Event-triggered 3 D Needle Control Using A Reduced-order Computationally Efficient Bicycle Model In A Constrained Optimization Framework
Long flexible needles used in percutaneous procedures such as biopsy and brachytherapy deflect during insertion, thus reducing needle-tip placement accuracy. This paper presents a surgeon-in-the-loop system to automatically steer the needle during manual insertion and compensate for needle deflection using an event-triggered controller. A reduced-order kinematic bicycle model incorporating needle-tip measurement data from ultrasound images is used to determine steering actions required to minimize needle deflection. To this end, an analytic solution to the reduced-order bicycle model, which is shown to be more computationally efficient than a discrete-step implementation of the same model, is derived and utilized for needle-tip trajectory prediction. These needle-tip trajectory predictions are used online to optimize the insertion depths (event-trigger points) for steering actions such that needle deflection is minimized. The use of the analytic model and the event-triggered controller also allows for limiting the number and extent of needle rotations (to reduce tissue trauma) in a constrained optimization framework. The system was tested experimentally in three dierent ex-vivo tissue phantoms with a surgeon-in-the-loop needle insertion device. The proposed needle steering controller was shown to keep the average needle deflection within 0.47 +/- 0.21 mm at the nal insertion depth of 120 mm.