Data-Driven Spectral Submanifold Reduction for Nonlinear Optimal Control of High-Dimensional Robots

TL;DR

This paper introduces a novel data-driven spectral submanifold reduction method for modeling and controlling high-dimensional nonlinear robots, emphasizing structure preservation and improved generalization over existing approaches.

Contribution

It presents a new approach for extracting low-dimensional models from data using spectral submanifold reduction that better captures system dynamics and enhances control performance.

Findings

SSMR outperforms Koopman-based methods in trajectory tracking.

Models preserve dominant dynamics and generalize to unseen trajectories.

Demonstrated on high-dimensional robotic systems.

Abstract

Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address these challenges, they broadly lack generalizability to different control tasks and rarely preserve the structure of the dynamics. In this work, we propose a new, data-driven approach for extracting low-dimensional models from data using Spectral Submanifold Reduction (SSMR). In contrast to other data-driven methods which fit dynamical models to training trajectories, we identify the dynamics on generic, low-dimensional attractors embedded in the full phase space of the robotic system. This allows us to obtain computationally-tractable models for control which preserve the system's dominant dynamics and better track trajectories radically different from the training data. We demonstrate the superior performance and generalizability of SSMR in dynamic trajectory tracking tasks vis-a-vis the state of the art, including Koopman operator-based approaches.