Evaluation of Dynamic Relaxation to Solve Kinematics of Concentric Tube Robots

Concentric tube robots are based on the deformation of elastic pre-curved tubes mounted in a telescopic manner. Their kinematic model consists in a boundary value problem which must be solved during analysis and design. When arbitrary properties and number of the tubes are considered, this model must be solved numerically. We consider in this paper the use of dynamic relaxation to perform this resolution. Its performances in terms of accuracy and computation time are assessed in a case study involving a two-tube CTR. Robustness of the method tuning to variations of CTR behaviour as encountered during a deployment is finally assessed.