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

Robotic needle insertion in moving soft tissues using constraint-based inverse Finite Element simulation

“…Indeed, Coulomb friction is simulated along the shaft of the needle and unilateral constraints are used to simulate contacts based on Signorini's law. This equation is solved using a modified Gauss-Seidel algorithm allowing for the iterative computation of λ and δ (see [16] for details).…”

“…Following [16], errors of the model are corrected in real time thanks to a non-rigid registration. Although this step is necessary, the non-rigid registration of deformable bodies is not addressed here as it goes far beyond the scope of this paper.…”

“…The method was validated performing the insertion of a flexible needle inside a deformable polyurethane foam [16]. A set of markers m (i) located on the surface of the model were used to register the models and enforce their consistency with real structures (see Fig.…”

“…All the physical interactions used in the inverse simulation are expressed through Lagrangian multipliers (needle/tissue constraints, attach of the needle with the robotic arm and registration constraints), allowing this way to obtain the complete mechanical coupling between constraints in the condensed system matrix W. This choice is necessary to compute the Compliance matrix once for all the inverse steps as proposed in [16]. Yet, the computation of the J requires the evaluation of the objective functions in the motion's space.…”

“…The coauthors of the present article recently proposed to rely on a Finite Element simulation to steer a needle in deformable environment [15], [16]. The robot-assisted needle insertion relies on the actuation of the 6 DOF of the base of the needle.…”