Search Results for: Jacobian matrix

We consider a robot, which has two rotary joints and an arm.

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

Time varying coordinate frames are required to describe how the end-effector of a robot should move to grab an object, or to describe objects that are moving in the world. We make an important distinction between a path and a trajectory.

Let’s learn how to import a color image into MATLAB and see how the data is organized as a matrix with three dimensions.

Once a digital image exists as a matrix in the MATLAB workspace we can manipulate it to extract information that a robot could use. We will discuss some fundamental algorithms that operate on single images.

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.

We describe the velocity coupling terms of the robot as a matrix which represents how the torque on one joint depends on the velocity of other joints.

We describe inertia of the robot as a matrix which represents how inertia of a joint depends on the position of all the joints, and how the torque on one joint depends on the acceleration of other joints.

We can factorise the joint torque expression into an elegant matrix equation with terms that describe the effects of inertia, Coriolis and centripetal and gravity effects.

We have a quick revision of the skew-symmetric matrix. If you’re comfortable with this topic then go straight on to the next section.