When it comes to describing a blob we can do more than just area, centroid position and bounding box. By looking at second order moments we can compute an ellipse that has the same moments of inertia as the blob, and we can use its aspect ratio and orientation to describe the shape and orientation […]
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The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.
As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.
We learn how to use information from three magnetometers to determine the direction of the Earth’s north magnetic pole.
We recap the important points from this lecture.
We revisit the fundamentals of 3D geometry that you would have learned at school: coordinate frames, points and vectors.
Now we introduce a variant of the Jacobian matrix that can relate our angular velocity vector back to our rates of change of the roll, pitch and yaw angles.
A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.
We consider multiple objects each with their own 3D coordinate frame. Now we can describe the relationships between the frames and find a vector describing a point with respect to any of these frames. We extend our previous 2D algebraic notation to 3D and look again at pose graphs.
We learn how to describe the 2D pose of an object by a 3×3 homogeneous transformation matrix which has a special structure. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.