We discuss the structure of a right-handed 3D coordinate frame and the spatial relationship between its axes which is encoded in the right-hand rule.
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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 summarise the important points from this lecture.
We consider the simplest possible robot, which has one rotary joint and an arm.
We learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.
We store movies in files, typically in an MPEG format. Let’s look at what’s inside one of those movie files, and how we can grab a frame from a movie as an image and put it into the MATLAB workspace.
The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.
We consider multiple objects each with their own 3D coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our previous 2D algebraic notation to 3D and look again at pose graphs.