Unit Quaternions to Express Orientations in Robotics

Unit Quaternions to Express Orientations in Robotics

In the lesson about the Exponential Coordinate Representation of the orientation, we saw that the logarithm could be numerically sensitive to small rotation angles θ because of the division by sinθ. We also saw that all other three-parameter representations of SO(3), like Euler angles and roll-pitch-yaw angles, suffer from similar singularities in representation, and this means that the solution will not always exist for the inverse problem where we want to find a set of parameters for a given orientation. Therefore, an alternative representation of the orientation named Unit Quaternion is used that alleviates the singularity at the cost of…
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Other Explicit Representation for the Orientation in Robotics: Roll-Pitch-Yaw Angles

Other Explicit Representation for the Orientation in Robotics: Roll-Pitch-Yaw Angles

In the previous lesson, we learned about Euler Angles Representation which is one of the ways to explicitly represent an orientation. This lesson will continue with explicit ways to represent the orientation, and we will learn about Roll-Pitch-Yaw Angles. This lesson is part of the series of lessons on foundations necessary to express robot motions. For the full comprehension of the Fundamentals of Robot Motions and the necessary tools to represent the configurations, velocities, and forces causing the motion, please read the following lessons (note that more lessons will be added in the future): https://www.mecharithm.com/category/fundamentals-of-robotics/fundamentals-of-robot-motions/ Also, reading some lessons from the…
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