Fabrication and Characterization of Additively Manufactured Stretchable Strain Sensors Towards the Shape Sensing of Continuum Robots

TL;DR

This work addresses shape sensing for continuum robots under large deformations by developing stretchable resistive sensors fabricated via direct ink writing on TPU. It compares conductor-elastomer and liquid metal inks, finding gallium–indium liquid metal (ELMNT) offers the best combination of near-linear response ($R^2$ near $0.98$–$0.99$), modest gauge factor ($GF$ around $0.9$–$1.3$), and minimal drift, enabling exterior installation without rigid enclosures. Shape-sensing validation on a concentric push-pull robot and a notched-tube wrist demonstrates promising linearity and repeatability, albeit with hysteresis and drift that motivate future hysteresis compensation and local sensing arrays. The results suggest a practical, quickly fabricable path toward exterior shape sensing for continuum robots, with broader implications for soft robotics and wearable robotics applications. $GF$ and $R^2$ values, along with maximum strains of $3.15\%$ and $7.40\%$ on tested robots, underscore the approach's relevance to cm- and mm-scale sensing tasks.

Abstract

This letter describes the manufacturing and experimental characterization of novel stretchable strain sensors for continuum robots. The overarching goal of this research is to provide a new solution for the shape sensing of these devices. The sensors are fabricated via direct ink writing, an extrusion-based additive manufacturing technique. Electrically conductive material (i.e., the \textit{ink}) is printed into traces whose electrical resistance varies in response to mechanical deformation. The principle of operation of stretchable strain sensors is analogous to that of conventional strain gauges, but with a significantly larger operational window thanks to their ability to withstand larger strain. Among the different conductive materials considered for this study, we opted to fabricate the sensors with a high-viscosity eutectic Gallium-Indium ink, which in initial testing exhibited high linearity ($R^2 \approx$ 0.99), gauge factor $\approx$ 1, and negligible drift. Benefits of the proposed sensors include (i) ease of fabrication, as they can be conveniently printed in a matter of minutes; (ii) ease of installation, as they can simply be glued to the outside body of a robot; (iii) ease of miniaturization, which enables integration into millimiter-sized continuum robots.

Figures (8)

• Figure 1: (Top): Stretchable strain sensor installed onto a concentric push-pull robot Oliver2021. (Bottom): Sensor specimen. The strain sensors we describe in this letter can withstand much larger strains than traditional strain gauges and are therefore suitable for installation on the exterior surface of a continuum robot.
• Figure 2: (a) Stretchable strain sensors manufactured with different conductive materials: (Top) Silver-based sensor; (Middle) Carbon-based sensor; (Bottom) Gallium-Indium (ELMNT®) sensor. Sensor dimensions are 112mm (length), 2.2mm (width), with a trace width of 0.6mm. For further specifications on these materials, refer to Table \ref{['tab:1']}. (b) Schematic showing the structure of conductor-elastomer composite based sensors. (c) Schematic for liquid metal based sensors.
• Figure 3: Experimental apparatus and test for the evaluation of the conductive inks. (a) Schematic of the test setup. Each sensor is attached to an Acrylonitrile Styrene Acrylate (ASA) beam, which is controllably bent to simulate different loading conditions. (b) Actual ASA specimen under load with a sensor attached. Bending is achieved by attaching one of the two ends of the beam to a linear stage controlled by a stepper motor. The electrical resistance of the sensor is monitored with an IM3536 LCR meter (Hioki E.E. Corporation, Nagano, Japan), not pictured here. The position of the moving terminal of the linear stage was recorded using a magnetic linear encoder, the AS5048A-HTSP (ams OSRAM AG, Premstätten, Austria), and used to estimate the applied strain, as explained in the following. Both strain and resistance measurements were captured at 10Hz and timestamped with Robot Operating System 2 (ROS 2) running on Ubuntu 20.04, on a laptop equipped with an i7-8750H CPU (Intel Corp., Santa Clara, CA, USA). (c) Beam shape reconstruction based on the applied load, using a simple model of beam buckling under compressive loads Hibbeler2023. (d) Estimated strain distribution along the beam.
• Figure 4: Raw sensor output and characteristic curves observed under experimental condition (a). The sensor using the ELMNT® ink exhibited higher linearity and significantly less drift than the ones based on the conductor-elastomer composite inks (silver and carbon). The initial resistance of the ELMNT® sensor is slightly higher during the first cycle, attributed to imperfect mechanical activation.
• Figure 5: (Top): ELMNT® stretchable strain sensors installed onto a notched tube wrist Pacheco2021. The sensing area measures 17mm in length and 0.6mm in width, with a trace width of 0.3mm.