We give an overview of the recent approach to the integration of rough paths that reduces the problem to an inhomogeneous analogue of the classical Young integration . As an application, we extend an argument of Schwartz  to rough differential equations, and prove the existence, uniqueness and continuity of the solution, which is applicable when the driving path takes values in nilpotent Lie group or Butcher group.
"The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations." J. Math. Soc. Japan 67 (4) 1681 - 1703, October, 2015. https://doi.org/10.2969/jmsj/06741681