Problem 44837. Composing relative poses in 2D: problem 1

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 are two robots (robot 1 and robot 2) on the playing field, with attached body-fixed coordinate frame {B} and {C} respectively with their origins at the centre of the robot. The x-axis of each robot's frame points in the robot's forward direction.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The rigid-body displacement of robot 1 with respect to the world frame is estimated by GPS to be 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> . The displacement of robot 2 with respect to robot 1 is estimated by a novel radar sensor and 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>TBC</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>Where is robot 2 with respect to the field?</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

123 Solutions
42 Solvers

Last Solution submitted on Jun 20, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers42

Problem Tags

composition homogeneous transformation

Community Treasure Hunt

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

Start Hunting!

Problem 44837. Composing relative poses in 2D: problem 1

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers42

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Problem 44837. Composing relative poses in 2D: problem 1

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers42

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Players