Shape Control for Modular Continuum Soft Arms: A Distributed Approach to Address Redundancy

Modular continuum soft arms represent an emerging class of robotic systems characterized by flexible, highly deformable structures. Designing shape controllers for these arms poses significant challenges due to their modeling complexity and hyper-redundant nature. Our goal is to develop a scalable control framework for modular arms, where each module is self-contained. Starting from distributed control theory, we assign a collaborative controller to each soft module. Through collaboration among modules, the framework enables the system to achieve the desired tip position and shape. Each controller relies on the minimal model, such as the Constant Curvature, of its self-contained module and the local transformation shared by adjacent modules. We present three kinematic control strategies - Consensus, Bipartite Consensus, and Formation Control - for a modular continuum soft arm, that progressively relax constraints to achieve more complex, adaptable shapes. In addition, we develop a decentralized curvature-based dynamic controller to manage dynamic coupling among modules. The validation is carried out through numerical analysis and dynamic simulations of soft arms with varying numbers of modules.