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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.  

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