Image-based Approach to Reconstruct Curling in Continuum Structures

This paper proposes an image-based approach to reconstruct the shape of continuum biological (e.g., tendrils of climbing plants) and artificial (continuum soft robots) structures which can deform into coils or curls with variable curvature that depends on the arc length. The proposed method is based on 2D clothoid curves, for which we explore two resolution approaches: i) single-segment clothoid representation, with optimal curve parameters search; ii) piece-wise clothoid representation, with G1 Hermite-fitting solution. Besides, we propose a novel algorithm to sort 2D unarranged points that addresses the issue of possible undesired branches and discontinuities. We numerically evaluate the performance of the method and compare it with a constant curvature fitting. We obtain an improvement of more than 100% in tendril and up to 5% with a soft continuum robotic artefact, demonstrating the feasibility and the reliability of our approach. The proposed model can be applied for shape representation and reconstruction on both long slender living organisms and continuum soft robots with curling-like behavior.