Exponential Coordinates in Robotics - Fundamentals of Robotics

Explore the concept of exponential coordinates in robotics through this comprehensive 29-minute video lesson. Delve into the explicit representation of orientation space, covering topics such as exponential coordinate representation of orientation, interpretations of rotation matrices, and matrix logarithm of rotations. Gain insights from physical demonstrations, including tangent velocity in circular motion and a two-degree-of-freedom robot wrist. Learn about cross products between vectors and draw analogies between exponential coordinates of orientation and linear differential equations. Enhance your understanding of robotics fundamentals with this in-depth exploration of exponential coordinates and their applications in robotic systems.

​​ 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