Liu Yang, Alambeigi Farshid
Walker Department of Mechanical Engineering and the Texas Robotics at the University of Texas at Austin, Austin, TX, 78712, USA.
IEEE Robot Autom Lett. 2022 Apr;7(2):3624-3631. doi: 10.1109/lra.2022.3147903. Epub 2022 Feb 1.
We present a novel physically-intuitive mathematical formulation to investigate the effects of a fully-constrained generic tendon routing (GTR) on the correlation between tension loss and deformation behavior of a variable-curvature tendon-driven continuum manipulator (TD-CM). The proposed model can account for distributed friction forces/moments along a GTR path that have been typically ignored in the previous approaches (e.g., the well-known frictionless Cosserat rod model). For the first time, the internal distributed forces on a GTR are expressed using three physically-intuitive generic functions. Solely relying on the known actuation input(s), the proposed mathematical formulation can also solve the entangled and unknown correlation between GTR, internal distributed forces, tension loss and deformation behavior of TD-CMs. To evaluate the performance of the proposed approach, we performed various simulation studies using eight different GTR paths. Additionally, we fabricated two different types of TD-CMs with different GTRs to experimentally evaluate the efficacy and performance of the proposed mathematical framework. The results demonstrate the proposed model can successfully and accurately (i.e., about <10% error) capture the trends of substantial tension loss (e.g., about <50%) on fully constrained GTRs, which reveals the importance of considering tension loss in modeling these TD-CMs.
我们提出了一种全新的、具有物理直观性的数学公式，以研究完全约束的通用肌腱布线（GTR）对可变曲率肌腱驱动连续体机械手（TD-CM）的张力损失与变形行为之间相关性的影响。所提出的模型能够考虑沿GTR路径的分布摩擦力/力矩，而这些在先前的方法中（例如，著名的无摩擦柯塞尔杆模型）通常被忽略。首次使用三个具有物理直观性的通用函数来表示GTR上的内部分布力。仅依靠已知的驱动输入，所提出的数学公式还能够解决TD-CM的GTR、内部分布力、张力损失和变形行为之间纠缠且未知的相关性。为了评估所提方法的性能，我们使用八种不同的GTR路径进行了各种模拟研究。此外，我们制造了两种具有不同GTR的不同类型的TD-CM，以通过实验评估所提数学框架的有效性和性能。结果表明，所提出的模型能够成功且准确地（即误差约<10%）捕捉完全约束GTR上大量张力损失（例如，约<50%）的趋势，这揭示了在对这些TD-CM进行建模时考虑张力损失的重要性。
