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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.

Most computers today have a built-in camera. Let’s look at how we can grab images directly from such a camera and put them in the MATLAB workspace.

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.

For a redundant robot the inverse kinematics can be easily solved using a numerical approach.

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

We learn how to describe the orientation of an object by a 3×3 rotation matrix which has some special properties.

We summarise the important points from this lecture.

We run into problems when we take all of the pixels in a box around an input pixel and that pixel is close to one of the edges of the image. Let’s look at some strategies to deal with edge pixels.

Building a highly accurate robot is not trivial yet we can perform fine positioning tasks like threading a needle using hand-eye coordination. For a robot we call this visual servoing.

The pinhole camera simplifies the geometry but in practice it results in very dark images. Cameras, as well as our eyes, use a lens to form a brighter image but there are consequences.