Let’s recap the important points about spatial operators. Linear operators can be used to smooth images and determine gradients. Template matching can be used to find a face in a crowd. Non-linear operators such as rank filters can be used for noise removal, and mathematical morphology treats shapes according to their compatibility with a structuring […]
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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.
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.
We revisit the important points from this masterclass.
For real robots such as those with 6 joints that move in 3D space the inverse kinematics is quite complex, but for many of these robots the solutions have been helpfully derived by others and published. Let’s explore the inverse kinematics of the classical Puma 560 robot.
Much of what we know about robots comes from fiction. Let’s look at fictional robots and the underlying reality.
The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.
We learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.