⚡ electrical engineering

TriSeq: soft triaxial force sensor with sequential excitation and temporal reconstruction

This paper presents TriSeq, a monolithic laser-induced graphene soft triaxial tactile sensor that utilizes sequential four-electrode excitation and a hysteresis-aware latent-dynamics reconstruction framework to accurately decode contact forces and loading histories without mechanical decoupling, achieving high precision in both force magnitude and direction across diverse loading conditions.

Original authors: Zhinan Zhang, Shunsuke Yoshimoto, Tetsuro Miyazaki, Kenji Kawashima

Published 2026-10-05

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CC BY 4.0

Original authors: Zhinan Zhang, Shunsuke Yoshimoto, Tetsuro Miyazaki, Kenji Kawashima

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Robots have long been masters of strength and precision, yet they often struggle with the subtle art of touch. While a human hand can instantly feel the difference between a ripe strawberry and a hard stone, or sense the slightest slip of a tool, most robotic grippers rely on rigid sensors that can only measure a single push or pull. To make robots truly dexterous, capable of handling delicate objects or navigating complex environments, engineers need them to feel forces from every direction at once: a push down, a slide sideways, and a twist, all simultaneously. The challenge lies in building a sensor that is soft enough to conform to the shape of what it touches, yet smart enough to untangle these mixed signals into a clear picture of the force being applied.

This is the problem researchers at the University of Tokyo and the University of Osaka have tackled with a new device called TriSeq. Instead of trying to build a complex machine with many moving parts to separate these forces, they created a single, solid piece of soft material that acts like a skin. This skin is made of a flexible rubber base topped with a thin layer of laser-induced graphene, a conductive material that changes its electrical properties when stretched or squeezed. The key innovation is how they read the signals from this skin. Rather than trying to measure the force directly, they send a small electrical current through the material in a specific sequence, turning on and off different contact points around the edge of the sensor. As the sensor is pressed, the internal structure of the rubber deforms, stretching the graphene and altering how electricity flows through it. By measuring the voltage at the edges during this sequence, the system captures a unique electrical fingerprint of the touch.

However, soft materials have a tricky habit: they are "hysteretic." This means the sensor does not react the same way every time it is touched. If you press down slowly and then let go, the electrical signal on the way up is different from the signal on the way down, even if the force is identical. This happens because the rubber takes time to relax and the internal structure of the material remembers the path it just took. A simple computer program that looks only at the current electrical signal would get confused, unable to tell if the sensor is being pressed or released. To solve this, the researchers developed a new way of thinking about the data. Instead of treating each measurement as a snapshot, they trained a computer model to look at the entire sequence of electrical changes over time. This model acts like a memory, keeping track of the history of the touch to understand exactly where the sensor is in its cycle of pressing and releasing.

To test this idea, the team built a sophisticated robotic platform that could press the sensor with extreme precision. They used a robot arm to push a small, rounded tip against the sensor from hundreds of different angles, ranging from straight down to sharp, glancing blows. They applied forces from a gentle 0.3 Newtons up to 3 Newtons, moving at three different speeds to see how the sensor reacted to fast and slow touches. Crucially, they compared the sensor's electrical readings against a high-precision reference sensor that measured the actual force being applied, creating a massive dataset of real-world touches. This allowed them to teach their computer model to translate the complex, history-dependent electrical signals back into accurate force measurements.

The results were striking. When the researchers tested the sensor on directions it had never seen before, it could predict the strength of the force with an average error of just 0.0528 Newtons. More importantly, it could determine the direction of the force with an average error of only 5.22 degrees. To put this in perspective, if the sensor were trying to point a finger at a target, it would be off by less than the width of a thumb at arm's length. When they compared their new method to older approaches that ignored the history of the touch, the improvement was dramatic. The old methods made errors that were more than three times larger, often failing to distinguish between a pressing motion and a releasing motion. The new system, by remembering the sequence of events, resolved this confusion and provided a stable, reliable reading regardless of how the force was applied.

The researchers also tested three separate sensors to ensure the design worked consistently across different units. In every case, their new method outperformed existing techniques, including other advanced computer models designed to handle time-based data. The secret to this success was not just the soft material, but the specific way the computer model processed the data. By using a "latent dynamics accumulator," a component that acts as a memory bank for the sensor's state, the system could distinguish between identical electrical signals that occurred at different points in a touch cycle. This allowed the sensor to remain accurate even when the material was behaving unpredictably.

This work demonstrates that soft, single-piece sensors can be just as effective as complex, multi-part systems if paired with the right way of interpreting the data. The device is simple to build, requiring no intricate internal wiring or mechanical decoupling mechanisms, yet it delivers a full three-dimensional force reading. This makes it an ideal candidate for integration into the fingertips of future robots, where it could help machines grasp fragile objects without crushing them or detect the onset of a slip before an object falls. By solving the problem of how to read soft, memory-filled materials, the researchers have taken a significant step toward giving robots the kind of intuitive touch that humans take for granted.

Technical Summary: TriSeq – Soft Triaxial Force Sensor with Sequential Excitation and Temporal Reconstruction

Problem Statement
Soft triaxial tactile sensors are essential for robotic end-effectors to perceive normal and shear forces, enabling grasp stability and slip detection. However, soft materials exhibit nonlinear, hysteretic, and path-dependent transduction behaviors, meaning the sensor-to-force relationship cannot be described by a static mapping. Existing approaches face a trade-off: multi-unit arrays rely on mechanical priors and idealized stress distributions, while single-module designs often require complex internal structures or dense wiring that compromise robustness and fabrication simplicity. Furthermore, existing evaluations often lack unified protocols for characterizing hysteresis, directional continuity, and cross-axis coupling, making reported accuracies difficult to compare. The core challenge is to reconstruct triaxial contact forces stably under intrinsic hysteresis and nonlinearity while maintaining a structurally simple, monolithic design.

Methodology
The paper presents TriSeq, a monolithic soft triaxial tactile sensor based on a laser-induced graphene (LIG) sensing layer and a sequential four-electrode excitation scheme.

Sensor Design: The sensor consists of a compliant Ecoflex 00-30 elastomer bump and substrate, topped with a circular LIG sensing layer (6 mm diameter) and four peripheral electrodes. It utilizes sequential excitation of the four electrodes to generate six independent configurations, yielding 12 boundary voltage measurements per time step. This field-based sensing approach encodes triaxial contact forces into electrical boundary responses without structural force-decoupling mechanisms.
Reconstruction Framework: To address the path-dependent nature of soft materials, the authors propose a hysteresis-aware latent-dynamics reconstruction framework. Unlike static models that map instantaneous observations to force, this framework processes the observation sequence $\{s_t\}$ ${s_{t}}$ .
- Residual-Modulated Observation Encoding: A learnable modulation vector adapts observation weights to account for element-wise sensitivity variations caused by contact direction and structural non-uniformities.
- Latent Dynamics Accumulator: A learnable dynamics model updates a latent state $z_t$ at each time step based on the previous state and the modulated observation. This state accumulates history, allowing the system to distinguish between identical instantaneous electrical responses that result from different loading trajectories (e.g., loading vs. unloading branches).
- Output: The final triaxial force estimate is derived from the terminal latent state and the final observation.
Experimental Platform: A robot-automated characterization platform was constructed using a UR3e collaborative robot and a six-axis force/torque (F/T) reference sensor. This platform enables force-guided loading across a densely sampled directional space (217 directions) at three loading rates (0.5, 2, and 4 mm/s). The system provides ground-truth triaxial force labels and quantifies directional, loading-path, and rate-dependent electrical responses.

Key Contributions

Monolithic Sensor Design: A soft triaxial sensor using a single LIG layer and sequential electrode excitation, avoiding complex internal structures.
Hysteresis-Aware Framework: A latent-dynamics reconstruction method that explicitly models path-dependent transduction, resolving ambiguities where identical electrical responses correspond to different forces based on loading history.
Unified Characterization Protocol: A robot-automated platform providing dense directional sampling and multi-rate validation, establishing a rigorous benchmark for triaxial soft sensing.
Systematic Evaluation: Comprehensive testing across three individually calibrated sensors and multiple loading rates, demonstrating the superiority of temporal reconstruction over static and other sequential baselines.

Results
The system was evaluated on three sensors (D1, D2, D3) with pooled calibration at 0.5, 2, and 4 mm/s.

Accuracy: On held-out loading directions, the proposed method achieved a mean absolute force magnitude error (MAEF) of 0.0528 N and a mean direction error of 5.22° for reference forces between 0.3 N and 3 N.
Comparison: This represents a 71.0% reduction in magnitude error compared to a static Multi-Layer Perceptron (MLP) baseline (0.1824 N). On individually calibrated sensors, the reduction ranged from 74.9% to 80.8%.
Ablation Studies: Removing the latent dynamics accumulator degraded performance to the level of the static baseline (MAEF ~0.18 N), confirming that the history-dependent state accumulation is the primary source of performance gain. The residual modulation component contributed minimally beyond the accumulator.
Baselines: The proposed method outperformed other sequential baselines (ESN, TCN, GRU, LSTM) in both accuracy and parameter efficiency.
Path Dependence: The study quantified that the electrical response loop widens significantly with loading rate, and identical observation vectors can occur at different forces depending on the loading branch. The latent dynamics accumulator successfully separated these branches, whereas static models failed to do so.

Significance and Claims
The paper claims that TriSeq demonstrates that accurate triaxial force reconstruction is achievable in soft sensors through a combination of simple monolithic hardware and advanced temporal modeling, rather than complex mechanical decoupling. The work highlights that treating soft sensing as a system-level modeling problem—specifically one that accounts for hysteresis and loading history via latent dynamics—is critical for stability. The authors state that the sensor's compact structure and direct triaxial output make it suitable for integration into robotic end-effectors for tasks such as grasp-force regulation and slip detection. The paper does not claim to solve all soft sensing challenges but establishes a validated methodology for high-fidelity triaxial sensing under realistic, hysteretic conditions. Future work is noted to focus on demonstrating these capabilities in industrial manipulation and extending the framework to cross-instance deployment and multi-contact estimation.

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