Modeling Tendon-actuated Concentric Tube Robots

Mechanics-based models have been developed to describe the shape of tendon-actuated continuum robots. Models have also been developed to describe the shape of concentric tube robots, i.e., nested combinations of precurved superelastic tubes. While an important class of continuum robots used in endoscopic and intracardiac medical applications combines these two designs, existing models do not cover this combination. Tendon-actuated models are limited to a single tube while concentric tube models do not include tendon-produced forces and moments. This paper derives a mechanics-based model for this hybrid design and assesses it using numerical and physical experiments involving a pair of tendon-actuated tubes. It is demonstrated that, similar to concentric tube robots, relative twisting between the tendon-actuated tubes is an important factor in determining overall robot shape.