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We learn a method for succinctly describing the structure of a serial-link manipulator in terms of its Denavit-Hartenberg parameters, a widely used notation in robotics.

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

Let’s recall the key techniques we’ve covered including monadic and dyadic image processing operations and efficient ways to write these in MATLAB using vectorization.

Images contain many pixels and the normal way to process them is with nested for loops that index each pixel in turn. This is slow and somewhat cumbersome to write. MATLAB has a facility called vectorization that allows us to perform complex matrix operations without any loops.

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.

We will learn about the relationship, in 3D, between the velocity of the joints and the velocity of the end-effector — the velocity kinematics. This relationship is described by a Jacobian matrix which also provides information about how easily the end-effector can move in different Cartesian directions. To do this in 3D we need to […]

We recap the important points from this lecture.

The linear algebra approach we’ve discussed is very well suited to MATLAB implementation. Let’s look at some toolbox functions that can simulate what cameras do. If you are using a more recent version of MVTB, ie. MVTB 4.x then please change>> cam.project(PW ‘Tcam’, transl(0.1, 0, 0)) to >> cam.project(PW ‘pose’, transl(0.1, 0, 0)).

Digital images are everywhere: in your phone, on your hard drive, on the internet. We can access still pictures, movies and streams from live cameras all around the world. Let’s talk about digital images and how we can get them into the MATLAB environment where we can work on them.

When a camera moves in the world, points in the image move in a very specific way. The image plane or pixel velocity is a function of the camera’s motion and the position of the points in the world. This is known as optical flow. Let’s explore the link between camera and image motion.