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Imagine a scene with bright objects against a dark background. Thresholding is a very common monadic operation which transforms the image into one where the pixels have two possible values: true or false which correspond to foreground or background. It can be performed with a single vectorized MATLAB operation.

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.

The end-effector is not able to move equally fast in all directions, and that in fact depends on the pose of the robot. We will introduce the velocity ellipse to illustrate this.

We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.

We summarise the important points from this lecture.

We revisit the fundamentals of geometry that you would have learned at school: Euclidean geometry, Cartesian or analytic geometry, coordinate frames, points and vectors.