Inverse geometry for Kirchhoff elastic rods
O. Roussel, M. Renaud and M. Taïx
https://doi.org/10.19124/ima.2015.001.07
Abstract
In this paper, we address the problem of inverse geometry for a Kirchhoff elastic rod at equilibrium manipulated at its ends by robotic grippers. 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.