Nonlinear Model Predictive Control of a Robotic Soft Esophagus
Authors: Dipankar Bhattacharya, Ryman Hashem, Leo K. Cheng, Weiliang Xu
Abstract
Strictures caused by esophageal cancer can narrow down the esophageal lumen, leading to dysphagia. Palliation of dysphagia has driven the development of a Robotic Soft Esophagus (RoSE), which provides a novel in vitro platform for esophageal stent testing and food viscosity studies. In RoSE, peristaltic wave generation and control were done in an open-loop manner since the conduit lacked visibility and embedded sensing capability. Hence, in this work, RoSE version 2.0 (RoSEv2.0) is designed with embedded Time Of Flight (TOF) and pressure sensors to measure conduit displacement and air pressure, respectively, for modeling and control. Model Predictive Control (MPC) of RoSEv2.0 is implemented to govern the peristalsis and air pressure profile autonomously. The implemented MPC used Sparse Identification Nonlinear Dynamics with Control (SINDYC) models to estimate the future states of ROSEv2.0. The dynamic models are discovered from the TOF and pressure sensor data. Peristalsis waves of speed 20 mm/s, wavelength 75 mm, and amplitudes 5, 7.5, and 10 mm were successfully generated by the MPC. Additionally, RoSEv2.0 with the MPC was employed to perform stent migration testing with various food bolus consistencies. The major contribution claimed in this paper is the application of SINDYC-based MPC to solve the closed-loop control problem of RoSE for achieving desired peristaltic waves.
Soft robotic systems are well suited for developing devices for biomedical applications. A bio-mimicking robotic soft esophagus (RoSE) is developed as an in vitro testing device of endoprosthetic stents for dysphagia management. Endoprosthetic stent placement is an immediate and cost-effective therapy for dysphagia caused by malignant esophageal strictures from esophageal cancer. However, later stage complications, like stent migration, could weaken swallow efficacy in the esophagus. The stent radial force (RF) on the esophageal wall is pivotal in avoiding stent migration. Due to limited randomized controlled trials in patients, stent design and stenting guidelines remain incomplete. To address this knowledge deficit, we investigate RoSE by implanting two stents (A and B) of different radial stiffness characteristics, to measure stent RF and its effect on migration. Endoscopic manometry under peristalsis is also performed to study the impact of stenting and stent dysfunction on intra-bolus pressure signatures (IBPSs) and swallowing efficacy. Each implanted stent undergoes experiments with varied peristalsis velocity, wavelength, and bolus concentrations. The results show that stiffer stent B has a higher RF, whereas stent A maintains a lower RF profile due to lesser stiffness. High RF is necessary to minimize migration under prolonged peristaltic contractions in RoSE. For manometry, stent A slightly increases IBPS, but stiffer stent B significantly decreases IBPS, especially for higher-concentration boluses. If a stiffer stent buckles, it can reduce swallow efficacy and cause recurrent dysphagia. RoSE is therefore an innovative soft robotic platform for testing endoprosthetic stents and addressing clinical challenges in stent evaluation.
Dipankar Bhattacharya, Sherine Jesna V. A., Leo K. Cheng +1
Precise control of soft manipulators remains challenging due to the difficulty of developing accurate yet computationally tractable models for model-based estimation and control. Reduced Cosserat-rod models provide a physics-based and control-oriented description of soft-robot dynamics, offering an explicit alternative to purely data-driven input-output representations. In this paper, we propose a moving-horizon estimation (MHE) and nonlinear model predictive control (NMPC) framework for cable-driven soft manipulators based on reduced Cosserat dynamics. A smooth cable-length-driven modeling formulation is developed by approximating the complementarity relationship between cable tension and cable slackness, enabling cable-length control without direct tension sensing. Based on this formulation, an MHE method is introduced to estimate the reduced state and reconstruct the manipulator configuration from end-effector pose measurements and cable-length information. An NMPC controller is then formulated to achieve task-space control under cable-length and cable-rate constraints. The proposed framework is validated through numerical simulations and experiments. Simulation results demonstrate the effectiveness of the estimator and controller for pose and strain-related regulation on a multi-cable soft manipulator. Experimental results on a four-cable prototype further show that the proposed MHE-NMPC scheme can be implemented in real time and enables accurate end-effector position tracking through cable-length control.
In this paper, we design feedback control laws for soft robots modelled using the Cosserat rod, which is spatially discretised using the Piecewise Constant Strain (PCS) approach. The PCS approach transforms the nonlinear PDEs describing the Cosserat rod to a system of nonlinear ODEs. This simplification results in a model describing soft robots which is similar to the serial rigid-link manipulators. We design feedback control laws for the quasi-static PCS model by using external wrenches as control inputs. The control laws are designed based on state-feedback linearisation in strain and task spaces. An extensive set of numerical results demonstrates the performance of the control laws for end-effector trajectory tracking and shape control of soft robots.