Considerations for follow-the-leader motion of extensible tendon-driven continuum robots

Path following and follow-the-leader motion is particularly desirable for minimally-invasive surgery in confined spaces which can only be reached using tortuous paths, e.g. through natural orifices. While path following and followthe- leader motion can be achieved by hyper-redundant snake robots, their size is usually not applicable for medical applications. Continuum robots, such as tendon-driven or concentric tube mechanisms, fulfill the size requirements for minimally invasive surgery, but yet follow-the-leader motion is not inherently provided. In fact, parameters of the manipulator's section curvatures and translation have to be chosen wisely a priori. In this paper, we consider a tendon-driven continuum robot with extensible sections. After reformulating the forward kinematics model, we formulate prerequisites for follow-the-leader motion and present a general approach to determine a sequence of robot configurations to achieve follow-the-leader motion along a given 3D path. We evaluate our approach in a series of simulations with 3D paths composed of constant curvature arcs and general 3D paths described by B-spline curves. Our results show that mean path errors <;0.4mm and mean tip errors <;1.6mm can theoretically be achieved for constant curvature paths and <;2mm and <;3.1mm for general B-spline curves respectively.