arXiv:2611.06625v1 Announce Type: new Abstract: Controlling the shape profile of soft trunk robots extends their reach into complex regions of the workspace and enhances their use in practical applications. Recent advances in soft robot design have enabled soft trunk robots to achieve greater flexibility in conforming to complex shapes. Specifically, trunk robots whose geometries are designed as helicoids have been shown to enable extreme shape-changing capabilities. Their compliance makes them highly nonlinear, which in turn makes shape control difficult. On similar tendon-driven trunk robots, model-based controllers based on the theory of adiabatic spectral submanifolds (aSSMs) have achieved high accuracy in closed-loop end-effector tracking. We extend this approach by learning an aSSM model of the full body of a trimmed-helicoid soft trunk robot from data and use this in a model predictive control (MPC) scheme to demonstrate a range of shape control tasks on hardware. On closed-loop dynamic shape regulation, our method outperforms the available linear baselines by a factor of 10. In human-in-the-loop interactive demos, our method completes section-by-section shaping and balances a tennis ball for over 25 seconds, while the linear baselines fall short. A model-free reinforcement learning policy trained for 12 hours on hardware fails on the same balancing task. These results establish aSSM-based MPC as a practical route to full-body shape control on real soft hardware.