Shape Control of Concentric Tube Robots via Approximate Follow-the-Leader Motion

Concentric tube robots (CTRs) are miniaturized continuum robots that are promising for robotic minimally invasive surgeries. Control methods to date have primarily focused on controlling the robot tip. However, small changes in the tip position can result in large deviations in the shape of the robot body, motivating the need for shape control to ensure safe navigation in constrained environments. One proposed method for shape control, known as follow-the-leader (FTL) motion, allows the robot to deploy while occupying minimal volume but is limited to specific CTR designs and deployment sequences. In this letter, we propose a shape control method that approximates FTL motion and is applicable to arbitrary tip navigation tasks without requiring a predefined trajectory or specific tube design. This shape control method is framed as a nonlinear optimization problem, and through linearization of the CTR's kinematics, we turn it into a quadratic program solved by a shape controller that requires minimal knowledge of the robot's shape. Simulations show that our method enables better approximate FTL motion compared to a state-of-the-art Jacobian-based tip controller across different tube sets and tip paths while remaining computationally comparable. Furthermore, a hardware demonstration validates the effectiveness of the shape controller on a physical system during teleoperation.