Surgical Retraction of Non-Uniform Deformable Layers of Tissue: 2D Robot Grasping and Path Planning

Robotic surgical assistants (RSAs) have the potential to facilitate surgeries and reduce human fatigue. In this paper we focus on surgical retraction, the common surgical primitive of grasping and lifting a thin layer of tissue to expose an underlying area. Given a 2D cross-sectional model of heterogeneous tissue with embedded structures (such as veins) and a desired underlying exposure region, we present an algorithm that computes a set of stable and secure grasp-and-retract trajectories, and runs a 3D finite element (FEM) simulation to certify the quality of each trajectory. To choose secure candidate grasp locations, we introduce the continuous spring method and combine it with the Deformation Space (D-Space) approach to grasping deformable objects with a linearized potential energy model based on the locations of embedded bodies. Experiments show that this method produces many of the same grasps as an exhaustive computation with an FEM mesh, but is orders of magnitude cheaper: our method runs in O(υ log υ) time, when υ is the number of veins, while the FEM computation takes O(pn ³) time, where n is the number of nodes in the FEM mesh and p is the number of nodes on its perimeter. Furthermore, we present a constant tissue curvature (CTC) retraction trajectory that distributes strain uniformly around the medial axis of the tissue, by moving the gripper such that the tissue follows a constant-curvature, constant-length arc. 3D FEM simulations show that the CTC achieves retractions with lower tissue strain than circular and linear trajectories. Overall, our algorithm computes and certifies a high-quality retraction in about one minute on a PC.