An Euler–Bernoulli beam model for soft robot arms bent through self-stress and external loads

Abstract

Soft robot arms remain challenging to model effectively. The arm’s primary deformation is bending, coupled with extension or compression, but the strains experienced can be high, the materials are generally nonlinear, and the deformations are large. Existing work has focused on models intended to improve control, which rely on post-manufacturing empirical characterization of each arm design. This article presents a quasi-static model based on Euler–Bernoulli beam theory that generalizes across a broad set of arm designs. The model is implemented for fluid-driven soft arms constructed with McKibben actuators. Actuators are treated as active materials, and their force is characterized as a nonlinear function of pressure and uniaxial strain. The model is validated for multiple soft arms under external loads, and further use is demonstrated through an investigation of the soft arms’ loaded workspace. Higher load capacities are shown to be concentrated at the arms’ midlines. Distal taper is examined in an example arm design, and is shown to improve range of motion and load resistance when compared to a constant width arm. The model can be used to evaluate variations on the number and arrangement of actuators in an arm, and it is proposed as a first order design and analysis method for soft robot arms.