Category theory as a foundation for soft robotics

TL;DR

This paper introduces a category theory-based mathematical foundation for soft robotics, aiming to establish rigorous design principles and better understand the interaction between soft robots and their environment.

Contribution

It proposes a novel category theory framework for modeling soft robotics, providing a formal basis for understanding their characteristics and adaptation behaviors.

Findings

Applied the theory to a model system of universal grippers.

Highlighted the adaptation behavior of soft robots through the category of mobility.

Established a foundation for future theoretical development in soft robotics.

Abstract

Soft robotics is an emerging field of research where the robot body is composed of compliant and soft materials. It allows the body to bend, twist, and deform to move or to adapt its shape to the environment for grasping, all of which are difficult for traditional hard robots with rigid bodies. However, the theoretical basis and design principles for soft robotics are not well-founded despite their recognized importance. For example, the control of soft robots is outsourced to morphological attributes and natural processes; thus, the coupled relations between a robot and its environment are particularly crucial. In this paper, we propose a mathematical foundation for soft robotics based on category theory, which is a branch of abstract math where any notions can be described by objects and arrows. It allows for a rigorous description of the inherent characteristics of soft robots and their relation to the environment as well as the differences compared to conventional hard robots. We present a notion called the category of mobility that well describes the subject matter. The theory was applied to a model system and analysis to highlight the adaptation behavior observed in universal grippers, which are a typical example of soft robotics. This paper paves the way to developing a theoretical background and design principles for soft robotics.