Deformation invariant bounding spheres for dynamic active constraints in surgery

Abstract

Active constraints are collaborative robot control strategies, which can be used to guide a surgeon or protect delicate tissue structures during robot-assisted surgery. Tissue structures of interest often move and deform throughout a surgical intervention, and therefore, dynamic active constraints, which adapt and conform to these changes, are required. A fundamental element of an active constraint controller is the computation of the geometric relationship between the constraint geometry and the surgical instrument. For a static active constraint, there are a variety of computationally efficient methods for computing this relative configuration; however, for a dynamic active constraint, it becomes significantly more challenging. Deformation invariant bounding spheres are a novel bounding volume formulation, which can be used within a hierarchy to allow efficient proximity queries within dynamic active constraints. These bounding spheres are constructed in such a way that as the surface deforms, they do not require time-consuming rebuilds or updates, rather they are implicitly updated and continue to represent the underlying geometry as it changes. Experimental results show that performing proximity queries with deformation invariant bounding sphere hierarchies is faster than common methods from the literature when the deformation rate is within the range expected from conventional imaging systems.