Learning Actuator-Aware Spectral Submanifolds for Precise Control of Continuum Robots

TL;DR

This paper introduces actuator-aware spectral submanifolds (caSSMs) that incorporate control inputs for better modeling and control of continuum robots, achieving significant reductions in prediction error and tracking error in real-time applications.

Contribution

The paper develops a novel control-augmented spectral submanifold (caSSM) approach that explicitly models nonlinear state-input couplings in continuum robots, simplifying training and improving control accuracy.

Findings

Reduced open-loop prediction error by 40%

Decreased tracking error by 52% in closed-loop control

Demonstrated real-time control on a tendon-driven robot

Abstract

Continuum robots exhibit high-dimensional, nonlinear dynamics which are often coupled with their actuation mechanism. Spectral submanifold (SSM) reduction has emerged as a leading method for reducing high-dimensional nonlinear dynamical systems to low-dimensional invariant manifolds. Our proposed control-augmented SSMs (caSSMs) extend this methodology by explicitly incorporating control inputs into the state representation, enabling these models to capture nonlinear state-input couplings. Training these models relies solely on controlled decay trajectories of the actuator-augmented state, thereby removing the additional actuation-calibration step commonly needed by prior SSM-for-control methods. We learn a compact caSSM model for a tendon-driven trunk robot, enabling real-time control and reducing open-loop prediction error by 40% compared to existing methods. In closed-loop experiments with model predictive control (MPC), caSSM reduces tracking error by 52%, demonstrating improved performance against Koopman and SSM based MPC and practical deployability on hardware continuum robots.