On the computational design of concentric tube robots: Incorporating volume-based objectives

Concentric tube continuum robots provide an infinite-dimensional design space, consisting of individual tube space curves and other tube parameters. Even when design choices are made to restrict the design space to a small number of discrete parameters, ad hoc selection of parameter values to achieve coverage of a desired volume, in the presence of geometric workspace constraints, is essentially impossible - even for experienced researchers. General design algorithms proposed to date have focused on reaching a discrete set of specific points, and have made non-physical approximations in the robot model (most significantly assuming infinite torsional rigidity), to speed up model computation. In this paper, we extend prior algorithms to use more accurate models and incorporate volume-based objectives. These extensions are illustrated in a case study on the design of a concentric tube robot for endonasal pituitary surgery. We show that volume-based design optimization increases the reachable percentage of the surgical workspace by an average of approximately 50%, in comparison to various sets of manually selected design parameters. We conclude that volume-based objectives should be included in future multi-objective design optimization procedures for concentric tube continuum robots.