Exponential Coordinates in Robotics - Fundamentals of Robotics

This lesson explains exponential-coordinate representations of orientation, including interpretations of rotation matrices and matrix logarithms. It connects these concepts to linear differential equations, cross products, circular-motion tangent velocity, and a two-degree-of-freedom robot wrist.

Syllabus

Introduction
Exponential Coordinate Representation of Orientation
Interpretations for the Exponential Coordinate Representation for a Rotation Matrix
Demo for the first Interpretation for the Exponential Coordinate Representation for a Rotation Matrix
The second Interpretation for the Exponential Coordinate Representation for a Rotation Matrix
The third Interpretation for the Exponential Coordinate Representation for a Rotation Matrix
Some Notes from Linear Differential Equation Theory
The Analogy between the Exponential Coordinates of Orientation and the Linear Differential Equations
Physical Demonstration of the Tangent Velocity in Circular Motion
Definition of Cross Product between Two Vectors
Matrix Logarithm of Rotations
Example for Matrix Logarithm of Rotations with demo
Demonstration: The Orientation of a Two Degrees of Freedom Robot Wrist