Variable Stiffness Soft Pneumatic Sensing Chambers

This repository contains MATLAB code for simulating and analyzing the static performance of Variable Stiffness Soft Pneumatic Sensing Chambers (SPSCs). The complete SPSC design framework is detailed in the following paper:

Duretto, S., Colucci, G., Tagliavini, L., Botta, A. and Quaglia, G. (2026). Variable Stiffness Soft Pneumatic Sensing Chambers for Tactile Sensing and Haptic Devices.

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Code Overview

The code covers:

• SPSC Geometry Definition: defining four notable SPSC types (A, B, C, D) starting from a generalized super-ellipse curve.
• Variable Stiffness Mechanism: modeling the effect of opening or closing a directional valve to connect the SPSC volume $V_b$ to a rigid reservoir $V_r$. This changes the volume of air that undergoes deformation, resulting in a low (open valve) or high (closed valve) stiffness configuration.
• Deformation Modeling: implementing a numerical model (converting a boundary-value problem into an initial value problem for ODE integration) to predict the SPSC deformation during inflation and compression by a rigid plate.
• Exporting SPSCs for Additive Manufacturing: exporting SPSC geometries as STL files for 3D printing.

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Key Geometric Parameters

The geometry of a generic SPSC is described by a set of seven parameters:

Parameter	Description	Role
$w, h, l$	Encumbrance (semi-width $w$, height $h$, length $l$).	Define the physical dimensions of the SPSC.
$t_0$	Thickness of the SPSC membrane.	Influenced by manufacturing technology (e.g., minimum of $0.8\text{ mm}$ in Additive Manufacturing). Affects the SPSC structural stiffness.
$n_1$	Form factor controlling top flatness.	Increasing $n_1$ makes the top surface flatter.
$n_2$	Form factor controlling lateral verticality.	Increasing $n_2$ makes the lateral surface more vertical.
$c_y$	Form factor controlling bulging.	Translates the super-ellipse along $\hat{j}$, controlling SPSC bulging.

Four notable SPSC families (A, B, C, D) are identified based on specific combinations of the form factors ${n_1, n_2, c_y}$.

SPSC relevant parameters and family types

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MATLAB Code Structure

The project is structured around the VSSPSC MATLAB class, which contains all modeling and visualization methods.

Directory Structure

.
├── Main.m                  # Main script to run simulation and visualization
├── Simulation_Data/        # Results of the simulation
│   ├── Geometry_01/
│   │   └── ...
│   └── Geometry_02/
│       └── ...
├── Simulation_Parameters/  # Files defining geometry, material, and pneumatic settings used in simulation
│   ├── Geometry_01/
│   │   └── ...
│   └── Geometry_02/
│       └── ...
├── STL/                    # Sample geometries for 3D-printing
│   ├── Geometry_01/
│   │   └── ...
│   └── Geometry_02/
│       └── ...
└── VSSPSC_Class/           # VSSPSC class definition and utility functions.
    ├── @VSSPSC/            # Class directory containing all VSSPSC methods
    │   └── ... 
    └── utils/              # General utility functions
        └── ... 

Sample geometries

Simulation parameters, simulation results and STL files are provided for the following sample geometries:

	Geometry 1				Geometry 2
Type	A	B	C	D	A	B	C	D
w (mm)	10				11
h (mm)	10				13
l (mm)	10				3
t0 (mm)	1				1
n1	5	2	2	2	3	2	2	2
n2	2	2	1	2.5	4	2.2	1	2.2
cy	0	0	0	0.67	0	0	0	0.6

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Getting Started: Running the Simulation

Follow these steps to set up and run a simulation:

1. Select Parameters: All simulation parameters (geometry, material, pneumatic settings) are contained within dedicated .m files located in the Simulation_Parameters folder. Templates for various geometries (e.g., TypeA_SimParams.m) are provided in this folder.

2. Run the Main Script: Open and modify the Main.m file. You must execute the desired parameter file using the run() command to load all simulation parameters into the MATLAB workspace before the VSSPSC object is initialized.

   Example of parameter selection inside Main.m:

   % Select and run the desired simulation parameters script:
   run("Simulation_Parameters\Geometry_01\TypeA_SimParams.m")
   % SPSC initialization and simulation steps follow below...

3. Execute: Run Main.m. The script will execute the numerical model, generate plots for the cross-sections, display the deformation animation, and export the 3D STL file.

Tested in MATLAB R2023b.

Code Output Example

Type A SPSC - nominal configuration, inflation process, and compression by a rigid plate

Type_A_Deformation.mp4

Type A SPSC - volume change ($\Delta V$), contact area ($A$), internal pressure change ($\Delta p$) and contact force ($F-F_{el}$) as a function of compression depth $y_s$ (high stiffness configuration)

Type A SPSC - mesh for STL export

How to Cite

@article{2026:Duretto_VSSPSC,
  title={Variable Stiffness Soft Pneumatic Sensing Chambers for Tactile Sensing and Haptic Devices},
  author={Duretto, Simone and Colucci, Giovanni and Tagliavini, Luigi and Botta, Andrea and Quaglia, Giuseppe},
  journal={...},
  year={...}
}