Shape Control for the Elastica Through Load Optimization

Flexible elastic beams can function as dexterous manipulators at multiple length-scales and in various niche applications. As a step toward achieving controlled manipulation with flexible structures, we introduce the problem of approximating desired quasi-static deformations of a flexible beam, modeled as an elastica, by optimizing the loads applied. We presume the loads to be concentrated, with the number and nature of their application prescribed based on design considerations and operational constraints. For each desired deformation, we pose the problem of computing the requisite set of loads to mimic the target shape as one of optimal approximations. In the process, we introduce a novel generalization of the forward problem by considering the inclinations of the loads applied to be functionals of the solution. This turns out to be especially beneficial when analyzing tendon-driven manipulators. We demonstrate the shape control realizable through load optimization using a diverse set of experiments.