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arXiv 2603.08232cs.RO
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连续软机器人建模的通用李群框架

A General Lie-Group Framework for Continuum Soft Robot Modeling

Sorbonne Université, CNRS UMR 7222, Inserm U1150, ISIR(索邦大学,CNRS UMR 7222,Inserm U1150,ISIR);Université de Strasbourg, CNRS, INSERM, ICube, UMR7357(斯特拉斯堡大学,CNRS,INSERM,ICube,UMR7357)

Lingxiao Xun, Benoît Rosa, Jérôme Szewczyk, Brahim Tamadazte

AI总结:

本文提出了一种基于李群的通用框架,结合柯西-罗德理论和累积参数化,用于高效建模连续软机器人,解决了传统方法的局限性,并提升了模拟和控制性能。

摘要:

本文介绍了一种通用的李群框架,用于建模连续软机器人,结合了柯西-罗德理论与在李群SE(3)上的累积参数化。该新方法通过提供几何局部控制并消除单位四元数约束,解决了当前基于应变和配置的方法的局限性。论文推导了运动学、静力学和动力学的统一解析表达式,包括递归雅可比计算和适用于实时模拟和控制的能量守恒积分器。此外,该框架还扩展到处理复杂的机器人结构,包括分段、分支、嵌套和刚-软复合配置,从而实现模块化和统一的建模策略。通过各种场景,包括大变形杆、同心管机器人、并联机器人、缆驱动机器人和关节手指,展示了所提出方法的有效性、通用性和计算效率。这项工作提高了建模的灵活性和数值性能,为设计、模拟和控制软机器人系统提供了改进的工具集。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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