Concentric Tube Robot Redundancy Resolution via Velocity/Compliance Manipulability Optimization

Concentric Tube Robots (CTR) have the potential to enable effective minimally invasive surgeries. While extensive modeling and control work have been proposed in the past decade, limited efforts have been made to improve the path tracking performance from the perspective of manipulability, which can be critical to generate safe motion and feasible actuator commands. In this letter, we propose a gradient-based redundancy resolution framework that optimizes velocity/compliance manipulability-based performance indices during path tracking for a kinematically redundant CTR. We efficiently calculate the gradients of manipulabilities by propagating the first- and second-order derivatives of state variables of the Cosserat rod model along the CTR arc length, reducing the gradient computation time by 68% compared to the finite difference method. Task-specific performance indices are optimized by projecting the gradient into the null-space of path tracking. Simulation results show that the proposed method is able to accomplish the required tasks while commonly used redundancy resolution approaches underperform or even fail.