Search Results for: matrix

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 can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

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.

Let’s recap some of the most important topics we’ve covered about treating an image as a matrix within MATLAB which we can display or index into.

We introduce serial-link robot manipulators, the sort of robot arms you might have seen working in factories doing tasks like welding, spray painting or material transfer. We will learn how we can compute the pose of the robot’s end-effector given knowledge of the robot’s joint angles and the dimensions of its links.

For a real 6-link robot our previous approach to computing the Jacobian becomes unwieldy so we will instead compute a numerical approximation to the forward kinematic function.

We consider the simplest possible robot, which has one rotary joint and an arm.

The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object.   In the MATLAB example starting at 3:48 I use the Quaternion class.  For Toolbox version 10 (2017) please use UnitQuaternion instead.

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

If it’s been a while since you last dealt with eigenvalues and eigenvectors here’s a quick recap of the basics.