TITLE: What are the applications of Differential Geometry in Robotics?
QUESTION [9 upvotes]: I am taking up a grad level course on Differential Geometry. Can any one please tell me the immediate applications of Differential Geometry in Robotics ?
Thanks

REPLY [2 votes]: Although the question is far from recent and I am not explicitly answering your question, let me give a link to a book which exemplifies the use of differential geometry in robotics perfectly, in case someone comes across this question and is in search of a good start:
"A Mathematical Introduction to Robotics" by Murray, Sastry & Li
For example the exponential map allows for a very intuitive and efficient description of rigid body motion. Furthermore, you have the entire field of geometric control, for which I would suggest having a look at:
"Is it worth learning differential geometric methods for
modelling and control of mechanical system" by Lewis