#### Angle-axis representation of rotation in 3D

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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.

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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.

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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 […]

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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 […]

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Vision is useful to us and to almost all forms of life on the planet, perhaps robots could do more if they could also see. Robots could mimic human stereo vision or use cameras with superhuman capability such as wide angle or panoramic views.

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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.

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Building a highly accurate robot is not trivial yet we can perform fine positioning tasks like threading a needle using hand-eye coordination. For a robot we call this visual servoing.

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The pinhole or lensed camera is very similar to our eye, but there are lots of other ways to build a camera.

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We learn how to use information from three magnetometers to determine the direction of the Earth’s north magnetic pole.

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We introduce serial-link robot manipulators, the sort of robot arms you might have seen working in factories doing tasks like welding, spray painting or material transfer. We will learn how we can compute the pose of the robot’s end-effector given knowledge of the robot’s joint angles and the dimensions of its links.

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The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.