Before revision: Robotics research has found numerous important applications of Riemannian geometry , despite the background mathematical material being strikingly challenging. This material is often remains inaccessible to roboticists, and despite many natural generalizations within the mathematical literature, there remain very few applications of modern highly-relevant geometric generalizations such as spray or Finsler geometry .
After revision: Robotics research has found numerous important applications of Riemannian geometry . Despite that, the concept remain challenging to many roboticists because the background material is complex and strikingly foreign. Beyond Riemannian geometry, there are many natural generalizations within the mathematical literature, there remain very few applications of modern highly-relevant geometric generalizations such as spray or Finsler geometry .