Abstract
In this work, the Piecewise Variable-strain (PVS) approach is applied to
the case of Concentric Tube Robots (CTRs) and extended to include the
tubes’ sliding motion. In particular, the currently accepted continuous
Cosserat rod model is discretized onto a finite set of strain basis
functions. At the same time, the insertion and rotation motions of the
tubes are included as generalized coordinates instead of boundary
kinematic conditions. Doing so, we obtain a minimum set of closed-form
algebraic equations that can be solved not only for the shape variables
but also for the actuation forces and torques for the first time. This
new approach opens the way to torque-controlled CTRs, which is poised to
enhance elastic stability and improve interaction forces’ control at the
end-effector.