To fully describe an object on the plane we need to not only describe its position, but also which direction it is pointing. This combination is referred to as pose. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.
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The pose of the working part of a robot’s tool depends on additional transforms. Where is the end of the tool with respect to the end of the arm, and where is the base of the robot with respect to the world?
A more efficient trajectory has a trapezoidal velocity profile.
Let’s recap the basics of homogeneous coordinates to represent points on a plane.
We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.
We can also derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame.
This is an exercise in which you can build a 3D coordinate frame by printing, cutting, folding and stapling.
We run into problems when we take all of the pixels in a box around an input pixel and that pixel is close to one of the edges of the image. Let’s look at some strategies to deal with edge pixels.
We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.
Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.