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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.

Diadic operations involve two images of the same size and result in another image. For example adding, subtracting or masking images. As a realistic application we look at green screening to superimpose an object into an arbitrary image.

We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

An alternative for smooth motion between poses is Cartesian interpolated motion which leads to straight line motion in 3D space.

The orientation of a body in 3D can also be described by two vectors, often called the approach and orientation vectors.

A number of strategies exist to reduce the effect of these coupling torques between the joints, from introducing a gearbox between the motor and the joint, to advanced feedforward strategies.

As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.

Robots today are ubiquitous in manufacturing but they can do much, much more.

Frequently we want a trajectory that moves smoothly through a series of points without stopping.