Mathematical Modeling of a Multi-Chamber Pneumatic Soft Actuator

Abstract

Owing to their compliance with most shapes, soft actuators are regarded as cost-effective solutions for grasping irregular objects. The material properties of nonlinear elastic polymers are considered necessary for the correct implementation of these actuators. The analysis tends to be complex even for simple movements defined by theoretically infinite degrees of freedom. This study offers a mathematical model that outlines a relationship between the energy provided by a pressure source and the expected behavior of multi-chamber pneumatic soft actuators through hyper-elastic material deformation interpretation, geometric approximations, and the vectorial representations of their segments. Digitally analyzed empirical results measured through lateral pictures of an actuator were taken at different pressure references. Direct comparisons between the average value of the tested angles and those calculated through the tuned mathematical model provide a maximum error of 0.647° for small deformations and an improved accuracy at higher pressure inputs. This study offers a valid tool applicable to the design of soft actuators and their further analysis without the need for overly complex methods.