Concentric Tube Robots (CTR) have the potential to enable effective minimally invasive surgeries. While extensive modeling and control schemes have been proposed in the past decade, limited efforts have been made to improve the trajectory tracking performance from the perspective of manipulability , which can be critical to generate safe motion and feasible actuator commands. In this paper, we propose a gradient-based redundancy resolution framework that optimizes velocity/compliance manipulability-based performance indices during trajectory 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 finite difference method. Task-specific performance indices are optimized by projecting the gradient into the null-space of trajectory tracking. The proposed method is validated in three exemplary scenarios that involve trajectory tracking, obstacle avoidance, and external load compensation, respectively. Simulation results show that the proposed method is able to accomplish the required tasks while commonly used redundancy resolution approaches underperform or even fail.

翻译：同心管机器人（CTR）具有实现高效微创手术的潜力。尽管过去十年中已提出多种建模与控制方案，但鲜有研究从可操作度角度提升轨迹跟踪性能——而这对于生成安全运动及可行执行器指令至关重要。本文针对运动学冗余的CTR，提出一种基于梯度的冗余求解框架，在轨迹跟踪过程中优化基于速度/柔顺可操作度的性能指标。通过沿CTR弧长传播Cosserat杆模型状态变量的一阶和二阶导数，我们高效计算了可操作度的梯度，相比有限差分法将梯度计算时间减少68%。通过将梯度投影到轨迹跟踪的零空间中，优化了任务特定性能指标。该方法在分别涉及轨迹跟踪、避障及外部负载补偿的三种典型场景中完成验证。仿真结果表明，所提方法能够完成既定任务，而传统冗余求解方法在此类场景中表现不佳甚至完全失效。