The finite element method (FEM) is a powerful modeling tool for predicting soft robots' behavior, but its computation time can limit practical applications. In this article, a learning-based approach based on condensation of the FEM model is detailed. The proposed method handles several kinds of actuators and contacts with the environment. We demonstrate that this compact model can be learned as a unified model across several designs and remains very efficient in terms of modeling since we can deduce the direct and inverse kinematics of the robot. Building upon the intuition introduced in (Ménager et al., 2023), the learned model is presented as a general framework for modeling, controlling, and designing soft manipulators. First, the method's adaptability and versatility are illustrated through optimization-based control problems involving positioning and manipulation tasks with mechanical contact-based coupling. Second, the low-memory consumption and the high prediction speed of the learned condensed model are leveraged for real-time embedding control without relying on costly online FEM simulation. Finally, the ability of the learned condensed FEM model to capture soft robot design variations and its differentiability are leveraged in calibration and design optimization applications.

Needle-based procedures such as biopsies or radiofrequency ablation (RFA) of tumors are often considered to diagnose and treat liver cancer for their low invasiveness but raise difficulties for practitioners related to needle placement and visibility of internal anatomical structures. Efforts are being conducted to build real-time needle insertion simulators with both visual and haptic rendering, facing challenges related to model accuracy and real-time computational performance. This work focuses on the contact model involved in needle-tissue interactions in order to improve the realism of the resulting haptic rendering. We present a novel method to update the compliant coupling at high rates of a complete contact system involving the mechanics of a large object and the complete model of a flexible needle. These updates allow to adapt the contact directions to the needle deformations in the haptic thread, with the aim of improving the resulting haptic feedback. Updates of contact directions and the related mechanical system according to high-rate deformations decrease force feedback artifacts associated with low-rate mechanics while maintaining high-rate performances for the haptic loop.

The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the computation to make it real-time. In this paper, we propose a learning-based approach to obtain a compact but sufficiently rich mechanical representation. Our choice is based on non-linear compliance data in the actuator/effector space provided by a condensation of the FEM model. We demonstrate that this compact model can be learned with a reasonable amount of data and, at the same time, be very efficient in terms of modeling, since we can deduce the direct and inverse kinematics of the robot. We also show how to couple some models learned individually in particular on an example of a gripper composed of two soft fingers. Other results are shown by comparing the inverse model derived from the full FEM model and the one from the compact learned version. This work opens new perspectives, namely for the embedded control of soft robots, but also for their design. These perspectives are also discussed in the paper.

In this paper, we propose a physics-based model of suction phenomenon to achieve simulation of deformable objects like suction cups. Our model uses a constraint-based formulation to simulate the variations of pressure inside suction cups. The respective internal pressures are represented as pressure constraints which are coupled with anti-interpenetration and friction constraints. Furthermore, our method is able to detect multiple air cavities using information from collision detection. We solve the pressure constraints based on the ideal gas law while considering several cavity states. We test our model with a number of scenarios reflecting a variety of uses, for instance, a spring loaded jumping toy, a manipulator performing a pick and place task, and an octopus tentacle grasping a soda can. We also evaluate the ability of our model to reproduce the physics of suction cups of varying shapes, lifting objects of different masses, and sliding on a slippery surface. The results show promise for various applications such as the simulation in soft robotics and computer animation.

The robotics community has seen an exponential growth in the level of complexity of the theoretical tools presented for the modeling of soft robotics devices. Different solutions have been presented to overcome the difficulties related to the modeling of soft robots, often leveraging on other scientific disciplines, such as continuum mechanics, computational mechanics, and computer graphics. These theoretical and computational foundations are often taken for granted and this leads to an intricate literature that, consequently, has rarely been the subject of a complete review. For the first time, we present here a structured overview of all the approaches proposed so far to model soft robots. The chosen classification, which is based on their theoretical and numerical grounds, allows us to provide a critical analysis about their uses and applicability. This will enable robotics researchers to learn the basics of these modeling techniques and their associated numerical methods, but also to have a critical perspective on their uses.

In this article, we propose a new continuum robotics approach for haptic rendering and comanipulation. This approach is illustrated using a robotic interface with six motorized fixed axes connected by deformable beams, in parallel, to an end effector with 5 degrees of freedom. Apart from the rotation of the motors, this design has no articulation, and the motion of the end effector is achieved by deformation of the beams. The flexible beams are equipped with bending sensors, and the motors have encoders. We use a nonlinear finite element mechanical model of the robot based on a mesh of beam elements that is computed in real time at 20 Hz. The bending sensors are incorporated into the model, which allows us to obtain an accurate estimate of the force exerted by the user on the end effector. The model enables a new methodology for calculating the workspace of the continuum haptic device. The model also is propagated to a higher frequency loop (500 Hz), which performs sensing and control of the robot at high rates, using an admittance-type control to command new positions of the actuators. We show that this control methodology allows haptic rendering of virtual walls that are stiffer than the natural stiffness of the robot. Finally, we demonstrate the use of the device for simple comanipulation tasks.

To aid in real-world situations, soft robots need to be able to estimate their state and external interactions based on proprioceptive sensors. Estimating disturbances allows a soft robot to perform desirable force control. However, even in the case of rigid manipulators, force estimation at the end-effector is seen as a non-trivial problem. And indeed, current approaches to address this challenge have shortcomings that prevent their general application. They are often based on simplified soft dynamic models, such as the ones relying on a piece-wise constant curvature approximation or matched rigid-body models that do not represent enough details of the problem. This severely limits applications in complex human-robot interaction. Finite element method (FEM) based modeling allows for predictions of soft robot dynamics in a more generic fashion. Here, using the soft robot modeling capabilities of the frame-work SOFA, we built a detailed FEM model of a multi-segment soft continuum robotic arm composed of compliant deformable materials and fiber-reinforced pressurized actuation chambers. In addition, a model for sensors that provide orientation output is presented. This model is used to establish a state observer for the manipulator. The sensor model is adequate for representing the output of flexible bend sensors as well as orientations provided by IMUs or coming from tracking systems, all of which are popular choices in soft robotics. Model parameters were calibrated to match imperfections of the manual fabrication process using physical experiments. We then solve a quadratic programming inverse statics problem to compute the components of external force that explain the pose mismatch. Our experiments show an average force estimation error of around 1.2%. As the methods proposed are generic, these results are encouraging for the task of building soft robots exhibiting complex, reactive, sensor-based behavior that can be deployed in human-centered environments.

Proximity perception is a technology that has the potential to play an essential role in the future of robotics. It can fulfill the promise of safe, robust, and autonomous systems in industry and everyday life, alongside humans, as well as in remote locations in space and underwater. In this survey article, we cover the developments of this field from the early days up to the present, with a focus on human-centered robotics. In this domain, proximity sensors are typically deployed in two scenarios: first, on the exterior of manipulator arms to support safety and interaction functionality, and second, on the inside of grippers or hands to support grasping and exploration. Therefore, based on this observation, in the beginning of this article, we propose a categorization to organize the use cases of proximity sensors in human-centered robotics. Then, we devote effort to present the sensing technologies and different measuring principles that have been developed over the years, also providing a summary in form of a table. Following, we review the literature regarding the applications that have been proposed. Finally, we give an overview of the most important trends that will shape the future of this domain.

Parallel Continuum Robots (PCR) have received a lot of attention in recent years. This paper presents a new 6-degrees-of-freedom PCR derived from the conventional 3-PPSR parallel manipulator. This robot is driven by three limbs consisting of two flexible rods each and replacing the spherical and revolute joints of the original version. Each limb is mounted onto two linear axes arranged in series. To allow a direct comparison between the articulated and the continuum version, the parallel mechanism of an industrial manipulator has been replaced by an elastic structure of the same size. The simulations and the experiments show that the flexible counterpart of the manipulator is able to achieve a larger workspace, increasing the range of motion by 150% for rotations and by 157% in elevation. Moreover, the position repeatability is improved by 47% (reaching 3.4 µm) and the orientation repeatability by 57% (reaching 14.3 µrad). This can be explained by the removal of the spherical and revolute joints but also by the constant stress in the structure that acts as an anti backlash system on leadscrew actuators.

This paper introduces a method for robotic steering of a flexible needle inside moving and deformable tissues. The method relies on a set of objective functions allowing to automatically steer the needle along a predefined path. In order to follow the desired trajectory, an inverse problem linking the motion of the robot end effector with the objective functions is solved using a Finite Element simulation. The main contribution of the article is the new constraint-based formulation of the objective functions allowing to: 1) significantly reduce the computation time; 2) increase the accuracy and stability of the simulation-guided needle insertion. The method is illustrated, and its performances are characterized in a realistic framework, using a direct simulation of the respiratory motion generated from in vivo data of a pig. Despite the highly non-linear behavior of the numerical simulation and the significant deformations occurring during the insertion, the obtained performances enable the possibility to follow the trajectory with the desired accuracy for medical purpose.

Soft robot is an emergent research field which has variant promising applications. However, the design of soft robots nowadays still follows the trial-and-error process, which is not at all efficient. This paper proposes to design soft robots by pre-checking controllability during the numerical design phase. Finite-element method is used to model the dynamics of silicone soft robots, based on which the differential geometric method is applied to analyze the controllability of the points of interest. Such a verification is also investigated via model order reduction technique and Galerkin projection. The proposed methodology is finally validated by numerically designing a controllable parallel soft robot.

While suction cups are widely used in Robotics, the literature is underdeveloped when it comes to the modelling and simulation of the suction phenomenon. In this paper, we present a novel physically-based approach to simulate the behavior of active suction cups. Our model relies on a novel formulation which assumes the pressure exerted on a suction cup during active control is based on constraint resolution. Our algorithmic implementation uses a classification process to handle the contacts during the suction phenomenon of the suction cup on a surface. Then, we formulate a convenient way for coupling the pressure constraint with the multiple contact constraints. We propose an evaluation of our approach through a comparison with real data, showing the ability of our model to reproduce the behavior of suction cups. Our approach paves the way for improving the design as well as the control of robotic actuators based on suction cups such as vaccum grippers.

In this paper, a method for dexterous manipulation of 3D soft objects for real-time deformation control is presented, relying on Finite Element modelling. The goal is to generate proper forces on the fingertips of an anthropomorphic device during in-hand manipulation to produce desired displacements of selected control points on the object. The desired motions of the fingers are computed in real-time as an inverse solution of a Finite Element Method (FEM), the forces applied by the fingertips at the contact points being modelled by Lagrange multipliers. The elasticity parameters of the model are preliminarly estimated using a vision system and a force sensor. Experimental results are shown with an underactuated anthropomorphic hand that performs a manipulation task on a soft cylindrical object.

Obtaining an accurate mechanical model of a soft deformable robot compatible with the computation time imposed by robotic applications is often considered an unattainable goal. This paper should invert this idea. The proposed methodology offers the possibility to dramatically reduce the size and the online computation time of a finite element model (FEM) of a soft robot. After a set of expensive offline simulations based on the whole model, we apply snapshot-proper orthogonal decomposition to sharply reduce the number of state variables of the soft-robot model. To keep the computational efficiency, hyperreduction is used to perform the integration on a reduced domain. The method allows to tune the error during the two main steps of complexity reduction. The method handles external loads (contact, friction, gravity, etc.) with precision as long as they are tested during the offline simulations. The method is validated on two very different examples of FEMs of soft robots and on one real soft robot. It enables acceleration factors of more than 100, while saving accuracy, in particular compared to coarsely meshed FEMs and provides a generic way to control soft robots.

In this work we propose a new method for online motion planning in the task-space for hydraulic actuated soft robots. Our solution relies on the interactive resolution of an inverse kinematics problem, that takes into account the properties (mass, stiffness) of the deformable material used to build the robot. An accurate modeling of the mechanical behavior of hydraulic components is based on a novel GPU parallel method for the real-time computation of fluid weight distribution. The efficiency of the method is further increased by a novel GPU parallel leveraging mechanism. Our complete solution has been integrated within the open-source SOFA framework. In our results, we validate our simulation with a fabricated silicone cylinder and we demonstrate the usage of our approach for direct control of hydraulic soft robots.

Knowledge of externally applied forces is crucial for compliant robotic manipulators in minimally-invasive and endoluminal robotic surgery for both patient safety and controllability of the device. We developed a novel continuum manipulator which comprises hydraulic actuation. In this work we investigate the use of the hydrostatic pressure feedback inside the inflatable actuation chambers to determine the normal and shear forces which are applied to the tip of the robot. For that purpose a nonlinear finite element model is derived and experimentally validated, showing a good approximation between experiment and simulation. The model is then used to derive descriptions for the normal and shear forces applied to the robot tip. The normal force estimation shows good results over the range of experimentally validated tip angles, while the shear force estimation shows good results for small tip deflection angles with an increasing error, with the tip orientation. The algorithm indicates good applicability to force control tasks as the forces are fast to compute.

In this paper, we propose a strategy for the control of soft robots with visual tracking and simulation-based predictor. A kinematic model of soft robots is obtained thanks to the Finite Element Method (FEM) computed in real-time. The FEM allows to obtain a prediction of the Jacobian matrix of the robot. This allows a first control of the robot, in the actuator space. Then, a second control strategy based on the feedback of infrared cameras is developed to obtain a correction of the effector position. The robust stability of this closed-loop system is obtained based on Lyapunov stability theory. Otherwise, to deal with the problem of image features (the marker points placed on the end effector of soft robot) loss, a switched control strategy is proposed to combine both the open-loop controller and the closed-loop controller. Finally, experiments on a parallel soft robot driven by four cables are conducted and show the effectiveness of these methods for the real-time control of soft robots.

Haptic rendering of soft bodies is essential in medical simulations of procedures such as surgery or palpation. The most commonly used approach is to recreate the sense of touch using a specific design and control of a robotic arm. In this paper, we propose a new approach, based on soft-robotics technology. We create a tangible deformable device that allows users to “touch” soft tissues and perceive mechanical material properties, in a realistic manner. The device is able to dynamically provide user touch with different stiffness perceptions, thanks to actuators placed at the boundaries. We introduce a control algorithm, based on inverse Finite Element Analysis, which controls the actuators in order to recreate a desired stiffness that corresponds to the contact with soft tissues in the virtual environment. The approach uses antagonistic actuation principle to create a wide range of stiffness. We validate our algorithm and demonstrate the method using prototypes based on simple mechanisms.

This paper aims at providing a novel approach to modeling and controlling soft robots. Based on real-time Finite Element Method (FEM), we obtain a globally defined discrete-time kinematic model in the workspace of soft robots. From the kinematic equations, we deduce the soft-robot Jacobian matrix and discuss the conditions to avoid singular configurations. Then, we propose a novel observer based control methodology where the observer is built by Finite Element Model in this paper to deal with the control problem of soft robots. A closed-loop controller for position control of soft robot is designed based on the discrete-time model with feedback signal being extracted by means of visual servoing. Finally, experimental results on a parallel soft robot show the efficiency and performance of our proposed controller.

This paper presents a development of a new method dedicated to the modeling and control of Continuum Robots, based on the Finite Element Method (FEM) using quasi-static assumption. The modeling relies on a discretization of the continuum robots using 6 DoFs Frames along the structure of the robot that is compatible with the modeling of a sequence of rigid vertebras. When the robot's structure relies on rods with constant sections, internal forces are computed with beam elements, placed between two adjacent frames, that applies forces and torques. In the opposite, when the robot is composed of a complex shape deformable backbone separated by the rigid vertebras, a domain decomposition strategy is used to obtain an equivalent stiffness between two vertebras using volumetric FEM. In both cases, for solving the whole robot model and inverting it in real-time, the numerical method takes advantage of the serial nature of continuum robots, using a Block-Tri-Diagonal solver. The factor of improvement in the computation time reaches several order of magnitude compared to a classical FEM model, while keeping a good precision. The method has also been implemented and tested on a real pneumatic CBHA trunk designed by Festo Robotics and some complementarity examples have been generated numerically.

Finite Element analysis can provide accurate deformable models for soft-robots. However, using such models is very difficult in a real-time system of control. In this paper, we introduce a generic solution that enables a high-rate control and that is compatible with strong real-time constraints. From a Finite Element analysis, computed at low rate, an inverse model of the robot outputs the setpoint values for the actuator in order to obtain a desired trajectory. This inverse problem uses a QP (quadratic-programming) algorithm based on the equations set by the Finite Element Method. To improve the update rate performances, we propose an asynchronous simulation framework that provides a better trade-off between the deformation accuracy and the computational burden. Complex computations such as accurate FEM deformations are done at low frequency while the control is performed at high frequency with strong real-time constraints. The two simulation loops (high frequency and low frequency loops) are mechanically coupled in order to guarantee mechanical accuracy of the system over time. Finally, the validity of the multi-rate simulation is discussed based on measurements of the evolution in the QP matrix and an experimental validation is conducted to validate the correctness of the high-rate inverse model on a real robot.

This paper presents an original method for interactions' haptic rendering when treating hyperelastic materials. Such simulations are known to be difficult due to the non-linear behavior of hyperelastic bodies; furthermore, haptic constraints enjoin contact forces to be refreshed at least at 1000 updates per second. To enforce the stability of simulations of generic objects of any range of stiffness, this method relies on implicit time integration. Soft tissues dynamics is simulated in real time (20 to 100 Hz) using the Multiplicative Jacobian Energy Decomposition (MJED) method. An asynchronous preconditioner, updated at low rates (1 to 10 Hz), is used to obtain a close approximation of the mechanical coupling of interactions. Finally, the contact problem is linearized and, using a specific-loop, it is updated at typical haptic rates (around 1000 Hz) allowing this way new simulations of prompt stiff-contacts and providing a continuous haptic feedback as well.

Interactive dexterous manipulation of virtual objects remains a complex challenge that requires both appropriate hand models and accurate physically-based simulation of interactions. In this paper, we propose an approach based on novel aggregate constraints for simulating dexterous grasping using soft fingers. Our approach aims at improving the computation of contact mechanics when many contact points are involved, by aggregating the multiple contact constraints into a minimal set of constraints. We also introduce a method for non-uniform pressure distribution over the contact surface, to adapt the response when touching sharp edges. We use the Coulomb-Contensou friction model to efficiently simulate tangential and torsional friction. We show through different use cases that our aggregate constraint formulation is well-suited for simulating interactively dexterous manipulation of virtual objects through soft fingers, and efficiently reduces the computation time of constraint solving.

In this paper, we present a new method for the control of soft robots with elastic behavior, piloted by several actuators. The central contribution of this work is the use of the Finite Element Method (FEM), computed in real-time, in the control algorithm. The FEM based simulation computes the nonlinear deformations of the robots at interactive rates. The model is completed by Lagrange multipliers at the actuation zones and at the end-effector position. A reduced compliance matrix is built in order to deal with the necessary inversion of the model. Then, an iterative algorithm uses this compliance matrix to find the contribution of the actuators (force and/or position) that will deform the structure so that the terminal end of the robot follows a given position. Additional constraints, like rigid or deformable obstacles, or the internal characteristics of the actuators are integrated in the control algorithm. We illustrate our method using simulated examples of both serial and parallel structures and we validate it on a real 3D soft robot made of silicone.

The dynamic response of deformable bodies varies significantly in dependence on mechanical properties of the objects: while the dynamics of a stiff and light object (e. g. wire or needle) involves high-frequency phenomena such as vibrations, much lower frequencies are sufficient for capturing the dynamic response of an object composed of a soft tissue. Yet, when simulating mechanical interactions between soft and stiff deformable models, a single time-step in the time integration is usually employed to compute the dynamics of both objects. However, this can be a serious issue when the haptic rendering of complex scenes composed of various bodies is considered. In this paper, we present a novel method allowing for the haptic simulation of a scene composed of colliding objects modeled at different frequencies: typically, the dynamics of soft objects is calculated at a frequency of about 50Hz, while the dynamics of stiff object is simulated at 1 kHz, being directly connected to the computation of the haptic force feedback. The collision response is performed at both low and high frequencies employing data structures which describe the actual constraints and are shared between the high and low frequency loops. We show that during the simulation we show that the objects behave according to two mechanical principles: non-inter-penetration and action-reaction principles. Examples showing the scenes involving different bodies in interaction are given, demonstrating the benefits of the proposed method.

This paper presents a new asynchronous approach for haptic rendering of deformable objects. When stiff nonlinear deformations take place, they introduce important and rapid variations of the force sent to the user. This problem is similar to the stiff virtual wall for which a high refresh rate is required to obtain a stable haptic feedback. However, when dealing with several interacting deformable objects, it is usually impossible to simulate all objects at high rates. To address this problem we propose a quasi-static framework that allows for stable interactions of asynchronously computed deformable objects. In the proposed approach, a deformable object can be computed at high refresh rates, while the remaining deformable virtual objects remain computed at low refresh rates. Moreover, contacts and other constraints between the different objects of the virtual environment are accurately solved using a shared Linear Complementarity Problem (LCP). Finally, we demonstrate our method on two test cases: a snap-in example involving non-linear deformations and a virtual thread interacting with a deformable object.

We introduce a new method for simulating frictional contact between volumetric objects using interpenetration volume constraints. When applied to complex geometries, our formulation results in dramatically simpler systems of equations than those of traditional mesh contact models. Contact between highly detailed meshes can be simplified to a single unilateral constraint equation, or accurately processed at arbitrary geometry-independent resolution with simultaneous sticking and sliding across contact patches. We exploit fast GPU methods for computing layered depth images, which provides us with the intersection volumes and gradients necessary to formulate the contact equations as linear complementarity problems. Straightforward and popular numerical methods, such as projected Gauss-Seidel, can be used to solve the system. We demonstrate our method in a number of scenarios and present results involving both rigid and deformable objects at interactive rates.

In this paper, we present a new method for estimating the linear elasticity parameters of soft bodies directly from videos of solids getting deformed under external user action. Our method requires one standard camera, a regular light source, a deformable solid and its 3D geometrical model. We make those estimations using an inverse method based on a quasi-static FEM simulation, large displacements, and a visual error metric. The result is a set of two parameters, the Young's modulus and the Poisson's ratio, that can be used for more complex simulations, or force feedback applications like virtual surgery for example. We characterize different materials like silicon or synthetic sponge. Then we validate our results by comparing them to a Zwick universal hardness tester measurements. We also present a new simple device for capturing the external forces applied on the deformable solids.

In this work, we propose interactive and physically based animation of one-dimensional deformable models using geometrically exact energy formulation. The proposed mechanical model has a high level of accuracy: it is based on continuous spline support and continuum mechanics media equations. We also detail a new efficient solving scheme, that can automatically switch between dynamic and static during simulation. With this scheme, we want to raise inconsistencies that could show up when human user is interacting with a physical simulation. We finally present a practical example in which the proposed model provides high-quality interaction.

A new computer haptics algorithm to be used in general interactive manipulations of deformable virtual objects is presented. In multimodal interactive simulations, haptic feedback computation often comes from contact forces. Subsequently, the fidelity of haptic rendering depends significantly on contact space modeling. Contact and friction laws between deformable models are often simplified in up to date methods. They do not allow a "realistic" rendering of the subtleties of contact space physical phenomena (such as slip and stick effects due to friction or mechanical coupling between contacts). In this paper, we use Signorini's contact law and Coulomb's friction law as a computer haptics basis. Real-time performance is made possible thanks to a linearization of the behavior in the contact space, formulated as the so-called Delassus operator, and iteratively solved by a Gauss-Seidel type algorithm. Dynamic deformation uses corotational global formulation to obtain the Delassus operator in which the mass and stiffness ratio are dissociated from the simulation time step. This last point is crucial to keep stable haptic feedback. This global approach has been packaged, implemented, and tested. Stable and realistic 6D haptic feedback is demonstrated through a clipping task experiment.

In this paper we consider deformable objects in haptic simulations. The physical simulation that drives haptic perception requires a good dynamic behavior. The inputs of the deformable model come from the treatment of the collision. We propose to focus on the contact restitution between deformable objects to guarantee "physical and perceptual realisms" of the haptic feedback. Signorini, in 1933, proposed a physical model of contact for deformable objects interacting with rigid static bodies (Signorini, S, 1933). This paper shows that the Signorini's model extents to contacts between two deformable objects using Gauss-Seidel resolution of complementarity problems. An interactive resolution of the overall formulation is presented and experienced on deformable objects using the finite linear-elements method.

This paper discusses preliminary design of an interactive childbirth simulator with haptic feedback. This exploratory work started following a demand of the obstetrics and gynecology service of a Parisian hospital. Ideally, the final system should integrate cases-study database in order to provide a powerful teaching media by means of best of the virtual/augmented realities technology in terms of multimodal visualization and display. The difficulty of this new system lies in the haptic display function allowing to teach gesture interaction skill to obstetricians/midwifes students. This paper deals only on the feasibility of such a system. First, the system is presented and its "nominal ingredients" described in generic terms. Simple models of women pelvis, fetus and muscles have been considered. Pilot force feedback delivery is simulated and experienced; results are discussed.