RoSE-SINDYC-MPC — Nonlinear MPC of a Robotic Soft Esophagus

Background

Before a stent can be trusted, the swallow must be controlled.

Esophageal strictures from cancer narrow the lumen and cause dysphagia. Stents can restore patency — but migration under peristalsis remains a hard clinical risk, and ethical limits make in vivo design comparisons scarce.

Complete RoSEv2.0 bench: soft esophagus, TOF sensors, pneumatic valves, Raspberry Pi, and webcam — **Complete RoSEv2.0 setup** The soft conduit, embedded TOF sensing, valve bank with VPS, and Raspberry Pi host that runs DTSINDYC models and MPC.

Overview. This is the full electro-pneumatic bench used for closed-loop peristalsis: RoSEv2.0 on the left, valve manifold and host electronics on the right.

RoSE was built as an in vitro swallowing platform so stent designs can be tested under bolus transport without patients. Earlier RoSE operated open-loop: the conduit had no durable embedded sensing, so prescribed wave shapes could not be verified while a stent sat inside.

Soft continuum robots like RoSE are hard to model from first principles — infinite degrees of freedom, compliant silicone, and nonlinear pneumatics. This work closes that loop: RoSEv2.0 embeds TOF and pressure sensing, discovers sparse discrete-time dynamics with DTSINDYC, and runs nonlinear MPC so peristalsis tracks the desired wave for stent-migration experiments.

The system

RoSEv2.0 — a sensorized soft swallowing conduit

Use the tabs to explore each part of the setup. The figure matches the paper’s CAD overview.

Isometric CAD model of RoSEv2.0 with layers, chambers, PDMS casing, and TOF array

Architecture

12 identical layers

Layers L₁–L₁₂ stack along the conduit axis. At least three layers are needed to match physiological peristalsis wavelengths used for swallow experiments.

Focus layers for control: L₅, L₆, L₇

Fig. — Isometric view of RoSEv2.0. A transparent PDMS outer covering carries an array of TOF sensors that measure conduit displacement from outside the lumen.

See fabrication

Fabrication

How RoSEv2.0 is built

Lab photos of the Ecoflex conduit casting, PDMS outer layer, TOF integration, pneumatics, and full bench setup. Step through the process — each stage updates the photo and explanation.

Casting

Pour Ecoflex into the mold

Uncured Ecoflex 00-30 is poured into the custom ABS mold — housing, central rod, and chamber placeholders — then left to vulcanize at room temperature.

Method

DTSINDYC models inside nonlinear MPC

Discover sparse discrete-time dynamics from TOF or valve-pressure data, then optimize a receding-horizon control law that tracks a prescribed peristaltic wave. Tap the chips under each figure for a guided reading.

DTSINDYC model training on TOF states with staircase pressure inputs — **Discrete-time SINDYC (DTSINDYC)** Sparse regression finds the active polynomial terms that map (x_k, u_k) → x_k+1.

Staircase inputs. Time-shifted pressure staircases actuate L₅–L₇ while TOF records conduit displacement — the training corpus for the predictive model.

Block diagram of DTSINDYC-MPC with cost function minimization and prediction — **MPC block diagram** Receding horizon prediction with the discovered DTSINDYC plant model.

Cost minimization. At each step the CFM block penalizes tracking error, control effort, and control move size, then applies only the first optimized valve command.

MPC implementation diagram connecting host, model, valves, and sensors — **Implementation loop** Host computer, DTSINDYC prediction, valves, and sensor feedback.

Host. A Raspberry Pi host runs the online optimizer and streams DAC commands to electro-pneumatic valves while reading TOF or VPS feedback.

01

Sensorized conduit

TOF through PDMS measures lumen displacement; VPS tracks chamber pressure for an alternate plant model.

02

Sparse dynamics

DTSINDYC avoids derivative noise and black-box overfit — few polynomial terms explain the soft-robot response.

03

Constrained MPC

Prediction horizon N_p=4 balances tracking RMSE against real-time loop period for physiological wave speeds.

Workflow

Five steps from fabrication to stent testing

Scrub the pipeline. Each step updates the stage figure and caption.

Step 1 — Fabricate the soft conduit and embed sensing.

Results

Prescribed waves, verified occlusion, stent experiments

MPC tracks 5 / 7.5 / 10 mm amplitude peristalsis at 20 mm·s⁻¹ and 75 mm wavelength, stays robust under higher-frequency references, and enables closed-loop stent migration testing.

0 RMSE at high-frequency waves

0 Chosen prediction horizon N_p

0 Wave amplitudes demonstrated

Tracking · Model M₁

Peristalsis amplitudes under MPC

Reference waves of 5, 7.5, and 10 mm were tracked on L₅–L₇ with average loop time ≈0.15 s. Inflation (bolus-tail shaping) tracks more tightly than deflation.

Wave amplitudes tracked speed 20 mm/s · λ = 75 mm

Toggle tabs to compare amplitude setpoints vs horizon selection rationale.

Stent migration vs bolus 50 peristalsis cycles

Migration rises mildly with bolus consistency; closed-loop occlusion confirms the prescribed wave was achieved.

MPC TOF tracking results for three peristalsis amplitudes — **MPC tracking (TOF, model M₁)** Tap a cue to read reference, response, and control signals.

References. Orange solid lines are the prescribed sinusoidal displacement trajectories for L₅, L₆, and L₇.

High-frequency MPC tracking experiment — **High-frequency robustness** Amplitude 10 mm outside the training frequency content.

RMSE. Experimental tracking error remains about 0.8 mm under the higher-frequency reference — evidence the controller generalizes beyond the identification data.

MPC pressure tracking with valve pressure sensors — **Pressure MPC (model M₂)** Same recipe, VPS feedback instead of TOF.

Sensor-agnostic. Replacing TOF with VPS and rediscovering DTSINDYC yields successful chamber-pressure tracking — the method is not robot- or sensor-specific.

Stent migration results across bolus consistencies — **Stent migration application** Closed-loop peristalsis during bolus swallow experiments.

Bolus grades. Syrup-, custard-, and pudding-like boluses (≈0.45–3.0 Pa·s) are transported under 50 controlled peristalsis cycles.

MPC performance versus prediction horizon Np — **Horizon selection** RMSE improves up to N_p=4 while execution time grows; N_p=N_c=4 is chosen so physiological speeds (20–60 mm·s⁻¹) remain sampleable.

Previous work

The RoSE line that led to this work

This closed-loop control paper builds on the soft esophagus platform and sparse dynamics discovery developed in earlier studies.

Soft Robotics · 2020

RoSE: A Robotic Soft Esophagus for Endoprosthetic Stent Testing

D. Bhattacharya, S. J. V. Ali, L. K. Cheng, and W. Xu

Introduces the bio-mimicking RoSE platform for in vitro endoprosthetic stent testing under peristalsis — measuring radial force, migration, and intrabolus pressure signatures when open-loop swallow protocols drive the soft conduit.

Open DOI Publisher page

IEEE Trans. Ind. Electron. · 2020

Sparse Machine Learning Discovery of Dynamic Differential Equation of an Esophageal Swallowing Robot

D. Bhattacharya, L. K. Cheng, and W. Xu

Discovers governing dynamics of the swallowing robot from motion-capture data using POD and SINDy — reducing high-dimensional marker trajectories to sparse differential equations that motivate the later DTSINDYC models used inside MPC.

Open DOI IEEE Xplore

Publication

IEEE Transactions on Industrial Electronics

D. Bhattacharya, R. Hashem, L. K. Cheng, and W. Xu, “Nonlinear Model Predictive Control of a Robotic Soft Esophagus,” IEEE Trans. Ind. Electron., vol. 69, no. 10, pp. 10363–10373, Oct. 2022. doi:10.1109/TIE.2021.3121755

Open DOI

Supported financially by the Riddet Institute, Palmerston North, New Zealand (a national Centre of Research Excellence).

Open materials

Code & reproducible data pipeline

Implementation code for the RoSE-SINDYC-MPC framework is public. Datasets can be regenerated from the repository scripts.

GitHub repository

bhattner143/SINDYc_MPC_RoSE_symmetric_peristaltic — modeling, MPC, and experiment tooling used in this work.

Open repository Back to citation