Needle-based interventions are among the least invasive surgical approaches to access deep internal structures into organs' volumes without damaging surrounding tissues. Unlike traditional open surgery, needle-based approaches only affect a localized area around the needle, reducing this way the occurrence of traumas and risks of complications Cowan et al. (2011). Many surgical procedures rely on needles in nowadays clinical routines (biopsies, local anesthesia, blood sampling, prostate brachytherapy, vertebroplasty ...). Radiofrequency ablation (RFA) is an example of percutaneous procedure that uses heat at the tip of a needle to destroy cancer cells. Such alternative treatments may open new solutions for unrespectable tumors or metastasis (concerns about the age of the patient, the extent or localization of the disease). However, contrary to what one may think, needle-based approaches can be an exceedingly complex intervention. Indeed, the effectiveness of the treatment is highly dependent on the accuracy of the needle positioning (about a few millimeters) which can be particularly challenging when needles are manipulated from outside the patient with intra-operative images (X-ray, fluoroscopy or ultrasound ...) offering poor visibility of internal structures. Human factors, organs' deformations, needle deflection and intraoperative imaging modalities limitations can be causes of needle misplacement and rise significantly the technical level necessary to master these surgical acts. The use of surgical robots has revolutionized the way surgeons approach minimally invasive surgery. Robots have the potential to overcome several limitations coming from the human factor: for instance by filtering operator tremors, scaling the motion of the user or adding new degrees of freedom at the tip of instruments. A rapidly growing number of surgical robots has been developed and applied to a large panel of surgical applications Troccaz (2012). Yet, an important difficulty for needle-based procedures lies in the fact that both soft tissues and needles tend to deform as the insertion proceeds in a way that cannot be described with geometrical approaches. Standard solutions address the problem of the deformation extracting a set of features from per-operative images (also called visual servoing) and locally adjust the pose/motion of the robot to compensate for deformations Hutchinson et al. (1996). Nevertheless, visual servoing raises several limitations, in particular for the needle insertion: 1. Per-operative images usually offer poor visibility of internal structures (such as a tumor or vessels), and it is very challenging to extract essential data in real-time. This is especially true for disappearing liver metastases: due to chemotherapy effects, the shape of tumors may change or they may become invisible in intraoperative images, even if the lesions still contain active tumors Owen et al. (2016). 2. When large deformations occur the control law of the robot can be significantly modified which is extremely difficult to relate with image-based displacements. For instance, when the needle is deeply inserted inside the tissue, the needle shaft becomes completely constrained, preventing for any lateral motions of the needle. 3. Traditional controllers do not have access to any biomechanical models capable of predicting the deformation of organs in real-time. Yet, the trajectory taken by the needle at the beginning of the insertion has a significant impact on the ability to reach or not the target later. To overcome these limitations, we introduce a numerical method allowing performing inverse Finite Element simulations in real-time. We show that it can be used to control an articulated robot while considering deformations of structures during needle insertion. Our approach relies on a forward FE simulation of a needle insertion (involving complex non-linear phenomena such as friction, puncture and needle constraints). Control commands are then derived from two important steps: Corrective Step: As for \textit{visual servoing}, we extract a set of features from live images in order to enforce the consistency of the models with real-data. However, instead of directly steering the needle toward these features, we first register FE models with the observations. The advantage of relying on FE models lies in the fact that it provides a regularization technique to extrapolate the displacement field extracted from images. Moreover, it allows to interpolate the whole volume displacement of the organs (including internal structures such as tumors, vessels or non-visible tumors), even if only few landmarks are visible in the images. Predictive Step: Input commands of the robot are obtained from an optimization process based on inverse simulation steps of FE models. This allows anticipating the behavior of mechanical structures, in order to adapt input commands much faster than waiting for a correction from the images. Inverse steps are performed to numerically derive the so-called \textit{Jacobian of the Simulation}, which relates Cartesian displacements of the base of the needle with displacements of the tip inside the volume, allowing to compensate, or even induce, necessary deformations to reach a target.