Robotic Insertion of Flexible Needle in Deformable Structures Using Inverse Finite-Element Simulation

This paper introduces a new approach for the control of a robotic system interacting with deformable structures. The method is applied to needle insertion procedures, which are among the least invasive surgical approaches to access deep internal structures with sometimes poor access conditions. Yet, during the insertion both tissues and needles deform resulting in a displacement of targets identified at the planning step and significantly raising the technical difficulty of these approaches. Robotic assistance may offer new possibilities to enforce the accuracy of the needle's positioning, but the deformation of tissues remains an open problem. In this paper, we propose a numerical approach where finite-element (FE) models are used in a close-control robotic loop. We introduce a complete forward simulation of deformable structures (needle and environment) and constraint-based interaction models allowing for the simulation of needle insertion and complex nonlinear phenomena (friction, puncture, and insertion) at a high frequency. For the control, we numerically derive the so-called Jacobian of the Simulation using an inverse method. The most original aspect of this paper lies in the fact that inverse steps are performed in constraints space, allowing this way for fast estimation of the Jacobian (i.e., between 40 and 100 Hz). The method is validated both numerically and experimentally using a flexible needle inserted inside a deformable foam. We show that the robot is able to follow a given trajectory, defined during the planning step, taking into account any occurring deformation of both the needle and the foam during the insertion; without any need for tracking the needle neither the target nor the trajectory.