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Concentric Tube Robots (CTR) have the potential to enable effective minimallyinvasive surgeries. While extensive modeling and control schemes have beenproposed in the past decade, limited efforts have been made to improve thetrajectory tracking performance from the perspective of manipulability , whichcan be critical to generate safe motion and feasible actuator commands. In thispaper, we propose a gradient-based redundancy resolution framework thatoptimizes velocity/compliance manipulability-based performance indices duringtrajectory tracking for a kinematically redundant CTR. We efficiently calculatethe gradients of manipulabilities by propagating the first- and second-orderderivatives of state variables of the Cosserat rod model along the CTR arclength, reducing the gradient computation time by 68\% compared to finitedifference method. Task-specific performance indices are optimized byprojecting the gradient into the null-space of trajectory tracking. Theproposed method is validated in three exemplary scenarios that involvetrajectory tracking, obstacle avoidance, and external load compensation,respectively. Simulation results show that the proposed method is able toaccomplish the required tasks while commonly used redundancy resolutionapproaches underperform or even fail.

Concentric Tube Robot Redundancy Resolution via Velocity/Compliance Manipulability Optimization