Can Elastic Instability be Beneficial in Concentric Tube Robots?

Magnetic concentric tube robots: introduction and analysis

In this paper, we propose a new type of continuum robot, referred to as a magnetic concentric tube robot (M-CTR), for performing minimally invasive surgery in narrow and difficult-to-access areas. The robot combines concentric tubes and magnetic actuation to benefit from the ‘follow the leader’ behaviour, the dexterity and stability of existing robots, while targeting millimetre-sized external diameters. These three kinematic properties are assessed through numerical and experimental studies performed on a prototype of a M-CTR. They are performed with general forward and inverse kineto-static models of the robot, continuation and bifurcation analysis, and a specific experimental setup. The prototype presents unique capabilities in terms of deployment and active stability management, while its dexterity in terms of tip orientability is also among the best reported for other robots at its scale.

A Dynamic Model for Concentric Tube Robots

Existing static and kinematic models of concentric tube robots are based on the ordinary differential equations of a static Cosserat rod. In this paper, we provide the first dynamic model for concentric tube continuum robots by adapting the partial differential equations of a dynamic Cosserat rod to describe the coupled inertial dynamics of precurved concentric tubes. This generates an initial-boundary-value problem that can capture robot vibrations over time. We solve this model numerically at high time resolutions using implicit finite differences in time and arc length. This approach is capable of resolving the high-frequency torsional dynamics that occur during unstable "snapping" motions and provides a simulation tool that can track the true robot configuration through such transitions. Further, it can track slower oscillations associated with bending and torsion as a robot interacts with tissue at real-time speeds. Experimental verification of the model shows that this wide range of effects is captured efficiently and accurately.