Discovering dominant dynamics for nonlinear continuum robot control

Abstract Continuum robots, which emulate biological organisms’ dexterity and flexibility, hold transformative potential for terrestrial and extraterrestrial applications. While such capabilities present significant modeling and control challenges, these robots’ highly dissipative nature allows their behavior to be explained by low-dimensional, dominant dynamics. Despite extensive research to uncover these dynamics, existing methodologies often fail to produce models that accurately capture them, hindering precise control in diverse and safety-critical tasks. This work addresses this gap by discovering these dynamics and leveraging them in a control methodology that substantially outperforms existing methods. Our approach, grounded in Spectral Submanifold theory, enhances accuracy up to sixfold and improves tracking performance by up to 150 times across a diverse set of control tasks, achieving Pareto dominance in precision and computational efficiency. These advances enable the development of simple yet robust models suitable for real-time control, moving us closer to deploying highly adaptive, efficient, and safe continuum robots.