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

Created by Peter Corke

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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?

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161 Solutions
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Last Solution submitted on Dec 28, 2021

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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 :)

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composition homogenous transformation

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