Continuum-Based Geometry/Analysis Approach for Flexible and Soft Robotic Systems

Control and stability of flexible and soft robotic systems (FSRS), which have complex geometry and experience desirable and undesirable deformations, are of major concern, particularly when lightweight soft materials are used. Nonetheless, there is no unified continuum-based geometry/analysis approach that can be used for the efficient FSRS virtual prototyping and design. The goal of this article is to propose a new FSRS geometric modeling and analysis methodology by addressing fundamental virtual prototyping challenges that include: (1) integration of the robot geometry and analysis; (2) implementation of general and unconventional material models and actuation forces; (3) use of new concepts for modeling FSRS joints; and (4) development of efficient and robust algorithms for the FSRS virtual prototyping. To address these challenges, the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system computational algorithms are used. ANCF FEs allow for modeling arbitrarily large and coupled displacements, correctly capture complex geometries, allow for implementing general and nonconventional material models, provide accurate definitions of conventional and nonconventional actuation forces, lead to a constant inertia matrix that defines optimally sparse matrix structure of the dynamic equations, and allow for exploiting new geometry concepts to define linear and more general joint constraints instead of the less general and nonlinear joint constraints currently used for robot systems. Using the general structure of the FSRS nonlinear dynamic equations of motion, a nonmodal continuum-based approach can be developed and used to correctly capture the FSRS complex geometry and large deformations.