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.
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Now we introduce a variant of the Jacobian matrix that can relate our angular velocity vector back to our rates of change of the roll, pitch and yaw angles.
We extend what we have learnt to a 3-link planar robot where we can also consider the rotational velocity of the end-effector.
Humans are trichromats which means that our eyes have three types of cone cells which are sensitive to different parts of the spectrum: red, green and blue light. They perform a non-unique mapping from an arbitrary spectrum of light into three signals which are known as a tristimulus which we perceive as a particular color. […]
In order to determine the size and distance of objects in the scene our brain uses a number of highly evolved tricks. Let’s look at some of these.
We consider a robot with three joints that moves its end-effector on a plane.
Color is a very important concept for people. We have lots of words to describe colors and we even associate them with emotions.
Time varying coordinate frames are required to describe how the end-effector of a robot should move to grab an object, or to describe objects that are moving in the world. We make an important distinction between a path and a trajectory.
An image is a two dimensional projection of a three dimensional world. The big problem with this projection is that big distant objects appear the same size as small close objects. For people, and robots, it’s important to distinguish these different situations. Let’s look at how humans and robots can determine the scale of objects […]
Since an image in MATLAB is just a matrix of numbers, we could write code to fill in the elements of the matrix. Let’s look at some simple examples such as squares, circles and lines and more complex images formed by pasting these shapes together.