We can derive a linear relationship between the coordinates of points on an arbitrary plane in the scene and the coordinate of that point in the image. This is the planar homography and it has a number of everyday uses which might surprise you.
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We extend what we have learnt to a 3-link planar robot where we can also consider the rotational velocity of the end-effector.
For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.
We consider a robot with three joints that moves its end-effector on a plane.
We consider a robot, which has two rotary joints and an arm.
Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.
We revisit the simple 2-link planar robot and determine the inverse kinematic function using simple geometry and trigonometry.
As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.
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.