用李群框架统一建模软体机器人，支持复杂结构实时仿真。
A General Lie-Group Framework for Continuum Soft Robot Modeling
- 基于SE(3)李群的累积参数化，实现局部几何控制。
- 推导出统一的运动学、静力学与动力学解析表达式。
- 适用于分段、分支、复合结构，适合实时控制与仿真。
本文提出一种通用的李群框架用于连续型软体机器人建模，结合柯塞拉杆理论与李群SE(3)上的累积参数化。该方法克服了现有应变法与构型法的局限，实现几何局部控制并消除单位四元数约束。论文推导出运动学、静力学和动力学的统一解析表达式，包括递归雅可比计算与能量守恒积分器，适用于实时仿真与控制。框架进一步扩展至处理分段、分支、嵌套及刚-软复合结构，实现模块化统一建模。通过大变形杆、同心管机器人、并联机器人、缆索驱动机器人和关节手指等多种场景验证了方法的有效性、通用性与计算效率。该工作提升了建模灵活性与数值性能，为软体机器人的设计、仿真与控制提供更优工具集。
原文摘要 · Abstract (English)
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.
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