Impact of Generic Tendon Routing on Tension Loss of Tendon-Driven Continuum Manipulators with Planar Deformation

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.