogenous transformation |TS| .

There is a landmark with position described by a coordinate vector P with respect to the world coordinate frame {O}.

What is the range and bearing of the landmark as observed by the laser scanner?

Solve

Solution Stats

184 Solutions
37 Solvers

Last Solution submitted on Jun 20, 2022

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Sebastian Castro on 3 Apr 2019

Should specify whether the bearing is supposed to be in radians or degrees (FYI, it's radians).

Also, in the 3rd paragraph the word "displacement" is in there twice. Minor typo :)

Problem Recent Solvers37

Problem Tags

composition homogenous transformation

Community Treasure Hunt

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

Start Hunting!

Problem 44831. Composing relative poses in 2D: problem 2

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers37

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Problem 44831. Composing relative poses in 2D: problem 2

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers37

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Players