Kinetostatic Modeling of Tendon-Driven Parallel Continuum Robots

Tendon-driven parallel continuum robots (PCR) consist of multiple individual continuous kinematic chains, that are actuated in bending utilizing tendons routed along their backbones. This work derives and proposes a Cosserat rod based kinetostatic modeling framework for such parallel structures that allows for efficiently solving the forward, inverse and velocity kinetostatic problems. Using this model, the kinematic properties such as reachable workspace, singularities, manipulability, and compliance of tendon-driven PCR are studied in detail. Experiments are conducted using a real robotic prototype to validate the derived modeling approach. Overall, a median pose accuracy of 4.9 mm, corresponding to 3.4% of the continuum robots' lengths, and 6.2 $^\circ$ is achieved. The median of the model's computation time results in 0.51 s on standard computing hardware. Fast computations of below 100 ms can be achieved, if an appropriate initial guess for solving the kinetostatic model is available, making the model suitable for a range of different applications including optimization or control.