Title
Planning for Flexible Surgical Robots via Bézier Spline Translation
Abstract
In a minimally invasive surgery, new flexible instruments enable safer and easier access to difficult-to-reach anatomical regions. However, their introduction into the clinical workflow requires robust replanning because navigation errors during surgery render initially planned trajectories infeasible. Such replanning requires to regularly solve an expensive two-point boundary value problem (BVP) that connects the target pose of the instrument with the currently measured one. We propose a hybrid planning scheme that features both robust and safe replanning. This two-step approach first solves the BVP and then transforms the result to circular arcs that fit the motion of our instruments’ models. We exploit implicitly defined Bézier splines as a robust method for interpolation in the first step. A novel geometric translation of these splines, then, provides a convenient solution for movement along circular arcs. We consider two example applications: 1) planning for a drilling unit in temporal bone surgery; and 2) guidewires in catheter insertion. Evaluation on real patient data of both temporal bone and aorta show that our proposed hybrid two-step approach achieves, on average, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{55}\%}$</tex-math></inline-formula> higher replanning rates and provides <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\text{31}\%}$</tex-math></inline-formula> larger clearance to risk structures, thus improving trajectory quality with regard to clinical safety.
Year
DOI
Venue
2019
10.1109/LRA.2019.2926221
IEEE Robotics and Automation Letters
Keywords
Field
DocType
Surgical robotics: planning,flexible robots,motion and path planning,Bézier splines,circular arcs
Spline (mathematics),Boundary value problem,Control theory,Interpolation,Algorithm,SAFER,Bézier curve,Engineering,Robot,Workflow,Trajectory
Journal
Volume
Issue
ISSN
4
4
2377-3766
Citations 
PageRank 
References 
0
0.34
0
Authors
13