Physics-Driven Learning Framework for Tomographic Tactile Sensing

TL;DR

The paper tackles the ill-posed nonlinear inverse problem of EIT-based tomographic tactile sensing by introducing PhyDNN, which embeds a differentiable forward operator into a physics-informed loss to enforce physical plausibility. A CNN-based forward surrogate enables end-to-end differentiable training alongside a U‑Net conductivity reconstructor, yielding reconstructions with fewer artifacts and sharper boundaries. Extensive simulations and real-world experiments on a 16-electrode tactile sensor show PhyDNN outperforming NOSER, TV, and pure DNN approaches in shape, location, and pressure distribution accuracy, while maintaining real-time capability. This physics-driven approach demonstrates robust generalization and improved tactile perception for scalable, low-wiring tomographic sensing.

Abstract

Electrical impedance tomography (EIT) provides an attractive solution for large-area tactile sensing due to its minimal wiring and shape flexibility, but its nonlinear inverse problem often leads to severe artifacts and inaccurate contact reconstruction. This work presents PhyDNN, a physics-driven deep reconstruction framework that embeds the EIT forward model directly into the learning objective. By jointly minimizing the discrepancy between predicted and ground-truth conductivity maps and enforcing consistency with the forward PDE, PhyDNN reduces the black-box nature of deep networks and improves both physical plausibility and generalization. To enable efficient backpropagation, we design a differentiable forward-operator network that accurately approximates the nonlinear EIT response, allowing fast physics-guided training. Extensive simulations and real tactile experiments on a 16-electrode soft sensor show that PhyDNN consistently outperforms NOSER, TV, and standard DNNs in reconstructing contact shape, location, and pressure distribution. PhyDNN yields fewer artifacts, sharper boundaries, and higher metric scores, demonstrating its effectiveness for high-quality tomographic tactile sensing.

Figures (7)

• Figure 1: Fabrication process and sensing system of the proposed EIT-based tactile sensor. (a) Step-by-step fabrication of the biomimetic multilayer tactile structure, including silicone insulation preparation, mold casting, bubble removal, curing, and integration with the water-infused polyurethane foam layer. (b) Final assembled tactile sensor and the customized signal acquisition circuit based on a Teensy 4.1 controller with optimized PCB routing and impedance-matching design.
• Figure 2: Overall architecture of the proposed physics-driven neural network (PhyDNN) .
• Figure 3: Structure of the CNN-based forward-operator network.
• Figure 4: Evaluation of the learned forward operator. (a) Randomly selected conductivity distribution from the test set. (b) Comparison of boundary voltages predicted by the learned CNN-based operator and by the linear Jacobian operator $J$. The learned operator exhibits higher fidelity to the true simulated voltages, enabling more accurate physics-based supervision in PhyDNN.
• Figure 5: Training and evaluation of the PhyDNN framework. (a) Training and validation data loss $\mathcal{L}_{\mathrm{data}}$ for DNN and PhyDNN. (b) Training and validation physical loss $\mathcal{L}_{\mathrm{phy}}$. (c) Relative difference between the physical losses of DNN and PhyDNN, highlighting the effect of the physics constraint after the warm-up stage. (d) Grid-search results of the weighted reconstruction score for 52 values of $\beta$, showing that $\beta = 0.0029$ yields the best overall performance.