Two-dimensional needle steering with a "programmable bevel" inspired by nature: Modeling preliminaries

Percutaneous interventions have attracted significant interest in recent years, but most approaches still rely on straight line trajectories between an entry site and a soft tissue target. Thus, to this day, a flexible probe able to bend along predefined curvilinear trajectories within a highly compliant medium without buckling is still an open research challenge. In this paper, we describe the concept of a “programmable bevel” tip, which is inspired by the ovipositor of certain wasps: the offset between two parts of a probe determines the steering direction of the tip thanks to a set of bevels included at the tip of each segment. A kinematic model of the flexible probe and programmable bevel arrangement is derived. Several parameters of the kinematic model are calibrated experimentally using our first prototype of the flexible probe, codenamed STING. Open(feed-forward) and closed-loop (feedback) control strategies are then derived and implemented in simulation using the chained form representation, originally developed to control car-like robots. Simulated results demonstrate accurate two-dimensional needle steering in the presence of velocity, position, and initial posture disturbances.