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.
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Let’s look at some recent research results that vividly show how information from many 2D images taken from many different locations can be combined to form a detailed 3D model of the world.
Many technologies have been developed to determine the 3D-structure of the world. RGBD sensors such as the Kinect use structured light, projecting a pattern of light onto the scene and observing how it is distorted. Time of flight sensors measure the time it takes for a pulse of light to travel from the camera to […]
We extend the idea of relative pose, introduced in the last lecture, to 3D. We learn another right-hand rule that indicates the direction of rotation about an axis, and we see how we can attach 3D coordinate frames to objects to determine their pose in 3D space.
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 […]
We recap the important points from this lecture.
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 combine what we’ve learnt about smoothly varying position and orientation to create smoothly varying pose, often called Cartesian interpolation.
We learn how to describe the 3D pose of an object by a 4×4 homogeneous transformation matrix which has a special structure.
The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles. Note that in the MATLAB example at 8:24 note that recent versions of the Robotics Toolbox (9.11, 10.x) give a different result: >> rpy2r(0.1,0.2,0.3)ans = 0.9363 -0.2751 0.2184 0.2896 0.9564 -0.0370 -0.1987 0.0978 […]