Lagrangian inspired polynomial estimator for black-box learning and control of underactuated systems

The Lagrangian Inspired Polynomial (LIP) estimator (Giacomuzzo et al., 2023) is a black-box estimator based on Gaussian Process Regression, recently presented for the inverse dynamics identi- fication of Lagrangian systems. It relies on a novel multi-output kernel that embeds the structure of the Euler-Lagrange equation. In this work, we extend its analysis to the class of underactuated robots. First, we show that, despite being a black-box model, the LIP allows estimating kinetic and potential energies, as well as the inertial, Coriolis, and gravity components directly from the overall torque measures. Then we exploit these properties to derive a two-stage energy-based controller for the swing-up and stabilization of balancing robots. Experimental results on a simulated Pendubot confirm the feasibility of the proposed approach.