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Paths and Trajectories

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.  

Singularity in 3D rotation angle sequences

A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems.  

Relative pose in 3D

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.  

Pose in 3D

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.  

Introduction to 3D Geometry

We learn how to describe the position and orientation of objects in the 3-dimensional space that we live in. This builds on our understanding of describing position and orientation in two dimensions.  

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