Learning Actuator-Aware Spectral Submanifolds for Precise Control of Continuum Robots
Paul Leonard Wolff, Hugo Buurmeijer, Luis Pabon, John Irvin Alora, Mark Leone, Roshan Kaundinya, Amirhossein Kazemipour, Robert Kevin Katzschmann, Marco Pavone
AI summary
Problem
Continuum robots exhibit complex, nonlinear dynamics that are tightly coupled with their actuator mechanisms, making real-time control computationally prohibitive. Traditional model reduction techniques often ignore these actuator dynamics or require cumbersome calibration steps, leading to inaccurate predictive models.
Approach
The authors extend spectral submanifold reduction by embedding actuator states directly into the system's state space to capture nonlinear system-actuator couplings. The resulting caSSM models are trained solely from controlled decay trajectories, eliminating the need for additional actuator calibration.
Key results
- Automated pipeline for learning caSSM models from decay trajectories
- 40% reduction in open-loop prediction error compared to baselines
- 52% reduction in closed-loop MPC tracking error
- Successful real-time hardware deployment on a tendon-driven trunk robot
Why it matters
Provides a practical, data-driven framework for accurate real-time control of soft and continuum robots, bridging the gap between theoretical model reduction and hardware deployment.
Abstract
Continuum robots exhibit high-dimensional, non- linear 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 com- monly 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 per- formance against Koopman and SSM based MPC and practical deployability on hardware continuum robots.