A Lagrangian Dynamic Model for Soft Cylindrical Robots Without Internal Holonomic Constraint

Abstract

Mathematical modelling is an essential step in the study of systems. However for deformable soft robots, despite there is a variety of models in the literature, few provide a closed-form analytical structure useful for design and control. Unfortunately, the ones presenting such structure, [1], [2], [3], assumes a rigidity condition known as internal holonomic constraint (the distance among constitutive particles remains constant), therefore, the basic feature of continuum variable deformation is not considered. In this paper, we address the mathematical model of continuum soft, robot driven by pneumatic forces, based on Lagrangian formulation and considering variable distance among particles. Inspired by the above works, we formalize and test such a model by working out the fact that the rigid bodies’ holonomic constraints is no longer valid in the mechanics of soft bodies. The fundamental structural properties of the dynamic model are studied and analyzed, and simulations and preliminary experiments are presented.