Origami single-end capacitive sensing for continuous shape estimation of morphing structures

In this work, we propose a novel single-end morphing capacitive sensing method for shape tracking, FxC, by combining Folding origami structures and Capacitive sensing to detect the morphing structural motions using state-of-the-art sensing circuits and deep learning. It was observed through embedding areas of origami structures with conductive materials as single-end capacitive sensing patches, that the sensor signals change coherently with the motion of the structure. Different from other origami capacitors where the origami structures are used in adjusting the thickness of the dielectric layer of double-plate capacitors, FxC uses only a single conductive plate per channel, and the origami structure directly changes the geometry of the conductive plate. We examined the operation principle of morphing single-end capacitors through 3D geometry simulation combined with physics theoretical deduction, which deduced similar behavior as observed in experimentation. Then a software pipeline was developed to use the sensor signals to reconstruct the dynamic structural geometry through data-driven deep neural network regression of geometric primitives extracted from vision tracking. We created multiple folding patterns to validate our approach, based on folding patterns including Accordion, Chevron, Sunray and V-Fold patterns with different layouts of capacitive sensors using paper-based and textile-based materials. Experimentation results show that the geometry primitives predicted from the capacitive signals have a strong correlation with the visual ground truth with R-squared value of up to 95% and tracking error of 6.5 mm for patches. The simulation and machine learning constitute two-way information exchange between the sensing signals and structural geometry. By embedding part of the origami surface with morphing single-end capacitive sensors, FxC presents a unique solution that leverages both the mechanical properties of origami and sensing properties of capacitive sensing.