Efficient Steady-State Tissue Simulation for Surgical Robotics: A First-Order Position-Based Method

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-theart 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. We detail the selection of parameters and step sizes for efficient steady-state simulation. We further compare our approach to a state-of-the-art position-based method and show significant improvements in stability and realtime performance at surgical size scales.