Data-Driven Steering of Concentric Tube Robots in Unknown Environments via Dynamic Mode Decomposition

Concentric Tube Robots (CTRs) are a type of continuum robot capable of manipulating objects in restricted spaces and following smooth trajectories. CTRs are ideal instruments for minimally invasive surgeries. Accurate control of CTR's motion in presence of contact with tissue and external forces will allow safe deployment of the robot in a variety of minimally invasive surgeries. Here, we propose a data-driven controller that can repeatedly and precisely direct the robot along predetermined deployment trajectories. The proposed controller doesn't rely on a mathematical model of the robot and employs Extended Dynamic Mode Decomposition (EDMD) to learn the nonlinear dynamics of the robot and the interaction forces on the fly. This enables the robot to follow desired trajectories in the presence of unknown perturbations, such as external forces. Experiments are carried out to evaluate the accuracy of the controller in steering the robot on arbitrary trajectories. Results demonstrate that the robot can track trajectories with a mean accuracy of 2.4 mm in repeated trials. Furthermore, we simulate scenarios where the robot is in contact with a rigid obstacle and is cutting through phantom tissue. Results show the robot can reach various static targets with a minimum accuracy of 2 mm.