A method for reconstructing the shape of highly flexible, slender objects from distributed strain measurements

摘要

This paper presents a method for determining three-dimensional global displacement (forrnarbitrarily-sized deformation but “small” strain) of thin rod/tether-like structures from a limited set of scalar strainrnmeasurements. The approach is rooted in Cosserat rod theory with the adoption of a material-adapted referencernframe and a localized linearization approach that facilitates an exact local basis function set for the displacementrnas well as the material frame evolution itself. The solution set is shown to be robust to potential singularitiesrnfrom vanishing bending and twisting angle derivatives and from vanishing measured strain. Validation of thernapproach is performed through comparison with finite element simulations of a tube-like structure subjectedrnto arbitrary deformations. The average root mean square reconstruction error of 0.01%–1% of the total length,rnfor reasonably low sensor counts. Analysis of error due to extraneous noise sources and boundary conditionrnuncertainty shows how error scales with those effects. The algorithm involves relatively simple operations, thernmost complex of which is square matrix inversion, lending itself to potential low-power embeddable solutions forrnstructural monitoring applications requiring shape reconstruction. Experimental verification will also be shownrnin the presentation accompanying this paper.