Modern Robotics, All Videos - Modern Robotics, Chapter 3.3.3: Exponential Coordinates of Rigid-Body Motion

This is a video supplement to the book "Modern Robotics: Mechanics, Planning, and Control," by Kevin Lynch and Frank Park, Cambridge University Press 2017. See http://modernrobotics.org for information on the book, free software, and other materials. Any rigid-body transformation can be achieved from any other by following some 6-vector twist for unit time. The six coordinates of this twist are called the exponential coordinates. This video shows how the rigid-body transformation can be calculated using a matrix exponential with the se(3) matrix representation of the exponential coordinates. The matrix exponential maps an element of se(3) (the matrix representation of a twist) to an element of SE(3) (the 4x4 transformation matrix representing a rigid-body configuration) and the matrix logarithm maps an element of SE(3) to the element of se(3) that achieves it when integrated for unit time. This video is a brief summary of material from the book, and it is not meant to stand alone. For more details, such as an explanation of the notation, please consult the book and the other videos. Playlist for Chapter 3: https://www.youtube.com/playlist?list=PLggLP4f-rq01NLHOh2vVPPJZ0rxkbVFNc Playlist for all book videos: https://www.youtube.com/playlist?list=PLggLP4f-rq02vX0OQQ5vrCxbJrzamYDfx YouTube channel with all playlists: https://www.youtube.com/user/kevinl2145 Wiki for the book, including software and other supplements: http://modernrobotics.org Modern Robotics is now a series of online courses on Coursera! https://www.coursera.org/specializations/modernrobotics