An Analytically Computable Model and Energy-Based Control for a Realistic Series-Elastic 1D Hopper on Rough Terrain

In this paper, we describe modeling and control techniques to accurately representing a real-world series-elastic actuated 1D hopping robot. There is an abundance of work regarding the implementation of highly simplified hopper models, with the hopes of extracting fundamental control ideas for running and hopping robots. Accurately controlling a nonlinear system such as the hopper depends on a good forward model, and the inability to analytically solve even an idealized 2D case often leads to a largely simplified analysis, such as the classic SLIP model. However, real-world systems unfortunately cannot be accurately described by such simple models, as real actuators have their own dynamics including additional inertia and non-linear frictional losses. Therefore, an important step towards demonstrating high controllability and robustness to real-world, uneven terrain is in providing accurate higherorder models of real-world hopper dynamics. Motivated by actual hardware, our work here addresses 1D modeling and verification of the real-world dynamics of a hopper designed for energy efficiency, with the eventual goal of developing robust and agile control for 2D and 3D hoppers utilizing accurate feedforward predictions of dynamics.