On-line collision-free inverse kinematics with frictional active constraints for effective control of unstable concentric tube robots

Abstract

Abstract-Concentric tube robots are catheter-sized robots that can navigate natural pathways to reach deep anatomical locations. Their intraoperative telemanipulation in dynamic environments requires on-line computation of inverse kinematics with simultaneous avoidance of anatomical collisions. Moreover, unstable configurations, which arise for elongated curved robots that navigate extremely tortuous paths, must be avoided. This paper leverages state-of-the-art multi-core computer architectures to deliver real-time inverse kinematics solutions that avoid robot instabilities and anatomical collisions. Furthermore, it introduces frictional active constraints to concentric tube robots for intraoperative assistance in navigation. Our framework is evaluated in silico through clinical scenarios from heart surgery and neurosurgery.

Implicit active constraints for safe and effective guidance of unstable concentric tube robots

“…Stability, in a binary fashion, is calculated online according to [10], [12]. A quantative stability measure for a given tube i is here calculated as…”

“…An elasto-plastic friction model is used to generate the forces [18], [22], [12], due to its advantages of avoiding oscillations, instabilities, and redirecting kinetic energy to enforce constraints. Please refer to [12], [18] for a thorough explanation, omitted here due to lack of space. The parameterization of the algorithm is depicted in Table I.…”

“…The inverse kinematics are constantly solved, in real-time, to guide the user towards the path and estimate collisions with the anatomy and potential instabilities. Inverse kinematics are calculated using a solver improved over our previously presented work in [12]. A set of different optimization algorithms is used in parallel to minimize the cost,…”

“…These instabilities cause uncontrollable tube motion, which, if it occurs intraoperatively, may cause severe tissue trauma. For this reason, computational design, path-planners, and inverse kinematics solvers consider criteria not only to avoid such configurations but also to guide the human operator away from them [10], [11], [12], [13].…”

“…Our algorithms build on [12]. We leverage distributed computing to provide globally dense workspace roadmaps for CTRs in minutes, and combine ondemand path-planning with on-line local inverse-kinematics to guide the user along safe trajectories.…”