空间多段腱驱动连续体机器人的闭式笛卡尔正向运动静力学
Closed-Form Cartesian Forward Kinetostatics for Spatial Multi-Segment Tendon-Driven Continuum Robots
中文总结 AI 辅助
本文提出一种空间多段腱驱动连续体机器人的闭式力到笛卡尔构型映射模型，无需迭代求解，计算速度提升数千倍，且精度高。
中文摘要 AI 辅助
空间腱驱动连续体机器人的正向运动静力学通常需要对每个驱动输入进行非线性平衡求解。本文针对腱驱动下的空间多段机器人，提出了一种具有闭式求积解的力到笛卡尔构型映射模型。笛卡尔骨干中心线和累积材料扭转作为广义坐标，由此推导出应变测量和腱几何。变分平衡给出了显式的轴向和弯曲关系，并在所提出的模型中为可接受的纵向非螺旋布腱建立了零平衡材料扭转。该解逐段传播，无需迭代平衡求解，同时保留了轴向变形、空间变化的轴向和弯曲刚度及腱布直径，以及分段相关的腱参与。与全应变几何变应变模型（GVS）的数值比较表明，单段和三段机器人的最大长度归一化尖端位置差异分别为8.91×10^-6和1.01×10^-5。平均评估时间为1.52微秒和2.94微秒，相对于基线分别实现了约1864倍和3348倍的加速，证明了在所报告的基准测试中显式力到构型映射的计算优势。
英文摘要
Forward kinetostatics of spatial tendon-driven continuum robots typically requires a nonlinear equilibrium solve for each actuation input. This paper develops a force-to-Cartesian-configuration model with a closed-form solution in quadratures for spatial multi-segment robots under tendon actuation. The Cartesian backbone centerline and accumulated material twist serve as generalized coordinates, from which the strain measures and tendon geometry are derived. Variational equilibrium yields explicit axial and bending relations and establishes zero equilibrium material twist within the proposed model for admissible longitudinal non-helical routing. The solution is propagated segment by segment without an iterative equilibrium solve, while retaining axial deformation, spatially varying axial and bending stiffnesses and tendon-routing diameter, and segment-dependent tendon participation. Numerical comparisons with a full-strain geometric variable-strain model (GVS) yield maximum length-normalized tip-position discrepancies of 8.91 x 10^-6 and 1.01 x 10^-5 for the single- and three-segment robots, respectively. Mean evaluation times of 1.52 μs and 2.94 μs, with corresponding speedups of approximately 1864x and 3348x over the baseline, demonstrate the computational advantage of the explicit force-to-configuration mapping in the reported benchmark.
