Closed-forms of planar Kirchhoff elastic rods: application to inverse geometry

In this paper, we address the problem of inverse geometry for Kirchhoff elastic rods. Based on the explicit formulation of extremal curves in terms of elliptic functions, we derive closed forms for rod shape and sensitivity in the planar case and we show how this can be used efficiently in robotics applications. More specifically, a numerical optimization approach is presented to solve the inverse geometry problem in the general 3-D case and applied to the planar case using closed forms previously introduced.