Concentric tube robots (CTR) can traverse tightly curved paths and offer dexterity in constrained environments, making them advantageous for minimally invasive surgical scenarios that experience strict anatomical and surgical constraints. Their shape is controlled via rotation and translation of several concentrically arranged super-elastic precurved tubes that form the robot backbone. As the elastic energy accumulated in the backbone due to bending and twist of the tubes increases, robots can exhibit sudden snapping motions, which can damage the surrounding tissues. In this paper, we proposed an approach for closed-loop steering of a redundant CTR that allows for snap-free motion and enhances its force/velocity manipulability, increasing the capacity of the robot to move and/or exercise forces along any direction. First, a controller stabilizes the CTR end-effector on a desired time-variant trajectory. Next, an online optimizer uses the robot's redundant Degrees of Freedom (DoF) to reshape its manipulability in real-time and steer it away from potentially snapping configurations or increase its capacity in delivering force payloads. Simulations and experiments demonstrate the performance of the proposed control strategy. The controller can steer a generally unstable CTR along trajectories while avoiding instabilities with a mean error of 850 µm, corresponding to 0.6% of arclength, and improves robot ability to exercise forces by 55%.

This paper presents a Model Predictive Controller (MPC) developed for the autonomous steering of concentric tube robots (CTRs). State-of-the-art CTR control relies on differential kinematics developed by local linearization of the CTR's mechanics model and cannot explicitly handle constraints on robot's joint limits or unstable configurations commonly known as snapping points. The proposed nonlinear MPC explicitly considers constraints on the robot configuration space (i.e. joint limits) and the robot's workspace (i.e. mixed boundary conditions on robot curvature). Additionally, the MPC calculates control decisions by optimizing the model-based predictions of future robot configurations. This way, it avoids configurations it cannot recover from, joint limits, singular configurations and snapping. The proposed controller is evaluated via simulations and experimental studies with a variety of trajectories of increasing complexity. Simulation results demonstrate the capability of MPC to avoid singularities while satisfying robot mechanical constraints. Experimental results demonstrate that our solution enables following of trajectories unattainable by state-of-the-art controllers with mean error corresponding to 1% of robot arclength.