Search Results for: algebra

We repeat the process of the last section but this time consider it as an algebraic problem.

How is an image formed? The real world has three dimensions but an image has only two. We can use linear algebra and homogeneous coordinates to understand what’s going on. This more general approach allows us to model the positions of pixels in the sensor array and to derive relationships between points on the image […]

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)).

Let’s look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations. For RTB10.x please note that the mask value must be explicitly preceded by the ‘mask’ keyword. For example: >> q = p2.ikine(T, [-1 -1], ‘mask’, [1 1 0 0 0 0])

For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.

We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

We consider multiple objects each with their own 3D coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our previous 2D algebraic notation to 3D and look again at pose graphs.

We consider multiple objects each with its own coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our algebraic notation to ease the manipulation of relative poses. Try your hand at some online MATLAB problems. You’ll need […]