Elastic rod dynamics: Validation of a real-time implicit approach

The large dynamic deflections of continuum robots, soft robots, and slender elastic objects can be accurately modeled with classical rod theories in nonlinear elasticity. In this paper, we propose a real-time computational approach for solving the partial differential equations of a dynamic Kirchhoff rod. Our approach is based on implicit time discretization of the Kirchhoff equations and subsequent solution of the resulting continuous spatial boundary value problem at each time step. This modular approach can exhibit low numerical damping, handle arbitrarily large time steps, and provide an accurate, high-order representation of the rod shape in steady-state. We experimentally validated the method by capturing footage of a dynamic rod with a high speed camera and comparing this experimental data with simulations using the proposed approach. Soft-real-time performance is achieved, and the relationship between time step and real-time performance is explored in a plot.