Algebraic approach towards the exploitation of “softness”: the input–output equation for morphological computation

Abstract

Recently, soft robots that consist of soft and deformable materials have received much attention for their adaptability to uncertain environments. Although these robots are difficult to control with a conventional control theory owing to their complex body dynamics, research from different perspectives attempts to actively exploit these body dynamics as an asset rather than a drawback. This approach is called morphological computation, in which the soft materials are used for computation that includes a new kind of control strategy. In this article, we propose a novel approach to analyze the computational properties of soft materials based on an algebraic method, called the input–output equation used in systems analysis, particularly in systems biology. We mainly focus on the two scenarios relevant to soft robotics, that is, analysis of the computational capabilities of soft materials and design of the input force to soft devices to generate the target behaviors. The input–output equation directly describes the relationship between inputs and outputs of a system, and hence by using this equation, important properties, such as the echo state property that guarantees reproducible responses against the same input stream, can be investigated for soft structures. Several application scenarios of our proposed method are demonstrated using typical soft robotic settings in detail, including linear/nonlinear models and hydrogels driven by chemical reactions.