Using steerable needles to enable course correction and curved trajectories can improve surgical outcomes in numerous clinical interventions including electrode placement for deep brain stimulation. In this work, a physically motivated kinematic model for an actively steered magnetic-tipped needle is used in closed-loop control to perform insertion trajectories. The applied control law is derived using the Lyapunov redesign. Simulation results show this control method to be accurate for a wide range of conditions including randomized target trajectories. Control is performed experimentally in a brain tissue phantom for both initial position offset recovery and curved trajectories. Converged error results average 0.52 mm from target trajectory. Simulation results demonstrate the robustness of the control implementation, while experimental results exceed the accuracy required for the target application, encouraging future use in a clinical setting. Beyond needle insertion, this work has implications in general vehicle steering, as this model and control can apply to systems with similar kinematics such as boats and wheeled vehicles that could benefit from a relaxed slip constraint.
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