First-Order Position-Based Simulation of Deformable Concentric-Tube Robots Interacting with Tissue

Soft tissue simulation can play an essential role in the automation of robotic surgery by providing contextual information during surgery and generating datasets for training. Any time tissue deformations are simulated, computational speed, accuracy, and stability are key concerns. State-of-the-art tissue simulation resolves inertial dynamics solutions using position-based computational methods. However, existing methods fail to efficiently resolve steady-state solutions at surgical size scales because of transient inertial dynamics and the small time step required for stability at such size scales. We propose a position-based tissue simulation framework which is based on large-deformation Neo–Hookean elasticity and enables fast resolution to steady-state for efficient simulation. Our method replaces the inertial terms in the model with a virtual viscous damping term. This enables realistic tissue motion while eliminating the transient vibrations that require more computation. It also enables smooth and stable dynamic transitions between disparate static states. Using our method, we develop an interactive simulator capable of stable, real-time tissue manipulation with a deformable concentric tube robot (CTR) model. Stable collision and simulator realism are achieved through the inclusion of local iterations of collision areas and a novel hydrostatic strain energy formulation.