Length Modelling of Spiral Superficial Soft Strain Sensors Using Geodesics and Covering Spaces

Piecewise constant curvature soft actuators can generate various types of movements. These actuators can undergo extension, bending, rotation, twist, or a combination of these. Proprioceptive sensing provides the ability to track their movement or estimate their state in 3D space. Several proprioceptive sensing solutions were developed using soft strain sensors. However, current mathematical models are only capable of modelling the length of the soft sensors when they are attached to actuators subjected to extension, bending, and rotation movements. Furthermore, these models are limited to modelling straight sensors and incapable of modelling spiral sensors. In this study, for both the spiral and straight sensors, we utilise concepts in geodesics and covering spaces to present a mathematical length model that includes twist. This study is limited to the Piecewise constant curvature actuators and demonstrates, among other things, the advantages of our model and the accuracy when including and excluding twist. We verify the model by comparing the results to a finite element analysis. This analysis involves multiple simulation scenarios designed specifically for the verification process. Finally, we validate the theoretical results with previously published experimental results. Then, we discuss the limitations and possible applications of our model using examples from the literature.