Feedback-linearization-based 3D needle steering in a Frenet-Serret frame using a reduced order bicycle model

Robotics-assisted needle steering can enhance the performance of needle-based clinical procedures such as biopsy, brachytherapy, and drug delivery. We present an automated needle steering system capable of steering needles in 3D toward targets in tissue while avoiding anatomical obstacles. The system comprises a nonholonomic model of needle steering in tissue and a nonlinear controller for 3D trajectory tracking in soft tissue. First, a new reduced-order model of needle steering is presented. The proposed model is fully controllable and all the system states can be estimated on the fly. Next, the model is transformed to a local coordinate system using the Serret-Frenet formulation. By means of this transformation, the needle steering problem is converted to the regulation of the distance of the needle tip from a desired 3D trajectory. Finally, using the transformed model, a novel nonlinear controller is developed to steer the needle in 3D while avoiding anatomical obstacles. The control strategy is validated through simulations. The simulations indicate that the system is stable and can successfully follow a 3D trajectory. The results are promising, enabling future research in flexible needle path planning and control using the proposed reduced-order model and the controller.