Dynamic Shape Control of Soft Trunk Robots

Hehui Zheng, Marc Stampanoni, Roshan S. Kaundinya, Ronan Hinchet, George Haller, Robert K. Katzschmann

November 2026

TL;DR The authors learn a 6-dimensional nonlinear reduced model of a tendon-driven soft trunk from 5 h of hardware data and use it in MPC to control the shape of the whole body. On hardware it holds target shapes to 5.1 mm mean error, about 11x lower than the best linear model, and balances a tennis ball on the tip for over 25 s.

What they do

Soft trunk robots meant for confined spaces need control over the shape of their whole body, not just the tip, but their compliance makes the shape dynamics strongly nonlinear. The authors learn an adiabatic spectral submanifold (aSSM) model of the full trunk from hardware data. Earlier aSSM models were used only for end-effector tracking. Here, MPC on the model controls the poses of three points along a 500 mm helicoid trunk.

How it works

Hardware. Five 3D-printed TPU helicoid segments, nine tendons driving three independent sections, and motion-capture markers at the end of every segment. Nesting each tendon’s PTFE sleeve in an extension spring cuts the uncommanded bending of lower sections from up to 58° to 6°.
Model. About 5 h of responses to step inputs (20,000 static commands from a Sobol sequence) give a nonlinear map from motor commands to rest shape. Around that map they fit a 6-dimensional polynomial model of the dynamics.
Control. A sampling-based MPC scores three rounds of 1000 candidate inputs against the model and runs at 20 Hz. The baselines run the same MPC on three linear models (ERA, DMDc, LOpInf) fit to the same data.

Results

Open loop over 750 steps, the mean tip error is 27.5 mm, 2.9x lower than ERA, the best linear model.
Shape regulation: the aSSM reaches all 8 target shapes in 11.8 s on average with 5.1 mm mean error; no linear baseline reaches any target, and the best of them ends at 56.1 mm.
Tracking a 30 s moving shape: 5.6 mm mean position error and 2.6° orientation error, against 30.8 mm and 15.1° for ERA.
Following a hand-held wand, it balances a tennis ball on the tip for over 25 s. ERA and DMDc lose the ball after 2 s and 0.4 s. A PPO policy trained for 12 h directly on the robot drops it after 1.8 s.

Limitations

Tendon speed limits how fast the shape can change. Shape feedback comes from an eight-camera motion-capture system with markers on every segment. The authors frame the RL comparison as a sample-efficiency result under a 12 h hardware budget, not a head-to-head comparison of methods.

Figures

From Figure 1: Closed-loop full-body shape control of a five-segment trimmed-helicoid soft trunk with MPC on a learne... — From Figure 1: Closed-loop full-body shape control of a five-segment trimmed-helicoid soft trunk with MPC on a learned aSSM model: (a) tracking a target shape, (b) reshaping by following a hand-held wand, and (c) following the wand while holding the tip level to balance a tennis ball.

From Figure 2: The hardware platform. (a) Five trimmed-helicoid segments in series, with marker body 0 at the base an... — From Figure 2: The hardware platform. (a) Five trimmed-helicoid segments in series, with marker body 0 at the base and bodies 1-5 at the end of each segment; colored strips mark the three tendon groups. (b) With plain PTFE sleeves, which deform plastically, actuating one section bends the segments below it by up to 58 degrees. (c) Nesting each tube in an extension spring cuts this to 6 degrees.

From Figure 4: Closed-loop shape control toward one of the 8 targets with (a) aSSM, (b) ERA, (c) DMDc and (d) LOpInf.... — From Figure 4: Closed-loop shape control toward one of the 8 targets with (a) aSSM, (b) ERA, (c) DMDc and (d) LOpInf. The trunk is white and the target a yellow silhouette. The aSSM reaches the target within 4.2 s; none of the three linear baselines converges within 30 s.

From Figure 6: Human-in-the-loop tasks driven by a hand-held wand. (a) Section-by-section shaping: the active section... — From Figure 6: Human-in-the-loop tasks driven by a hand-held wand. (a) Section-by-section shaping: the active section (green) keeps a 10 cm standoff from the wand while the others hold their shape. (b) Tennis ball balancing: the tip follows the wand while keeping its face level. Under the aSSM the ball stays on for over 25 s; ERA and DMDc lose it after 2 s and 0.4 s, and LOpInf keeps it 19.5 s only by leaving the trunk almost undeflected.

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.

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Matt Strong