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We consider a robot, which has two rotary joints and an arm.

Much of what we know about robots comes from fiction. Let’s look at fictional robots and the underlying reality.

We learn how to create smoothly varying orientation in 3D by interpolating Euler angles and Quaternions. In the MATLAB example starting at 5:44 I use the Quaternion class.  For Toolbox version 10 (2017) please use UnitQuaternion instead.

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.

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. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]