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.
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We introduce the topic of robotics, the recent history, why we need robots and the future of robots.
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.
If your knowledge of dynamics is a bit rusty then let’s quickly revise the basics of second-order systems and the Laplace operator. Not rusty? Then go straight to the next section.
We have a quick revision of the skew-symmetric matrix. If you’re comfortable with this topic then go straight on to the next section.
A really important function when performing inverse kinematics is the inverse tangent or arctan function. We revise how this function works for angles in all quadrants of the circle and introduce a useful variant known as atan2.
Robots today are ubiquitous in manufacturing but they can do much, much more.