Cayley-Rodrigues Parameters to Express Orientations in Robotics

Cayley-Rodrigues Parameters to Express Orientations in Robotics

In this lesson, we will become familiarized with another representation for orientations in robotics that is called Cayley-Rodrigues Parameters. Cayley-Rodrigues parameters provide local coordinates for SO(3). They are local coordinates because the representation is not singularity-free, and not all orientations can be expressed by them. However, they have properties that make them intriguing. 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…
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Other Explicit Representation for the Orientation in Robotics: Euler Angles

Other Explicit Representation for the Orientation in Robotics: Euler Angles

In the lesson about the degrees of freedom of a robot, we learned that there are at least three independent parameters needed to express the orientation of a rigid body. In the previous lesson, we learned about the exponential coordinate representation for the orientation that is a three-parameter representation for a rotation matrix R and parameterizes the rotation matrix using a unit axis of rotation and the angle of rotation about this axis. There are also other explicit representations that are useful in different applications when dealing with orientations. In this lesson, we will talk about Euler Angles and will…
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Fundamentals of Robot Motions: Configurations (Introduction)

Fundamentals of Robot Motions: Configurations (Introduction)

This post is part one of the series of lessons on the fundamentals necessary to represent the robot's configuration, and it gives an introduction to what we mean when we are talking about representing a robot's configuration. In previous lessons, we learned that the robot's configuration answers the question of where the robot is, and we saw that there are two ways to represent the robot's configuration: Implicit representation, where the configuration is represented by embedding the curved space in higher-dimensional Euclidean space subject to constraints and explicit representation where configuration is represented with a minimum number of coordinates. You…
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