A General Lie-Group Framework for Continuum Soft Robot Modeling

TL;DR

This paper presents a comprehensive Lie group-based modeling framework for continuum soft robots, enabling accurate, flexible, and real-time simulation and control of complex robotic structures with improved geometric and computational properties.

Contribution

It introduces a unified Lie group approach that overcomes limitations of existing methods, providing analytical expressions and extensions for complex soft robot configurations.

Findings

Effective modeling of large-deformation rods demonstrated

Framework applicable to various robotic structures shown

Enhanced computational efficiency and flexibility achieved

Abstract

This paper introduces a general Lie group framework for modeling continuum soft robots, employing Cosserat rod theory combined with cumulative parameterization on the Lie group SE(3). This novel approach addresses limitations present in current strain-based and configuration-based methods by providing geometric local control and eliminating unit quaternion constraints. The paper derives unified analytical expressions for kinematics, statics, and dynamics, including recursive Jacobian computations and an energy-conserving integrator suitable for real-time simulation and control. Additionally, the framework is extended to handle complex robotic structures, including segmented, branched, nested, and rigid-soft composite configurations, facilitating a modular and unified modeling strategy. The effectiveness, generality, and computational efficiency of the proposed methodology are demonstrated through various scenarios, including large-deformation rods, concentric tube robots, parallel robots, cable-driven robots, and articulated fingers. This work enhances modeling flexibility and numerical performance, providing an improved toolset for designing, simulating, and controlling soft robotic systems.