Towards Modelling Multi-Arm Robots: Eccentric Arrangement of Concentric Tubes

This paper presents and experimentally evaluates a quasistatic mechanics-based model that describes the shape of concentric tube robotic (CTR) arms when they are eccentrically arranged along an also-flexible backbone. The model can estimate the shape of both the backbone and CTR arms, and can accommodate an arbitrary number of CTR arms arranged in an eccentric position with regards to the backbone's neutral axis. Experimental evaluation with a prototype system on the benchtop highlights the promise of the end-to-end proposed modelling approach, as the error between model and experiment is around 11% of the manipulator's overall length. The theory is the first step towards modeling multi-arm concentric tube robots, a class of continuum robots that is increasingly being considered for single-port surgical applications.