Before revision:  it is our hope that they will contribute to an increased understanding of these ideas within the robotics community and inspire future research into applications of generalized nonlinear, Finsler, and even Riemannian geometries .
After revision:  it is our hope that they will contribute to an increased understanding generalized nonlinear, and even classical Riemannian, geometry within the robotics community and inspire future research into applications of generalized nonlinear, Finsler, and even Riemannian geometries .