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

2026-03-24

AI Summary

This work addresses the challenge of accurate modeling and real-time control of continuum robots, which exhibit high-dimensional nonlinear dynamics strongly coupled with their actuation mechanisms. The authors propose a control-augmented spectral submanifold (caSSM) framework that, for the first time, explicitly incorporates control inputs into the spectral submanifold formulation. By leveraging only controlled decay trajectories, caSSM efficiently learns the nonlinear state-input coupling without requiring additional actuation calibration typically needed in conventional approaches. Integrated with model predictive control (MPC), the method achieves a 40% reduction in open-loop prediction error and a 52% decrease in closed-loop tracking error on a tendon-driven continuum robot, significantly outperforming both Koopman-based and standard SSM methods while enabling real-time deployment on hardware.

Technology Category

• Intelligent Robots: Manipulation
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• continuum robots
• nonlinear dynamics
• spectral submanifold
• actuation coupling
• model reduction

Innovation

• spectral submanifold
• continuum robot
• nonlinear dynamics
• model predictive control
• actuator-aware modeling