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 […]
Search Results for: Jacobian matrix
We will learn about the relationship, in 2D, 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.
We consider a robot with three joints that moves its end-effector on a plane.
We learn the mathematical relationship between angular velocity of a body and the time derivative of the rotation matrix describing the orientation of that body.
We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.
For an image stored as a variable in the MATLAB workspace let’s look at how we access the values of individual pixels in an image using their row and column coordinates. Using the MATLAB colon operator we can extract an intensity profile, extract a submatrix which is a region of the image, flip the image […]
We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.
We use MATLAB and some Toolbox functions to create a robot controller that moves a camera so the image matches what we want it to look like. We call this an image-based visual servoing system.
The relationship between world coordinates, image coordinates and camera spatial velocity has some interesting ramifications. Some very different camera motions cause identical motion of points in the image, and some camera motions leads to no change in the image at all in some parts of the image. Let’s explore at these phenomena and how we […]
We revisit the important points from this masterclass.