Quasistatic modeling of concentric tube robots with external loads

Concentric tube robots are a subset of continuum robots constructed by combining pre-curved elastic tubes. As the tubes are rotated and translated with respect to each other, their curvatures interact elastically, enabling control of the robot´s tip configuration as well as the curvature along its length. This technology is projected to be useful in many types of minimally invasive medical procedures. Because these robots are flexible by design, they deflect considerably when applying forces to the external environment. Thus, in contrast to rigid-link robots, their kinematic and static force models are coupled. This paper derives a multi-tube quasistatic model that relates tube rotations and translations together with externally applied loads to robot shape and tip configuration. The model can be applied in robot design, procedure planning as well as control. For validation, the multi-tube model is compared experimentally to a computationally-efficient single-tube approximate model.