Lagrangian Inspired Polynomial Estimator for black-box learning and control of underactuated systems

Aug 6, 2026

Upload by Maeve

The Lagrangian Inspired Polynomial (LIP) estimator is a black-box learning approach built on Gaussian Process Regression to enable inverse dynamics identification for Lagrangian systems. It uses a structured multi-output kernel embedding the Euler-Lagrange equation. This work extends LIP to underactuated robots: it demonstrates direct estimation of kinetic and potential energies and the inertial, Coriolis, and gravity components from overall torque measurements. The learned energy information is then used to design a two-stage energy-based controller for swing-up and stabilization, validated on a simulated Pendubot.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

AccessFree to download

Introduction

Learning for control in robotics

Black-box inverse dynamics learning for underactuated robots

Physics-informed learning and LIP estimator

Contributions and controller design

Lagrangian Inspired Polynomial Estimator for black-box learning and control of underactuated systems Giulio Giacomuzzo University of Padova, Padova, Italy Riccardo Cescon ´Ecole Polytechnique Fe´de´ rale de Lausanne, Lausanne, Switzerland Diego Romeres Mitsubishi Electric Research Lab, Cambridge, MA, USA Ruggero Carli University of Padova, Padova, Italy Alberto Dalla Libera University of Padova, Padova, Italy GIACOMUZZO @DEI. UNIPD . IT RICCARDO . CESCON @EPFL . CH ROMERES @MERL . COM CARLIRUG @DEI. UNIPD . IT DALLALIBER @DEI. UNIPD . IT Abstract 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 identification 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. Keywords: Learning for Control, Inverse Dynamics Identification, Gaussian Process Regression 1. Introduction In recent years, learning for control in complex robotics applications has gained increasing interest. Several machine learning methods have been presented, both for modeling and direct synthesis of the controller. In this context, under-actuated robots (UR) are an important class of systems. URare mechanical systems characterized by fewer control inputs than degrees of freedom (DOF) . Such systems are ubiquitous in robotics: examples are manipulators with passive joints, autonomous bicycles and motorcycles, bipedal robots, and most of aerospace and marine vehicles. To control such systems, for instance, several Reinforcement Learning algorithms have been explored. These algorithms aim at automatically learning a control law, see for example Lillicrap et al. (2015) for a model-free approach or Deisenroth and Rasmussen (2011); Amadio et al. (2022) for model-based solutions. Although effective, generally these methods ignore previous contributions on UR from control theory. As a result, they typically require a huge amount of interactions with the system and do not provide any performance guarantees. A viable alternative consists of combining model learning with classic model-based control methods. Within this approach, a model of the system dynamics is derived from experimental data using machine learning techniques without the need for manually deriving accurate models of the © 2024 G. Giacomuzzo, R. Cescon, D. Romeres, R. Carli & A. Dalla Libera. GIACOMUZZO CESCON ROMERES CARLI DALLA LIBERA dynamics, which is the main drawback of classic model-based methods. Then, the learned model is used inside a model-based controller, exploiting results from control theory. Typically, such control strategies rely on the inverse dynamics model, which relates torques to the robot trajectories. The problem of learning the inverse dynamics from data has been extensively explored in the literature Nguyen-Tuong and Peters (2010); Romeres et al. (2016); Camoriano et al.(2016); Dalla Libera and Carli (2020) . An interesting class of solutions is represented by black-box methods, which propose to learn the inverse dynamics map by means of universal approximators, without any knowledge about the underlying system kinematics and dynamics Gijsberts and Metta (2011); Polydoros et al. (2015); Schreiter et al. (2015); Rueckert et al. (2017) . However, learning inverse dynamics models for the control of UR is particularly challenging. I

FAQs

What is the LIP estimator and how does it differ from generic black-box models?

The LIP estimator is a black-box inverse-dynamics estimator based on Gaussian Process Regression. It differs by using a structured multi-output kernel that embeds the Euler-Lagrange equation, enabling physically meaningful components rather than purely unstructured mapping.

How does the method estimate system energies and dynamics terms for underactuated robots?

Despite being black-box, LIP can estimate kinetic and potential energies, as well as inertial, Coriolis, and gravity components. These quantities are derived directly from overall torque measurements.

How is the learned model used for control, and what tasks are demonstrated?

The work exploits the estimated energy properties to construct a two-stage energy-based controller for swing-up and stabilization of balancing robots. Experiments on a simulated Pendubot confirm feasibility of the approach.

Aug 6, 2026

Upload by Maeve